GRAPHIC METHODS
FOR
PRESENTING FACTS
WIZARD C. BRINTON
INDUSTRIAL MANAGEMENT LIBRARY
GRAPHIC METHODS
FOR
PRESENTING FACTS
BY
WILLARD C. BRINTOM
NEW YORK
THE ENGINEERING MAGAZINE COMPANY 1919
COPTBIGHT, 1914 BY THE ENGINEERING MAGAZINE COMPAICY
TO MY MOTHER
PREFACE
IN the preparation of this book there has been a constant effort to present the subject to suit the point of view of the business man, the social worker, and the legislator. Mathematics have been entirely eliminated. Technical terms are used practically not at all. Since the readers whom it is most desired to reach are those who have never had any statistical training, consistent effort has been made to keep the whole book on such a plane that it may be found readable and useful by anyone dealing with the complex facts of business or government. Though written primarily for the non-technical man, it is hoped that this book may, nevertheless, prove con- venient to the engineer, the biologist, and the statistician.
A definite effort has been made to produce a work which can serve as a hand book for anyone who may have occasional charts to prepare for reports, for magazine illustration, or for advertising. Unfortunately, there are extremely few draftsmen who know how to plot a curve or prepare any kind of a chart from data presented to them in the form of tabulated figures. Most draftsmen can plot a curve if they are given the data and an example showing the general type of chart desired. The execu- tive who desires a chart is usually too busy to stand by a draftsman and explain in detail just how the chart should be prepared as concerns those all important details of proportion, scale, width of line, etc. It is believed that the owner of this book will find it feasible to run through the various chapters and pages until he finds a chart most nearly like that which he desires to have made from his own data. A sample chart placed before any draftsman of average ability should give the drafts- man practically all the instruction needed for the preparation of a similar chart from other data.
Much careful labor has been expended in so arranging the book that a busy reader may get the gist of the matter by looking at the illustrations and reading only the titles and the sub-titles. The main title under each illustration is intended to show exactly what the chart represents, just as if it were used in some publication re- lating to the particular subject matter of the chart. The sub-titles relate to method and give criticism of each chart as a whole. Though the text gives much more de- tailed information concerning method than can possibly be put into any sub-titles, the reader who examines only the illustrations and the titles, without any reference to the text, will undoubtedly get a major portion of the vital material in the book. It is believed that an average reader may go through the illustrations and the titles in about one hour.
Vi GRAPHIC METHODS
Many of the illustrations which have been borrowed for use in this book are criticized adversely. It is the hope that all such criticisms will be accepted as an honest attempt toward an advance in the art of showing data in graphic form. In fairness to the authors of those charts which are criticized, it must be said that there has been a very rapid advance in the art of graphic presentation within the last few years and that many of these men would not present the material to-day by the methods which may have been used some years ago in the preparation of certain charts shown here. Where charts are used and criticized adversely, the charts have been included only because it is felt that they show a practice which is rather common but is nevertheless of questionable desirability.
Many of the suggestions for standard practice contained in this book should be taken as tentative only. The American Society of Mechanical Engineers has invited about fifteen of the chief American societies of national scope to co-operate by sending one member each to a Joint Committee on Standards for Graphic Presentation. Though this committee is not yet completely organized, and it will be some time before any report is available, the reader who desires further information regarding standard practice should be on the lookout for any reports which the joint committee may publish in the future.
This volume may arouse in the minds of many readers a desire for more detailed information than can possibly be given here. The following books are suggested for the person who wishes to take up the study of statistics as related to the collection and interpretation of data without special reference to the methods of graphic pres- entation. The present work is necessarily limited to the consideration of graphic presentation, and those who wish to go further in the general subject of statistics should by all means consult books of the type exemplified by "The Elements of Statistical Method," by Willford I. King, The Macmillan Company, New York; "An Introduction to the Theory of Statistics," by G. Udny Yule, Griffin and Com- pany, London; "Elements of Statistics," by Arthur L. Bowley, Charles Scribner's Sons, New York; "Primer of Statistics," by W. Palin Elderton and Ethel M. Elderton, Adam and Charles Black, London; "Statistical Averages," by Franz Zizek, Henry Holt and Company, New York; "Statistical Methods with Special Reference to Biological Variation," by C. B. Davenport, John Wiley and Sons, New York. Any list of this sort is, of course, incomplete and these books are mentioned as only a few of those which may be found useful to supplement the study of the subject considered in this volume.
Part of the matter here presented was given in lectures delivered at the Graduate School of Business Administration of Harvard University, the Amos Tuck School of Administration and Finance of Dartmouth College, the Northwestern University School of Commerce, and the College of Commerce and Administration of the Uni- versity of Chicago. Some of the material was presented before the American Society of Mechanical Engineers in New York. The advance presentation of matter in course of preparation for the press was made with the cordial assent and approval of the publishers of this work.
I am greatly indebted to Mr. Edward Scott Swazey, Mr. Curtis Prout, and Miss Katherine Tyng, for valuable assistance and suggestions received during the prep- aration of this book. Chapter XV is largely based on an article prepared at the
PREFACE Vll
suggestion of the author by Mr. Pierpont V. Davis of New York City and published by Mr. Davis in Moody's Magazine. I wish also to express my thanks to numerous friends who have given excellent suggestions and criticisms during the time the manuscript was in preparation.
If this book should receive any commendation, much of that commendation will be the result of good fortune in securing an unusually high grade of drafting skill on those charts which are original.
The author cannot be responsible for the accuracy of the data presented in many of the charts shown. The illustrations have been selected partly on account of the educational value of the facts, but chiefly because of the methods used in presentation. Though great care has been exercised to make the titles complete, the elaboration of titles beyond their wording in the original source may have resulted in some in- accuracies.
As far as the author is aware, there is no book published in any language covering the field which it has been attempted to cover here. If the presentation of the subject appears to be crude and incomplete, it is hoped that any critic will keep in mind that there is little precedent for guidance in a territory so unexplored.
It is impossible entirely to avoid errors in any book containing as much detail as results here from the numerous complex illustrations and the necessity of carefully worded language to give condensed information. Any corrections, criticisms or suggestions will be appreciated by the author.
WILLABD C. BEINTON New York, June, 1914
CONTENTS
PAGE
CHAPTER I. COMPONENT PARTS . 1
The need for graphic methods in presenting facts. The method of pres- entation as important as the data. Possibility for standard methods of presentation. Tabulated figures versus graphic methods. A total shown with its component parts. The horizontal bar. The circle and sectors. Subdivision of components. Separate bars totalling 100 per cent. Charts giving numerous subdivisions. Organization charts. Routing charts for manufacturing plants and offices.
CHAPTER II. SIMPLE COMPARISONS .20
Errors due to comparing by areas or by volumes instead of by one dimension only. The use of graphic methods in geography books. The data should be shown on the face of each chart if possible. Good and bad methods of including the data. "Eye-catchers" to attract the attention of the reader. Criticisms of methods commonly used. Certain bars made especially prominent. Increases and decreases. Lines connecting different bars. Examples of various good methods.
CHAPTER III. SIMPLE COMPARISONS INVOLVING TIME 36
Impossibility of accurate interpretation when circles of different size are compared. Errors when pictures of the human figure in different size are compared. Methods which are popular and accurate as well. Examples of bad practice in arrangement and the same data correctly represented. Vertical bars giving the general effect of a simple curve. Curve plotting.
CHAPTER IV. TIME CHARTS 53
Horizontal bars drawn to a scale of time. Complex time charts by which the relations of numerous horizontal bars may be studied. Time charts showing bars combined with a curve expressing totals. Curves to study whether time schedules are maintained. Rank charts to portray the rank of different individuals at various times. Rank charts showing actual rela- tive rank at any time and also changes in rank at various times. Tram- dispatching charts. Time-distance curves.
ix
GRAPHIC METHODS
CHAPTER V. CURVE PLOTTING 69
The desirability of using only well-known methods of presentation. Curves permit a more rapid and more accurate interpretation than possible by other methods. Studies of the causes of crests and valleys of curves. Curves especially needed for complex data. The use of curves in advertising. Polar co-ordinates objectionable for presenting statistical data. Examples of good practice in curve plotting.
CHAPTER VI. CURVE PLOTTING CONTINUED 84
Independent and dependent variables. Confusion caused if the inde- pendent variable is not used for the horizontal scale. Examples showing correct arrangement of scales. Curves to advertise newspaper circulation. Curve charts combining much complex information. The use of two sets of co-ordinate ruling for the vertical scale. Moving averages. Smoothing curves. Index numbers. Weighted averages. Curve studies of national prosperity.
CHAPTER VII. COMPARISON OF CURVES 107
Similarity and contrast of curves plotted in the same field. The zero of the vertical scale should be shown on the chart. Advantages of plotting curves for different years one above the other for comparison. Contrast in shape of curves plotted in separate fields. Advantage from shading the space under a curve. Numerous dissimilar but related curves on the same sheet. Errors resulting if curves not having the same zero line are compared. A total curve plotted from several other curves. Inverse relations, one curve trending downward when another trends upward. Study of correlation by plotting a curve from the data of two other curves. The angle of a curve on ordinary rectangular co-ordinates tells nothing about the percentage rate of growth. Disadvantages of the arithmetical scale ruling for curve plotting. Advantages obtained by plotting curves on logarithmically ruled paper.
CHAPTER VIII. COMPONENT PARTS SHOWN BY CURVES 138
Use of vertical bars with components totalling 100 per cent. Shaded area under a curve when the height of the total field represents 100 per cent. The use of several areas in a curve field which totals 100 per cent, in height. A contrasting method of showing all curves plotted separately but from the same zero line. Universal co-ordinate paper for convenience in curve plotting. Total curves with component areas so that any point on a curve totals 100 per cent for the height of the areas beneath.
CHAPTER IX. CUMULATIVE OR MASS CURVES 149
Factory production schedules and actual outputs plotted on a cumulative basis. Curves for income and expense on a cumulative basis. Various uses for cumulative curves. Cumulative curves with lines drawn to show rate
CONTENTS XI
PAGE
of change. A grand total cumulative curve plotted from several other cumulative curves. Cumulative curves for the determination of storage requirements for water supplies.
CHAPTER X. FREQUENCY CURVES. CORRELATION 164
The arrangement of objects so that their position shows a crude frequency curve. Vertical bars to represent frequency. Frequency curves. The "mode." Frequency curves much easier to interpret than charts using bars or areas. Cumulative frequency curves. The use of cumulative frequency curves for business problems. Cumulative frequency curves preferably plotted on a "more than" basis instead of on a "less than" basis. Necessity for making the independent variable the horizontal scale. Wage comparisons for industrial work. Studies of the percentage of clerical work and percentage of revenue from orders of various sizes. Pin boards to record costs of doing work on orders of different size. Theoretical curves for percentage of clerical work and percentage of revenue from orders of different size. The Lorenz curve. Correlation curves. "Shot- gun" diagrams. Plotting curves to represent numerous points. Shaded areas to represent numerous dots. Correlation charts for two independent variables. Isometrically ruled paper for chart work.
CHAPTER XI. MAP PRESENTATIONS , . . 208
Map presentation of prime importance. Shading of different areas. The Ben Day method of mechanical shading. Lines of equality. Profiles. Maps with circles or dots representing quantities. Shaded areas with a key to represent quantity. Miscellaneous methods. Map charts showing traffic. Map models with built up strips to show quantities.
CHAPTER XII. MAPS AND PINS 227
Map tacks projecting above the map. Map pins pushed in till the heads touch the map. Photographing pin maps. Mounting maps for use with map pins. Wall maps for use with pins. Map cabinet systems. Pin maps for advertising work. Pins bearing identifying numbers. Spot maps to a scale with each dot representing some large quantity. Routing systems. Various types of pins and beads available. Bead maps and their great advantages.
CHAPTER XIII. CURVES FOR THE EXECUTIVE 254
Peak-top curves versus flat tops. Methods for combining curves with figures recording the data. Cards for plotting curves for operating records. Advantages of the card method for instantaneous comparison of different curves. Typical operating curves for a manufacturing business. Typical records for a selling organization. Arrangement of the card system for exten- sion with increase of business. Moving average curves for operating re- cords. Record cards for preserving all information regarding each curve.
Xll GRAPHIC METHODS
CHAPTER XIV. RECORDS FOR THE EXECUTIVE 288
Need for complete records in curve form relating to all main features of a business. Curve-card filing methods. Blueprints from the curve cards allow a cross-index of all important operating curves. A complete rec- ord department for a business. Methods for keeping records as used by various large corporations. The need for education in the interpretation of curves. Curves in conference meetings by using a reflecting lantern and the curve-record cards without lantern slides. Curves on swinging-leaf dis- play fixtures.
CHAPTER XV. CORPORATION FINANCIAL REPORTS 307
The annual report of corporations not usually put in form to permit intelligent comparison by the stockholders. Records of previous years not usually given. The number of stockholders constantly increasing. Best policy is to give complete and clear information. Recent examples showing bad practice. Curves for the United States Steel Corporation as a suggestion for the type of chart to be included in a corporation annual report. Charts should be a feature of "the annual report of every large corporation.
CHAPTER XVI. GENERAL, METHODS 321
Methods for collecting and tabulating data. Punched-card sorting and tabulating machines. Use of tabulating machines for manufacturing records and for analyses of selling results. The slide rule as^ a great con- venience. The use and abuse of significant figures. Photographic copying of charts. Use of the reducing glass. Preparation of copy for the engraver. The Ben Day process. Charts for two independent variables. Card-board models. Solid models. The desirability of curves and charts in political campaigns. The projecting lantern with charts for campaign purposes. Methods for presenting election returns to large numbers of people. Charts in parades.
CHAPTER XVII. A FEW CAUTIONS " . . . 344
The importance of clear and accurate titles. Symbols which are easily remembered. No necessity for plotting curves vertically. Errors resulting in interpretation of curves if the zero of the vertical scale is not shown on the chart. The selection of scales for curve plotting. Different impressions from curves from the same data but with various scales. Optical illusions which may affect graphic work. A checking list for final inspection of graphic presentations. Need for standard rules of grammar for the graphic language. A few suggested rules for graphic presentation. Great ad- vantages may result if graphic methods are more widely used for portray- big quantitive facts.
GRAPHIC METHODS
FOR PRESENTING FACTS
CHAPTER I COMPONENT PARTS
AFTER a person has collected data and studied a proposition with great care so that his own mind is made up as to the best solution for the problem, he is apt to feel that his work is about completed. Usually, however, when his own mind is made up, his task is only half done. The larger and more difficult part of the work is to convince the minds of others that the proposed solution is the best one — that all the recommendations are really necessary. Time after time it happens that some ignorant or presumptuous member of a committee or a board of directors will upset the carefully-thought- out plan of a man who knows the facts, simply because the man with the facts cannot present his facts readily enough to overcome the opposition. It is often with impotent exasperation that a person having the knowledge sees some fallacious conclusion accepted, or some wrong policy adopted, just because known facts cannot be mar- shalled and presented in such manner as to be effective.
Millions of dollars yearly are spent in the collection of data, with the fond expectation that the data will automatically cause the cor- rection of the conditions studied. Though accurate data and real facts are valuable, when it comes to getting results the manner of presentation is ordinarily more important than the facts themselves. The foundation of an edifice is of vast importance. Still, it is not the
1
2 GRAPHIC METHODS
foundation but the structure built upon the foundation which gives the result for which the whole work was planned. As the cathedral is to its foundation so is an effective presentation of facts to the data.
We daily see facts presented in the hope of creating interest and action for some really worthy piece of work to benefit the people as a whole. In many of these cases the attitude of the person presenting the matter seems to be that the facts will speak for themselves and that they need little or no assistance. Ordinarily, facts do not speak for themselves. When they do speak for themselves, the wrong conclu- sions are often drawn from them. Unless the facts are presented in a clear and interesting manner, they are about as effective as a phono- graph record with the phonograph missing.
If it were more generally realized how much depends upon the method of presenting facts, as compared with the facts themselves, there would be a great increase in the use of the graphic methods of presentation. Unlimited numbers of reports, magazines, and news- papers are now giving us reams of quantitative facts. If the facts were put in graphic form, not only would there be a great saving in the time of the readers but there would be infinite gain to society, because more facts could be absorbed and with less danger of mis- interpretation. Graphic methods usually require no more space than is needed if the facts are presented in the form of words. In many cases, the graphic method requires less space than is required for words and there is, besides, the great advantage that with graphic methods facts are presented so that the reader may make deductions of his own, while when words are used the reader must usually accept the ready-made conclusions handed to him.
In many presentations it is not a question of saving time to the reader but a question of placing the arguments in such form that re- sults may surely be obtained. For matters affecting public welfare, it is hard to estimate the benefits which may accrue if a little care be used in presenting data so that they will be convincing to the reader. If the average citizen, and especially the business man, knew how to interpret charts and curves, it would be feasible to convey to him in effective form those facts relating to broad public improvements, public-service operation, and national, State, or municipal manage- ment, which might affect the whole fabric of our civilization. Archi- medes wanted only a fulcrum for his lever and he would move the world. If the world is ever moved it will probably be by facts properly
COMPONENT PARTS 3
presented. The method of presentation is the fulcrum without which facts, as a lever, are useless.
The preparation and interpretation of simple charts and curves should be taught in the public schools as a part of arithmetic. The work of kindergarten nature now done in the lower grades of the public schools could very readily be extended so that the pupils would be making charts and curves without realizing that the work (or play) had any relation to mathematics. Text-books for geography are al- ready making effective use of charts. In the public schools of Newark and of Trenton, New Jersey, grammar-school pupils are preparing charts and plotting curves relating to records which show the present condition and recent development of their home city. The principles of charting and curve plotting are not at all complex, and it is surprising that many business men dodge the simplest charts as though they involved higher mathematics or contained some sort of black magic.
If an editor should print bad English he would lose his position. Many editors are using and printing bad methods of graphic presenta- tion, but they hold their jobs just the same. The trouble at present is that there are no standards by which graphic presentations can be prepared in accordance with definite rules so that their interpretation by the reader may be both rapid and accurate. It is certain that there will evolve for methods of graphic presentation a few useful and definite rules which will correspond with the rules of grammar for the spoken and written language. The rules of grammar for the English language are numerous as well as complex, and there are about as many exceptions as there are rules. Yet we all try to follow the rules in spite of their intricacies. The principles for a grammar of graphic presentation are so simple that a remarkably small number of rules would be sufficient to give a universal language. It is interesting to note, also, that there are possibilities of the graphic presentation be- coming an international language, like music, which is now written by such standard methods that sheet music may be played in any country.
With oral and written language and with tabulated figures also the reader sometimes draws conclusions regarding the relative importance of different things from the comparative length of time or amount of space used in presentation. Graphic methods overcome this difficulty by showing quantitative facts in true proportions which give instantly the correct interpretation. In tabulations like that on page 4 it is only
4
GRAPHIC METHODS
the highly skilled reader who can refrain from regarding the five differ- ent items listed as of somewhere nearly equal numerical importance, simply because the five different items are given exactly the same space and prominence when written down on the page.
PERCENTAGE OF EACH RACE IN THE POPULATION OF THE WORLD
Yellow 45
White 41
Black 11
Brown 2
Red 1
It requires mental concentration in interpreting even these simple figures to get the correct impression of the very large percentage of the two chief races and the numerical insignificance of the one last named. If these data were shown in a simple horizontal bar, somewhat like that seen in Fig. 1, the relative proportions of the different races
Scale l*«lCeot»
5 Cents
Fig. i. Disposition of a 5-cent Fare Paid to the Boston Elevated Railroad in the Year
Ending September 30, 1909
The horizontal bar gives an especially good method for showing component parts
COMPONENT PARTS
would instantly be seen without any mental effort on the part of the reader.
Fig. 1 is a very satisfactory form of chart to bring out the component parts of any group total. The horizontal bar need be made only wide enough to show the various kinds of shading necessary to give a good contrast. Engineering dimension lines above each block in the bar are
of great advantage for convenient read- ing. The dimension lines permit of group- ing in such a manner that several of the detail blocks could be included in vari- ous sets of dimension lines to show such items as total fixed charges, total operat- ing expenses, etc.
In this type of chart the actual figures representing the value of the com- ponents should be given for the use of any reader who may wish to draw his own conclusions or to make new combina- tions of figures dif-
50%
•SALARIES & WAGES
Fig. 2. Disposition of the Gross Revenue of the Bell Tele- phone System for the Year 1911
This chart was taken from the annual report to the stockholders of the American Telephone and Telegraph Company for the year ending December 31, 1911
The circle with sectors is not as desirable an arrangement as the hori- zontal bar shown in Fig. 1
ferent from those shown in the chart. As a general thing it is always desirable to have full data given on any chart. Fig. 1 gives all the data without in any way detracting from the ease of reading the chart itself. It would be desirable to have a large number of the illustrations in this book printed in color. Charts which are made in color can read- ily bring out points which are not easily portrayed when only black ink is used. The reader should keep in mind for his own work that he should use colors in making those charts where colors are economically possible. For the purpose of this book, color printing is prohibitive
6
GRAPHIC METHODS
on account of the cost. In printed reports, in magazine articles, and in magazine advertising, color printing is not at the present time com- monly available. The illustrations of this book will accordingly show what can be done in printing complex charts with only one color of ink,
under the same conditions that would be found in the preparation of material for magazine articles, printed reports, and ordinary pro- spectus or other advertis- ing matter.
Fig. 2 is a form of chart used probably more widely than any other form to show component parts. The circle with sectors is not a desirable form of presenta- tion, however, because it does not have nearly such flexibility as the method shown in Fig. 1 . The sector method does not permit of convenient arrangement of names for the different components. Note that the direction of the lettering must be reversed as the eye proceeds around the circle. In this case, "Interest and Dividends" reads upward while "Materials, Rents, Traveling Ex- penses, etc." reads downward. Another disadvantage of the sector method is the impossibility of placing figures in such manner that they can be easily compared or added. The horizontal-bar method permits of placing figures so as to keep the decimal points in line, thus making it possible to add the whole column of figures relating to the various components.
The sector method is probably so widely known through presentation in exhibits, illustrations for popular magazines, etc., that it is more generally understood than any other method now in use. The more easy reading of the wedge or sector chart is, however, largely due to habit. If the horizontal-bar method of Fig. 1 were used as frequently as the sector method, it would be found in every way more desirable
Fig. 3-
The Survey
Disposition of a Family Income of from $900 to $1000
This cut shows an eltempt to put figures in popular form. The eye is likely to judge by the size of the pictures rather than by the angles of the sectors
COMPONENT PARTS
W»T THROUGH BAOtATION, LEAKAGE OF STEAM ETC
LOST THROUGH UNCONSUMED FUEL IN ASH
-
u. 30 O
160
14O
LOST IN VAPORIZING MOISTURE IN COAL
I
lOOj
UTILIZED 6V BOILER
than the sector method and would, in a very short time, become so well known that it would be read much more quickly and accurately than the method involving sectors.
In Fig. 4 a double scale is used by which the same data can be interpreted from two different standpoints. On the left the scale is given in millions of tons, and on the right in millions of dollars. The reader can interpret the chart from whichever standpoint he prefers. Though this chart is ar- ranged vertically instead of hori- zontally, it really makes little difference which way the bars are placed. As a general thing, the horizontal arrangement lends itself more readily to the use of type so that the reader may read type statements without having to turn the book.
In Fig. 5 the whole population of the United States is divided first into native white, foreign white, ,and colored, then each of these groups is subdivided according to place of birth. This is an excellent type of chart to use if subdivi- sions in the component parts of any unit have to be shown. If the scale to which the chart is drawn is specified, it is possible for the reader to measure, with an ordi- nary ruler or with an engineer's scale, the exact percentage size of each of the different components.
If the chart is made on co-ordinate paper with ruled squares, the reader can obtain the size of each component direct from the co-ordinate lines. The trouble, however, with using co-ordinate paper for charts of this sort is that the components are likely to begin and end at points not falling upon the co-ordinate lines, thus making it necessary to count
';.••:::';'.• ':' . .CONSU MEO UY stAin'iNA fWV v%
KtXPlKA (E»-lSI«e HOT1 WHILE if AHO(M<^ '- AND LEFT IN FIRE BOJCJCT fTNpO* «yN(EiTA.
Adapted from Data, Chicago
Fig. 4. Utilization and Accompanying Wastes of One Year's Coal Supply for Locomotives on Railroads of the United States
The double scale permits reading this chart in tons or in dollars
8
GRAPHIC METHODS
fractions of a division at both beginning and end of the component to be measured. The best thing in charts of this kind is to use unruled paper, and specify the scale. The reader, if he wants the exact data, can take his measurements with a ruler. The engineer's scale has its sub- divisions in decimals and hence is the most convenient scale for chart work. An engineer's scale should be part of the equipment of every person who has charts to make.
Another method of showing the relative size of the divisions and sub- divisions of a unit or group is shown in Fig. 6. In this case we have the total population of the United States split into its component groups accord- ing to the condition in regard to mar- riage. The subdivision bars, given be- low the total bars, show the conjugal condition in each of the main groups which enter into the total population. Each of these main-group bars is cross- hatched to show the conjugal condition within the group. The combined length of the four bottom bars is equal to the length of the total-population bar shown at the top. These same data could have been presented by the method shown in Fig. 5. It will be noted, however, that in Fig. 6 all the figures have been included, and are available for reference purposes with- out detracting from the utility of the chart itself. The lettering was done by hand and shows the possibilities for neatness resulting from hand work when a skilled draftsman is employed. In many ways the method of Fig. 5 is preferable, but it is probably true that Fig. 6 would be more readily understood by the average untrained reader.
Where there are a large number of items to be compared and the components of each item are given, the method of Fig. 7 is a very convenient one. The Census Atlas for the 1900 Census contained many pages of charts of this type for its comparisons of different States. By placing bars for all the States on one page, the total for the country is shown as 100 per cent in the vertical direction. No vertical scale
Scale p0 inch equals 5 percent United Slates Statistical Atlas for the Census of 1900
Fig. 5. Elements of the Population of the United States in 1900
Here the components of the total population are shown in their relative sizes on the vertical scale. Each component is also divided into different subdivisions whose percentage size may be read from the horizontal scale. This is an admirable method of presentation if components must be subdivided
COMPONENT PARTS
SJTAI. POPULATION. .76.3O3.S87
NATIVEorWHITE
NATIVE PARENTS
. . .40.049, 36 Z
FORCION WHITE 10,213.617
SINOLC
MARRIED WlDOWEO
DIVORCED
Fig. 6. Conjugal Condition of the Population of the United States in 1900
The four lower bars show components of the total population represented by the upper bar. The combined length of the four lower bars equals the length of the upper bar
is used, all the bars being made of equal width. In this particular case (Fig. 7) we have a total split into its components and again sub- divided so as to show the prevalence of a second factor which is in- cluded in the first. Thus, we see the proportion of illiterates in each of the main groups of population for each State. All of the States are shown on the same basis, since all are depicted by bars of the same length representing 100 per cent. It is not easy to make a clear black- and-white drawing if one kind of cross-hatching must be placed on top of another kind. Fig. 7 shows that it is possible, however, to superimpose two kinds of cross-hatching and get a drawing that is fairly clear. The facts in this chart would have been brought out better if colors had been used for the main divisions of population. Ruled cross-hatching in black to represent the percentages of illit-
New York
60%
North Dakota
57.8%
West Virginia
83. 2 °/0
Mississippi
Illiterate
Fig. 7. Males of Voting Age in certain States, in 1900, by Color and Nativity and
by Illiteracy
A method for two successive divisions into components is shown here. The proportion of illiterates in each group is brought out by the horizontal ruling
T«rr I90B.
crates would show clearly through the colored ink used for the main divisions.
Though it would have been possible to portray the data given in Fig. 7 in the form of the square shown in Fig. 5, the square would take up so much room on the page that the method would be prohib- itive if all the States had to be shown on one page for comparison. With the method of Fig. 7, it is possible to place on one page all the forty-eight States so that com- parison between States can be made instantly and accurately.
Fig. 8 shows another method of analyzing to 100 per cent in each of two directions. The method of Fig. 5 could be used for these data, but would not be as easy to under- stand as the method of Fig. 8. Fig. 5 would require most careful cross-hatching to bring out the ver- tical subdivisions for each of the different States. By using the method of Fig. 8, each State can be shown distinctly even if it is only the width of a line, as in the case of Nevada or Wyoming. The wide space between the different bars showing the States adds tre- mendously to the clearness of the diagram. The vertical scale for the width of bars is made accord- ing to the number of electoral votes from each of the States. New York has more electoral votes than any other State, and is there-
10
VER
ME:
DOTTED 'LINE. DIVIDES©
CENTAGE' TO THE. LEFT, BRYAN
HEAVY LINES DIVIDE. ® PAR
FROM THE. LEFT. TAFT, ROOS1
RE.P. PR
V//////////A
S IN I9O8,TAFT PER-
TO THE RIGHT.
IE.S IN 1912.- BEGINNING, VE.LT. WILSON. >G. DEM.
Prof. Irving Fisher in the New York Times
Fig. 8. The Vote for President in 1908 and in 1912 by States
Compare this with Fig. 5 where the vertical scale is continuous, without the gaps necessary here m order to distinguish different States.
COMPONENT PARTS
11
fore given greater width than any other State in proportion to the greater size of its electoral vote. The horizontal division has been made according to the percentage number of votes for each of the main political parties. Two different elections are shown by using solid lines and dotted lines. The chart proves that the Democratic vote of 1913 was essentially the same as the Democratic vote in 1908,
and that a Demo- crat was elected President in 1912 largely because there were three candidates in 1912 and only two in 1908. This is an admirable piece of presentation even though the lettering and draft- ing are not quite as good as they might have been if more care had been used, though probably al- lowance must be Fig. 9. The Factors Entering into the Annual Cost of made for the limita- Motor Trucking Service P ,
The scheme of this convenient form of tabulation is somewhat similar
to that of Fig. 5. Here, however, the components are only named preSSWOrk in daily without denoting their relative size or importance . .
newspaper printing.
When studying a number of varied components, and the relations of each to every other one, a chart like Fig. 9 is frequently of great assistance. This chart shows that certain components are affected by features which may not affect other components. We have here the total cost of motor trucking, studied according to the components of the cost and also according to the conditions which produce those component costs. We may consider either the service conditions or the cost components. We have 100 per cent in the horizontal direc- tion and 100 per cent also in the vertical direction. The total of the components in either direction is 100 per cent, but the actual size of each is not given because the size is not known or because it may vary from time to time.
|
Relations Between Annual Cost of Motor Trucks And Characteristics of Service. |
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|
E !- |
— ~a I e t~. |
« a |
1 5 s* |
I 1 K |
I |
1 K •o •a |
Amortization or DepreclAtlon |
Interest |
Insurance |
z H V| 'o B •3 < |
|||
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a |
I |
£ 3 J |
I |
3 |
•3 C 3 |
>_ 3 |
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a) Character of work: |
X X X X |
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X X I I Ir X X X |
d r rt re |
c 5 c y |
X I X X X «s IS T X X |
1 it t il |
X X lit lie X |
X X X 111 m : |
X X Iffor Iffer X |
X X X X X ts-c 8 d X X X |
sta istn |
X X HOP ice X |
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Number of stops per day .... |
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b) Roads and climate: |
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Climate |
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c) System of operating: |
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Loading and unloading |
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OverRDeedlnar |
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Massachusetts Institute of Technology — Vehicle Research
GRAPHIC METHODS
P^ g
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11
IH -f.
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tS -2 d- o
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COMPONENT PARTS
14
GRAPHIC METHODS
s se
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31
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jje-E M*
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I 1I!N l!«N |_J Sog ii»u
inre I«N I I ss°n uiw I
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I lure »•"!» I j IHK "iii I
tlUK Snmoa I _| 1IIK Snpaooi idna >q8im |~ |«l»aH *""! J"
COMPONENT PARTS
15
|
STOCKHOLDERS |
||
|
BOARD OF DIRECTORS |
||
|
f SECOND VICE PRESI- ENT AND SECRETARY cb til ti rh rh r*n BOOKKEEPERS , |
FIRST VICE-PRESIDENT |
TREASURER 1 ASSISTANT TREASURER |
|
ACCOUNTING 1 CHIEF CLERKJ | CHIEF CLERK | [ACCOUNTANT*) |
GENERAL SUPERINTENDENT (MAKING) |
SHIPPING DEPARTMENT (SALES DEPARTMENT! | MANAGER 1 |
|
1miftl^rIirtujT?^rI^TTtu]T?i 1 1 |
j »D»EiJT,.,Na cbbubbdd 66^66 |
|
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CONSTRUCTION AND, MECHANICAL DEPARTMENTS 1 |
[ |
FINISHING DEPARTMENT |
|
1 PATTERN MAKING- MOLDING AUfpLA- |
NG STEEL RANGE! 1 MOUNTING ING MAKING ] [(ASSEMBLING) |
|
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^L^&cpfe |
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r|~i ro«s.EN[^3 rh rot™ |
'EN | | | fAREii |
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66d] 6 til* b TTT . i"TT|T T |
Y"^CT@Y^ |
] * atiltiltblti ti6 INSPECTORS 1 1 1 1 1 1 1 1 |
|
cbcbiinb cb i± cb cb DcicbanananDacba WORKMEN WORKMEN WORKMEN |
System
Fig. 13. Organization Chart of a large Company Manufacturing Stoves
A complete organization chart should always include the stockholders and the Board of Directors as shown
here
A diagram like that of Fig. 10 may be of considerable assistance if a very complex relation of components has to be shown. In Fig. 9, the components have only one subdivision. In Fig. 10, however, we have fuel cost subdivided as many as five different times. Though the method of Fig. 10 could easily be used for the data of Fig. 9, that of Fig. 9 has its advantages in that it makes printing cheaper and is therefore desirable whenever it can be used. Fig. 9 can be prepared on a typewriter or can be set up by any printer, while Fig. 10 requires the making of a drawing.
In Fig. 11 the ramifications of the influence of the J. P. Morgan Company and various large banking concerns are shown. This chart, taken from the Pujo Money Report, was drawn originally in several different colors of ink. Though the windmill effect of the chart is rather disagreeable to the eye, the chart nevertheless shows the ap- plication of the graphic method to such complex situations as it is almost impossible to portray with language alone.
Organization charts are not nearly so widely used as they should be. As organization charts are an excellent example of the division of a total into its components, a number of examples are given here in the hope that the presentation of organization charts in convenient form will lead to their more widespread use.
16 GRAPHIC METHODS
It has been well stated that an organization chart closely resembles a genealogical tree.
Authority reaches down through the several branches of an organization like descent of blood, and, if properly planned, it will be as irregular for a factor in an organization to be in doubt as to the person in authority over him as for the child to deny the parentage of his father. Such a chart should be drawn for every or- ganization, even more especially for those organizations which are short-handed ex- panding businesses in which one man holds the authority of several positions. It should be graphically shown what positions are only temporarily filled, so that when new men are engaged they will fit into the scheme with functions planned. Then there will be no irritation, no feeling on the part of some that their authority has been usurped.
If such a chart is made there will be fewer cases of conflict or of short-circuiting of orders. Every command from the general that is given directly to the private over the head of the captain weakens the authority of the captain over the private and weakens the authority of the general over the captain. A military organization is so planned that each man knows from whom to take orders, but business proceeds too much on personal authority. An organization chart will help to prevent this.
Of course, no two businesses can have identical organizations. The skeleton may be the same, however, and just as the proper study of the functions of the human body begins with the skeleton, so the study of organization should begin with those simple outlines which appear, in the main, in all completely and successfully organ- ized businesses. Very few enterprises are organized properly. Very few have an organization that can be charted at all. That is one reason why there is such in- efficiency in industry.
As a general thing it is better to have an organization chart begin with the stockholders and then show the board of directors as inter- mediate between the stockholders and the president. In reality, a typical organization chart represents the shape of an hour glass or a double funnel, with the large number of stockholders on one side and the large number of employees on the other. The board of directors, the president, and the officers of the company are at the narrow part, with the president as the intermediary through which all transactions take place between the large number of stockholders and the large number of employees.
The routing of work through the many processes and departments of a large plant is a subject of such great importance that charts are frequently desired for the study of such routing. Fig. 14 is a fairly good example of this class of chart. In a complete chart, the depart- ments would of course be designated for easy reference, by names, numbers, or letters. Colored ink could bt used to keep one class of work distinct from another. Colored inks would help tremendously
COMPONENT PARTS
17
The Engineering aragazine
Fig. 14. Graphic Representation of Processes and Routing in a Representative Plant
Names of departments and operations are omitted by request of the proprietors of the establishment in
which this chart was made
18
GKAPHIC METHODS
w • ? /v — — '•' ' —
f'v ^f .1 Y — ^"^b — e^-^ !
COMPONENT PARTS 19
in simplifying Fig. 14, but are not available here because of the pro- hibitive expense of color printing. Colored drawing inks can be ob- tained at almost any stationery store. A bottle of each color should be a part of the equipment of any person who is regularly doing chart work. Note in Fig. 14 the small curves drawn where one route line crosses another line. By means of small curves like these it is very easy to keep the lines separate and to show clearly that the lines crossing each other are entirely independent.
Orders and other printed forms sent through a large organization must follow a routing entirely distinct from that actually followed by the heavy materials. The routing of printed forms in a large business is, in itself, a matter worthy of most careful study to get a true understanding of their complex movements. A clear idea of office system is almost impossible unless the data are charted. Fig. 15 may give some suggestions for a chart to show the movement of printed forms through an industrial plant. Here again printing by colored inks such as would be used on the original drawing would be of great service in making the chart easy to understand and easy to follow from department to department.
If a building contains many stories the routing diagram for mate- rials and also the routing diagram for printed forms can be made conveniently by a rough perspective drawing showing the different floors as planes one above the other. Colored ink lines on the perspective chart will show clearly the movement of materials through the manufacturing building, and will indicate the elevator movements for material in a manner not possible if the departments are repre- sented all in one plane on the ordinary sheet of paper. Perspective charts of floors, one above the other, are so simply made that their advantage should not be overlooked when preparing routing charts for plants having multi-story .buildings.
CHAPTER II
/ SIMPLE COMPARISONS
ONE of a business man's chief assets is his ability to show things to others in their true proportions. He is continually making contrasts, and holding up for comparison different propositions which come up in his daily affairs. The graphic method lends itself admirably to use in making comparisons. It is surprising how much clearer even simple comparisons of only two or three items will appear when their numerical value is put in graphic form rather than in figures. Fig. 16 is a cut taken from the report of the Metropolitan Sewage Commission. Most people know so little about bacteria that it would mean nothing to them to say that the Harlem River contains 15,600 bacteria per cubic centimeter of water. When, however, such a com- parison is made as is shown in Fig. 16, even the most casual glance would convince anyone that the Harlem River is not the most ideal
BACTERIA PER CUBIC CENTIMETER OF WATER
ISO I.6OO I5.GOO
ATLANTIC LOWER HARLEM
OCEAN NEW YORK RIVER
BAY
Fig. 16. Bacteria in the Waters of New York Harbor
This illustration is taken from the ~eport of the Metropolitan Sewage Commission. The representation as though seen through a micro- scope is decidedly effective
swimming place. The figures for the bacteria count are given with the chart so that all the data are available to anyone who may wish to study the facts from a scientific standpoint.
The drawing of Fig. 17 is of the cartoon type, effective for wall exhibitions or for use in the more popular magazines. This particular
20
SIMPLE COMPARISONS
The Independent
Fig. 17. Five Forms of Our National Waste
A cartoon type of chart like this will reach a popular audience. Accuracy of statement should not, however, be sacrificed as it has been here, in that there is no way of correctly comparing the money bags
diagram contains nothing by which accurate comparison may be made.
No figures are given, and it is impossible to tell whether the different
money bags should be compared on the basis of diameter, area, or volume. Almost the only conclusion which can be drawn from such a diagram is one regarding the relative rank of the different expenditures. The re- liability of even that is likely to be questioned because of the evident lack of accuracy in this kind of chart. Nevertheless the cartoonist style should not be broadly condemned, for it has tremendous possibilities. It is possible to combine the car- toonist's wonderful power of arous- ing interest with methods of present- ing facts which will give a numerical interpretation that cannot be
misunderstood. There is a great oppor- tunity waiting for the man who can
combine cartoon methods with accuracy
of numerical statement.
Fig. 18 gives a statement which the
illustration does not support. In the
first place, the dates of the two years
compared are not given. In the second
place, it is impossible for the reader to
tell whether the diagram is drawn on the
basis of one dimension, two dimensions,
or three dimensions. It would be a hope- less task to fit the area of the smaller
washing machine into the area of the
larger washing machine. Methods like
this cannot be too severely condemned. Commercial geography, as it is now
widely taught in the public schools by
listing the various imports and exports of
countries and the products of different
cities, fails to give a clear idea of the
The sale of washing- machines has increased sevenfold in the past three years.
Good Housekeeping
Fig. 1 8. Illustration Intended to Show that the Sale of Wash- ing Machines has Increased Sevenfold hi the Past Three Years
In comparing the two pictures it is not likely that the reader will obtain a ratio of seven to one. There is no way for the reader to tell on what basis the drawing was prepared, whether by height, area or volume. The title of this chart is also poor in that it does not name the two years for which the comparison is made
GRAPHIC METHODS
United States
11,483,000 Bales of 500 Ib
relative importance of the materials listed. It frequently happens that the second or third item on a list may have only one-tenth the impor- tance of the first item. Because the three names are given one after the other, the pupil is quite likely to consider the three items of equal
importance, just as three persons may be of differ- ent height, yet of about the same importance. The graphic method judi- ciously applied to school geography and to general commercial geography
India
3,082,000
Egypt Russia
1,506.000
900.000
China ,775,000 Brazil 810,000
Fig. 19.
Tan and McMurray's New Geographies
The Six Leading Cotton-producing Coun- tries in 1910
This arrangement is a bad one to place before school children. The eye cannot fit one square into another on an area basis so as to get the correct ratio
would make a tremen- dous difference in the student's grasp of the subject.
Fig. 19 is a typical example taken from a geography book in which the attempt was made to use the graphic method. The introduction of the picture of the bale of cotton in Fig. 19 is justifiable. There is, however, no justification for placing the picture inside of one of the series of squares. The picture detracts from the size of the square. Graphic comparisons, wherever possible, should be made in one dimension only. In such a case as this, one-dimension presentation is perfectly
feasible by the use of bars of different lengths. The pupil would find it an al- most hopeless task to fit one side of the block for Brazil into one side of the block for the United States and then square the result- ing ratio in order to learn that the United States pro- duces, roughly, thirty times as much cotton as Brazil. Bars in one dimension only would show the comparison accurately. Under any circumstances, the use of the squares of Fig. 19 with the center line through the centers of the squares gives an extremely poor arrangement.
|
1 Tlte World. ~>. United States |
) 2300 5000 7500 jooot | | 1 1 | 1 1 I 1 | I 1 I | 1 1 1 |
|
Indict |
The world's produc- tion of cotton, in 1905, in millions of pounds. Dodge's Advanced Geography rld's Production of Cotton in 1905 Millions of Pounds |
|
Egypt-* -••• |
|
|
Asiatic Pussia.,n...n Fig. 20. The We in |
The above illustration together with the title is shown exactly as given in a recent geography book. Charts like this greatly assist the pupil in getting the correct relative im- portance of the different things studied. Note the scale at the top of the chart
SIMPLE COMPARISONS
VA1TTK OF PHODUCTS FOB PRINCIPAL CITIES: 1909.
CITIES
NEW YORK
CHICAGO
PHILADELPHIA
ST. LOUIS
CLEVELAND
DETROIT
PITT8BURC
BOSTON
BUFFALO
MILWAUKEE
NEWARK
CINCINNATI
BALTIMORE
MINNEAPOLIS
KANSAS CITY, KANS.
6AN FRANCISCO
JERSEY CITY INDIANAPOLIS
PROVIDENCE ROCHESTER LOUISVILLE
SOUTH OMAHA
VOUNOSTOWN
LAWRENCE
NEW ORLEANS
WORCESTER
BAVONNE
AKRON
PERTH AMBOY
LYNN
PATERSON
LOS ANGELES
BRIDGEPORT
FALL RIVER
PEORIA
TOLEDO
OMAHA
DAYTON
LOWELL
VONKERS
ST. PAUL
KANSAS C'TY. MO.
NEW BEDFORD
DENVER
READING
NEW HAVEN
SEATTLE
WATERBURV
HUNDREDS OF MILLIONS 'SO 1000 I
Fig. 21. Value of Manufactured Products of Principal Cities of the United States
in 1909
This chart, taken from a Census office report, would have been greatly improved if the actual figures had been placed at the left of the bars in the manner shown in Fig. 27
It is stated by the author of the book in which Fig. 19 is used that tests have shown that children grasp relative quantities better when separate squares are used than when the information is shown by lines or bars. If this is the case, it is probably due to the fact that the squares appear more prominently to the eye than do the bars, and it would seem that the best kind of presentation might be made by using much wider bars so that the bars would be easily seen. Bars can be made as wide as some of the squares seen in Fig. 19 and, if it seems best, the bars could be made in outline rather than in solid
^4 GRAPHIC METHODS
black. Wide bars would give a striking visual effect and yet they would vary in one dimension only, so that relative proportions could be easily judged. Wide bars would probably have all the advantages and none of the disadvantages of the methods of either Fig. 19 or Fig. 20. Instead of showing the data of Fig. 19 by either bars or squares, another method would show pictures of bales in rows of dif- ferent lengths, on the general scheme of Fig. 41. The rows would be the same as the broad horizontal bars, but their numerical interpreta- tion would be less abstract.- Fig. 20 gives a diagram taken
IS NEWBURGH SATISFIED WITH THIS SMAU SCHOOL EXPENDITURE?
SCHOOL COST PER PUPIL
NovtoWlel MtYfcnwnl flu burn I
ii>..Mrrp»^li^HBBHMi^MHHBBiH '4O.27 -••IMHBBBM^MHHH 139.86 •^••••••^•••M I3G.13
Jamestown •^•••^•••••••H '35.41
Newbuigi ••••••^^•••••i »34.89
Cities 25.000 to 35, 000 People (JFi£ures based on average daily attendance)
Department of Surveys and Exhibits, Russell Sage Foundation
from another geography book. This is a much better form of presentation than used in Fig. 19. It could, however, be improved by giving the figures for each country in connection with its own bar.
Fig. 21 shows the horizontal- bar method applied to a larger number of items and proves the great utility of this method when
several different items must be Fig- 22. Comparison of School Cost per i ,r . IT Pupil in Cities of 25,000 to 35,000
shown in their proper rank. In Pe£ple ^ New York §££
this Case, however, the figures This iiiustration was photographed down from a should have been given for the wall exhibit to adapt it to a printed report. The
use of the figures at the right-hand end of the
Convenient USe of any One Who bars is bad practice. The eye is apt to make
. . - , . the comparison from the last figures rather than
might Wish tO make ratlOS Or tO from the ends of the bars
quote the actual value of products
for any one of the cities. It is exasperating to run across a diagram of this kind which contains valuable information in such form that it cannot be carried away or quoted for use elsewhere.
In Fig. 22 an attempt has been made to show in the graphic presentation the figures from which each horizontal bar was drawn. The method of placing the figures at the right of the bar is, however, unsafe. The eye is likely to make a comparison, not from the ends of the bars themselves, but from the right-hand end of the figures. Since the figures are of about constant length, visual ratios are in- accurate when made by comparing a short bar plus the constant length of .figures with a long bar plus the constant length of figures. If the shortest bar in Fig. 22 were about the same length as the space
SIMPLE COMPARISONS
25
United Kingdom
required for the figures, it would be possible to make a visual error of 100 per cent in the comparison. If the figures had been placed at the left of the bars, they would have been in a neat column and not
at all likely to affect the ac- curacy of the visual com- parison.
The chart, Fig. 22, was taken from a report devoted entirely to the city of New- burgh. On this account, it would have been much better if the word "New- burgh" had been printed in heavy-faced type so that it would stand out from the other cities in the list. Where the use of colored ink is possible, it is fre- quently desirable to make the item under foremost consideration stand out prominently by giving it a brilliant color such as red
United States
5O56 : ]
Germany
4..33O
Br Colonies
Vblues given in Thousands of Tons
Netherlands
SB
Fig. 23. Comparison of the Registered Shipping of the Principal Countries of the World
The picture at the top of the chart assists in attracting the attention of the reader. After the attention is gained, the bars set forth the comparison more accurately than it could be given by any pictures of ships of different sizes
or green.
Fig. 23 is an attempt to give a popular touch similar to that at- tempted in Fig. 19 by the bale of cotton. As a general thing, it is possible to attract attention by some such scheme as the steamship used in Fig. 23 and then, after the attention is attracted, to give the comparison by methods which are entirely correct and also familiar to the average observer. In Fig. 23 the figures are given for the data from which the bars are drawn. The values, however, were so large that it was necessary to leave off the last three ciphers and state that the values given are in "thousands of tons." Though the dropping of ciphers is very common, it is a practice likely to lead to serious error and should not be encouraged. Even with the ciphers omitted, the values could not possibly have been given inside the bar if more countries had been included in the list, or if the scale had been any smaller than that shown here. To place above each bar the title for that bar is not good practice. In general, it is desirable to have a
GRAPHIC METHODS
title for each bar at the left, then the figures, then the bar. With such an arrangement, one title will be below another, easily perceived by the eye, and the figures will all be in one column with the decimal points in a straight line.
Figures running into millions can be easily read from long columns if sufficient white paper is left between figures in
UNITED STATES . .493 MEXICO .61
SPAIN a. PORTUGAL .52
JAPAN 42
CHILE 42
AUSTRALIA. .34
GERMANY 32
CANADA . . . .28
THOUSAND! Of TOH»
Production of Copper in Different Countries for One Year
This chart is a redrawing of Fig. 25. The title here should state the year, but that was not given in the book from which Fig. 25 was taken
Fig. 24.
the vertical arrange- ment, and if each group of three figures in the horizontal arrangement is widely set oft" by means of a comma. For graphic work, the groups of three figures should, in general, be more widely set apart than they are ordinarily. Fig. 24 shows the arrangement with the figures at the left of the bars. Here again, however, the ciphers have been omitted when it would probably have been just as clear if they had been included and set off by means of a comma and a wide space. The drawing for the
pigs of copper shown at the left of the illustration
«(«<' gives an idea of
what can be done by hand drawing in order to at- tract attention to the subject which the chart itself is
intended to illu- minate. In this
\ „///„////
\ ..„/,.,;//// \ ...,„//////
X X
§
X
X
*?
^
^
United States 493,476
Chile Australia Germany Canada
Mexico Spain & Japan
Portugal 61,000 52,188 42,310 42,043 34,339 32,298 28,733
Philips' Chamber of Commerce Atlas CaSC the lettering
Fig. 25. A Year's Production of Copper in Tons
This illustration was copied from a prominent book on international trade. Accurate interpretation of the chart is impossible. Graphic work of this sort is dangerous because it may be misleading
also has been done by hand and is a good example of what a skilled
draftsman may do without any great expenditure of time. The solid black bars of Fig. 24 come out in much better contrast than the gray bars of Fig. 23.
SIMPLE COMPARISONS
27
Federated Malay States 68,856
Bolivia
Fig. 25 shows a chart of the same data from which Fig. 24 was drawn. It is readily seen that it would be impossible for the average reader to tell whether this chart was drawn on the basis of height or the basis of area. The pigs of copper are not of the same size in the different piles, and it is evident that a pictured pig of copper is not intended to be the unit. If Fig. 25 is drawn on an area basis, it is al- most impossible for the eye to fit the area for the right-hand pile into the area of the left-hand pile. This chart is a typical example of thousands of illustrations used by the popular magazines and even by some of the more pretentious reference books,
Fig. 26 is an even greater atrocity than Fig. 25. In Fig. 26, the observer is entirely un- able to tell whether comparison is made in one, two, or three dimensions and he has an addi- tional puzzle because of the large amount of perspective shown for the top of the pigs of tin. It would be surprising if one man in a thousand could guess any- thing near the ratio intended to be expressed between the largest and smallest pigs shown. In general, graphic work of this kind is much worse than the use of figures alone. There are times when an ab- sence of knowledge is better than incorrect knowledge.
Fig. 27 is a good example of what can be done as a standard arrange- ment for simple comparisons. On the left there is a symbol to attract the eye and interest the observer. Note that a dollar mark is shown on top of the picture of the bale of cotton in one case and the sheaf of wiieat in the other, to indicate that the value of the crop is con- sidered rather than the number of
Dutch E. Austra- United Siam
Indies lia Kingdom 29,937 15,807 12,755 5,052 3,000
Philips' Chamber of Commerce Atlas
Fig. 26. A Year's Production of Tin in Tons
This illustration, taken from the same source as Fig. 25, is even more confusing. The perspective of the tops of the pigs of tin is such that there is no way of telling whether visual comparison should be made by height, area or volume
COTTON $ ezo.zso.ooo
WHEAT $661,051,000
Fig. 27. Value of Cotton and of Wheat Produced in the United States in 1910
units AftfM* tnp rnrtnr^ wninn Her,e is a suggestion for a standard arrangement for UnitS. Alt eS, Wn horizontal-bar comparisons. The illustrations
may be thought of as "eye catch- ers," we have the figures, and then the bars plotted to scale for quick comparison by the reader. This cut could have been improved slightly if the spaces between the sep-
horizontal-bar comparisons. The illustrations at the left make the presentation popular in form, yet actual figures for the data are given at the left-hand end of the bars
GRAPHIC METHODS
arate groups of three figures had been made somewhat larger and if the black bars had been made about one and one-half times as wide as shown here.
TOTAL POPULATION
SINGLE
MARRIED
WIDOWED
DIVORCED
SINGLE
MARRIED WIDOWED DIVORCED
SINGLE MARRIED WIDOWEP DIVORCED
SINGLE MARRIED WIDOWED DIVORCED
NATIVE WHITE OF NATIVE PARENTS
NATIVE WHITE OF FOREIGN PARENTS
FOREIGN WHITE
NEGRO
SINGLE MARRIED WIDOWED | DIVORCED
w
m
Untied States Statistical Atlas. 1900 Census
Fig. 28. Status of the Population of the United States in 1900, in Regard to Marriage
This chart would have been improved if the figures had been given at the left «nd of the bars. Note that the four lower groups of bars are a cross-index of the information given in the upper group
Another application of the bar method is seen in Fig. 28. Each of the four lower groups of population is a subdivision of the total population shown in the upper group. The same data may be seen portrayed in a different way in Fig. 6. The arrangement of Fig. 6 is more desirable, in that the size of the components is more readily grasped when all are shown in the same horizontal bar. In Fig. 28 the eye does not readily make the addition necessary to fit together the four items "Single," "Married," "Widowed," and "Divorced" as percentages of the total 100 per cent in each group.
The drawing in Fig. 29 is a portion of an illustration intended to show how far different kinds of trucks could travel for an expend-
SIMPLE COMPARISONS
iture of one dollar. The placing of these trucks on different levels is somewhat confusing, but it was done in order that one truck would not have to be shown back of an- other. Note the bars behind each truck, to give the component parts of the total expenditure split into different kinds of charges. This chart is grossly misleading because the point where the race started is not shown. It appears, for in- stance, that for one dollar ex- pended a five-ton gasoline truck will run about twice as far as a five-ton horse truck. This con- clusion is entirely unwarranted, and would not be reached by any reader if the chart had been so drawn that the zero point or starting point for the race had been shown to scale at the left end of the chart.
The black bars used in Fig. 30 to show contagious diseases indi- cate an excellent method for differ- entiating items shown in graphic comparison. In the Boston health- report illustration from which this cut was adapted, the infectious diseases were shown in red. By making most of the bars in outline only, it was possible in Fig. 30 to use solid black to get the contrast obtained in the original report by means of red ink.
It is frequently necessary to show increases and decreases on the same chart so that they may
30
GRAPHIC METHODS
1,300
1.200
1.100
1,000
900
800
700
600
500
400
300
200
100
III
Ia If ... i -if 1 Hi -
*f fis I |&|?! ss I** -I I
^B Drathi from Infectious Diieun. CTZ) DMttw from other DiiMuu,
Annual Report of the Health Department, City of Boston, 1910
Fig. 30. Comparative View of Twenty- five of the Principal Causes of Death hi Boston During 1910
In the Boston report, the infectious diseases were represented by red bars. Here attention is called to the infectious diseases by using solid black bars in contrast with bars shown only in outline
zero line. The figures can be placed on the left-hand margin of the chart, immediately between the title for each bar and the end of the bar, in a manner similar to that shown in Fig. 27. Since the zero line must be near the center of the chart, rather than at the left-hand edge, when the right- and-left arrangement is used, it
be in contrast. In Fig. 31 an ex- ample of the contrast of increases and decreases is given, increases be- ing shown to the right of the zero line and decreases shown to the left of the zero line. This right-and- left arrangement of increases and decreases is fairly well known and is so convenient that it should be more widely used. The actual figures from wrhich each of the hori- zontal bars is drawn can be shown on the chart even if the horizontal bars are drawn to the left of the
REPAIRS AHD REF1EWAL3 Or LOCOHOTIVES PER TOn TRACWE FORCE.
Average of 6 Years Ending 1910 Compared with 4 tears Ending /9O5.
\ %ffKR£A3E. f
MJcW
&*o. LV.
CSI.&STP. &?./.**
c.tnw.
WROMS. I
WESTERN 'ROWS.
"Railroad Operating Costs," Suffern & Son, New York
Fig. 31. Increase is Here Shown to the Right of the Zero Line and Decrease to the Left of the Zero Line. A Heavier Zero Line and Arrows Pointing Right and Left from it Would Improve This Chart
SIMPLE COMPARISONS
would be well to have a broad line for the zero line, so that the eye may at once perceive that zero is not at the left-hand edge of the chart. It would have been better if the zero line in Fig. 31 were some- what broader. Another help to the reader could be given by placing an arrow pointing to the right with the word "increase" and an ar- row pointing to the left with the word "decrease."
Transformers
Transmission Line
Transformers
Notary Converters \
Contact Line
Power Delivered to Locomotives
Journal Amer. Soc. Mechanical Engineers
Fig. 32. Comparative Losses Between the Power House and Locomotives with Differ- ent Systems of Electric Traction
The comparison of the losses in the different power systems is very clearly shown in this illustration, which was taken from a paper by George Westinghouse
Broad bars can be used either vertically or horizontally. The hori- zontal arrangement is usually the more convenient, as it lends itself more readily to the use of type and horizontal lettering for the titles, data, etc., of each bar, without forcing the reader to turn the book at right angles. In Fig. 32, however, the lettering can perhaps be more conveniently grasped by the reader with the bars placed ver- tically instead of horizontally.
Note the lines connecting different bars to show how the com- ponents compare in size therein. These lines assist greatly in giving a clear and rapid interpretation of the chart.
Fig. 33 is an admirable example of what the graphic method can do to boil down complex facts for quick interpretation by the reader. In this case the schools of each of the forty-eight United States were
TEN TESTS OF EFFICIENCY
t. WASHINGTON 2. MASSACHUSETTS
3 NEW \ORK
4 CALIFORNIA
5 CONNECTICUT
6 OHIO
7 NEW JERSEY
8 ILLINOIS
9 COLORADO 10 INDIANA
I \ RHODE 15LAND
12 VERMONT
13 NEW HAMPSHIRE
14 UTAH
15 OREGON
16 MONTANA
17 MICHIGAN
18 N DAKOTA
19 IDAHO
£0 MINNESOTA
H IOWA
22 MAINE
& PENNSYLVANIA
iA KANSAS
25 NEBRASKA &> 5. DAKOTA £T NEVADA
Z8 WISCONSIN
^ WYOMING
30 ARIZONA
31 OKLAHOMA 5Z MISSOURI 33 W VIRGINIA M FLORIDA
35 DELAWARE 56 MARYLAND
37 TENNESSEE
38 TEXAS
39 LOUISIANA
40 NEW MEXICO
41 VIRGINIA
42 KENTUCKY
45 ARKANSAS
44 GEORGIA
45 MISSISSIPPI
Af> N.CAROLINA 4? 6- CAROHNA 49 ALABAMA
V//////WMMAV//////AV////M
'///////A i m
i i
Fig. 33. Rank of States in Each of Ten Educational Features, 1910. White Indicates that the State Ranks in the Highest 12 of the 48, Light Shading that it Ranks hi Second 12, Dark Shading that it Ranks hi Third 12, and Black that it Ranks hi Lowest 12
The above illustration is a photograph of one page of a pamphlet issued by the Division of Education of the Russell Sage Foundation, regarding the public schools of the United States. This type of chart is capable of wide application in other fields
32
SIMPLE COMPARISONS
33
considered from each of ten different view points. The different States were then arranged in grades one, two, three, or four, according to the efficiency of their schools from each of the ten different points of view from which they were considered. The best grade under each heading is shown by means of a white rectangle, the second grade by light cross-hatching, the third grade by dark cross- hatching, and the fourth and worst by solid black. States are shown in the complete chart in their com- parative rank. The State with the best schools is shown at the top of the chart and the State with the worst schools is shown at the bottom of the chart. On the chart as a whole, one can see at a glance just how the schools of any State rank with those in the other States, and wherein the greatest defects occur. The chart of Fig. 33 was in a thirty -page illustrated pamphlet sent broadcast over the United States by the Russell Sage Founda- tion to members of various legislatures, school boards, etc. This pamphlet has resulted in the appropriation
Fig. 34. Organization of the United States Adjutant General's Office Compared with Organization Proposed by President Taft's Commission on Economy and Efficiency
This method of connecting blocks with lines to show the dis- position of departments can be used in many types of chart presentation
of some millions of dollars for the improvement of public schools. The arrangement of the pamphlet itself is worthy of note in that each left-hand page is a chart, while each right-hand page, facing the chart, is devoted to a brief explana- tion of the conclusions which can be made from a study of the chart. This arrangement of alternate pages of chart matter and printed matter is tremendously effective and is well worth copying.
It is frequently necessary to contrast one grouping of components
34
GRAPHIC METHODS
with another grouping of components. In Fig. 34 we have a chart which may give a valuable suggestion to anyone who is considering the rearrangement of departments in any large organization. The present arrangement and the proposed arrangement are each clearly indicated, with connecting lines to show instantly the disposition of each of the old departments.
EnlhteJ Men'* Di- vision
Adjutant Cenenil
Explanation.
Steps under present
I. Receives.
•2. Drafuniemorun dum.
3. Transmits.
•I. Delivers.
5. Re eel ves and Irutisniiis.
6 Receives.
T Examine:
8 Dru fls report
9. 'I r:insmii> 10. Review*. 11 Tr;insmits
12. Helivers.
13. Exjj.iines. H. TmtumlU 15. Delivers I'j Examines 17. Indorses. M. Delivers.
19. Approves
20. Delivers.
21. Indorses.
22. Delivers. 2:1. Exumines. 21. Reviews.
25 Drafts order 26. Types order.
27-fiecordsuttibn 28. Kxnmincs.
-•9. lull inls.
so. Throws in "out,1 box.
:il Collects. :«. Tninsiniis
:«. HHiu-n.
31. SiKll«. :(.'.. IVIiv.-r-.
:u; Not.'* I inn'. :i7. Kxnmliit*. :«. Wrili-s ciinl. :!'.). PisiHilrlicV
Steps under projKised system
! c.V.1 II IT five ri.rrrsiionil-
rin ml draft.*
onlrr.
2 (•-".') R i> view* nnil initials.
:t CM) Throws in "mil" hox.
Fig. 35. Routing of a Letter Through the Adjutant General's Office Requesting the Discharge from the Army of an Enlisted Man hi Recruiting Service, Contrasted with the Routing Proposed by President Taft's Commission on Economy and Efficiency
By referring to the horizontal scale and to the vertical scale the steps can be studied either by departments or by operations
In Fig. 35 is given a convenient method to show the routing of papers through a large office, together with the operations through which these papers must pass. Across the top of the chart is a scale of departments. The circles drawn immediately below the space for
SIMPLE COMPARISONS 35
any department on the upper scale show that the papers receive some action in that particular department. At the right is a scale showing the nature of the work done in each of the departments. The chart is drawn on the basis of the intersection of vertical lines downward from the names of departments and horizontal lines through the names of the operations given at the right. Arrows joining the various circles then give the routing of the papers through the whole of the journey. The comparison of the existing routine with the proposed routine can be seen by considering the solid lines and the dotted lines and by comparing the two distinct columns or lists at the right. Thirty- nine operations may be counted in the present arrangement against five operations in the proposed arrangement. Though the drafting and the detail arrangement of this chart could be improved, the gen- eral scheme is nevertheless worthy of attention.
CHAPTER III
1900
1850
THOUGH in making comparisons, the horizontal bar divided into blocks is superior to the circle divided into sectors, the circle and sector arrangement is not inaccurate when only the com- ponent parts of any unit are to be shown. In the case of Fig. 36, how- ever, the comparison is between two circles, the divisions into com- ponent sectors being only an incidental feature. In this diagram, copied direct from the Statistical Atlas of the 1900 Census, it is practically impossible to tell how much larger the foreign-born population was in 1900 than it was in 1850, for it is necessary to com- pare the two circles on an area basis. To the average person this is an almost impossible task, because it is not feasible to fit one circle inside of the other visually as two horizontal bars may be fitted. If the circle for 1900 were esti- mated as twice the diameter of the circle for 1850, it would mean that the for- eign-born population
Irish Germans British IV\V;*.ViVJ Canadians
Scandinavians
Slavs
l\\Vn\\1 Italians fcyffv^ All Others
United States Statistical Atlas, Census of 1900
Fig. 36. Foreign-born Population of the United States in 1850 Compared with that in 1900, also the Proportion of the Different Nation- alities hi the Two Years Compared
in
The method of presentation by means of a circle with sectors is not inaccurate when only component parts are to be shown. Here, however, we have two different circles com- pared on the basis of total area. The reader cannot com- pare the areas visually so as to get the correct ratio meas- ure of the increase in total number of foreign-born popula- tion. Horizontal bars are much preferable to circles when comparisons are to be made
1900 was four times as great as that in 1850. If, how- ever, the ratio were some- thing less simple than this,
interpretation of the chart would be difficult even by the processes of mental arithmetic. If the ratio between the diameters were,
COMPARISONS INVOLVING TIME
37
1910
for example, one and a half, the average reader would be completely nonplussed, as he would not trouble to go through the mental arith- metic of multiplying one and a half by one and a half. In general, the
comparison of two circles of different size should be strictly avoided.
Many excellent works on statistics approve the comparison of circles of different size, and state that the circles should
189O
1900
1,647 2,244 3.3O2
Figures in Millions of Dollars
Fig. 37. Total Yearly Value for the United States always be drawn to rep-
of Combined Imports and Exports by Land and resent the facts on an
by Sea
In this illustration the data have been represented by circles drawn on a diameter basis. The right-hand circle appears more prominent than the data would justify. Circles com- pared on a diameter basis mislead the reader by causing him to over-estimate the ratios. Compare Fig. 38
area basis rather than on a diameter basis. The rule, however, is not al-
ways followed and the reader has no way of telling whether the circles compared have been drawn on a diameter basis or on an area basis, unless the actual figures for the data are given so that the dimensions may be verified.
In Fig. 37 the figures are given, and the circles have been drawn on a diameter basis. It will be noted that the figures for 1910 are roughly twice those for 1890. Thecircle, however, has roughly four times the area of the circle for 1890 and, according- ly, seems to have much more than twice the im- portance. In Fig. 38, the same data . have been shown on an area basis
1890
190O
1910
U647 2,244 3,302
Figures in Millions of Dollars
Fig. 38. Total Yearly Value for the United States of Combined Imports and Exports by Land and by Sea
Here the data of Fig. 37 have been shown by means of circles drawn on an area basis, as recommended by many authorities on statistical work. The right-hand circle, however, shows up less prominently than the figures would justify. Circles com- pared on an area basis mislead the reader by causing him to underestimate the ratios. Circles of different size should never be compared. Horizontal bars have all the advantages of circles with none of the disadvantages
as most of the authorities on statistical work recommend. If the figures were not given, the reader would be forced to fit the left-hand circle into the right-hand circle on an area basis, or else make a ratio between the diameters and then square the ratio. Either process is almost impossible to accomplish and there is
38
GRAPHIC METHODS
MINISTRY
LAW MEDICINE EDUCATION BUSINESS PUBLIC SERVICE
8
£ T to o>
00
MINISTRY
LAW
MEDICINE EDUCATION BUSINESS PUBLIC SERVICE
Independent
39- Proportion of College Graduates in Different Professions in 1696-1700 and
in 1896-1900
Charts of this kind with men represented in different sizes are usually so drawn that the data are represented by the height of the man. Such charts are misleading because the area of the pictured man increases more rapidly than his height. Considering the years 1696-1700, the pictured minister has about two and one- half times the height of the man representing public service. The minister looks over-important because he has an area of more than six times that of the man drawn to represent public service. This kind of graphic work has little real value
no necessity of inflicting such cruelty on a reader. Though the circles in Fig. 37, drawn on a diameter basis, exaggerate the ratios, the circles in Fig. 38, plotted on an area basis, make the reader underestimate the ratio. Comparison between circles of different size should be absolutely avoided. It is inexcusable when we have available simple methods of charting so good and so convenient from every point of view as the horizontal bar.
In Fig. 37 and in Fig. 38, it would have been better if the year had been given under each circle, with the figures for quantity placed above the circles, so as to follow the standard arrangement of having
COMPARISONS INVOLVING TIME
39
1911
1899
H.59 1,000 One Mite
32,837,000 One Mile
dates placed always at the base of the chart.
Another difficulty in the com- parison of areas is shown in Fig. 39. No figures have been given and the helpless reader must com- pare by means of the pictures alone. By measurement, it will be seen that the minister in 1700 has over three times the height of the minister in 1900. Since the man in each case is shown in his natural proportions, the picture of the minister in 1700 has over nine times the area of the picture for 1900. Whether the ratio should be roughly three or roughly nine, we cannot tell.
Another example of the same kind of difficulty appears in Fig. 40, but here the figures are given and we can check up the author to see whether he has drawn the 1911 man on the basis of height or on the basis of area. The 1911 man, on account of his far greater area, looks to be rather more than two and a quarter times as important as the man of 1899. Though this type of graphic work is quite common, it should be avoided, for its visual inaccuracy is serious enough to cause distrust of the whole graphic method. In considering Fig. 40, the point
14.591,000 ONE MILE
World's Wort
Fig. 40. Passengers Carried on the Rail- roads of the United States hi 1899 and in 1911 Compared
This illustration has all the bad features mentioned for Fig. 39. Here the numerical data are given and we can prove for ourselves that the two pictured men are compared on the basis of height. Because of the disproportionate area, the right-hand picture gives the reader a false and exaggerated impression of growth. See Fig. 41
1911
32,837000 ONE MILE
Fig. 41. Number of Passengers Carried on the Railroads of the United States in 1899
and hi 1911 Compared
Here is a chart drawn from the same data as Fig. 40. It was not a larger passenger, but more passengers, that the railroads carried. The ratio expressing increase in business can be clearly and accurately seen from this method of portraying the facts
40
GRAPHIC METHODS
World's Work,
Fig. 42. Comparison of the Total Amount of Freight Service on the Railroads of the United States in 1899 and in 1911
It would have improved this illustration if the two locomotives had been shown one exactly above the other facing to the left. The additional cars representing the increase in 1911 would then be seen as though added to the rear of the train
to be brought out is not that the railroads carried a larger passenger in 1911, but that they carried more passengers.
If it is necessary to have a popular method, we can at least be accurate by portraying the data in the form of Fig. 41, not as in Fig. 40. Copy for an illustration of this sort is very simply made by taking proofs from a cut of one man and then pasting these proofs on a long strip of paper until a row of the correct length is obtained. The whole arrangement can then be photographed down to produce the effect shown in Fig. 41. To avoid fractional men at the end of a row, it is usually easy to express the ratio with a sufficient number of men in each row or bar to get numerical correctness. Note that in Fig. 41 the whole arrangement is similar to that of Fig. 24 or Fig. 27 in Chapter II, the actual data being given at the left of the row or bar. It would have been better if the men in Fig. 41 had been faced to the left in- stead of to the right. The additional men in the row for 1911 would then appear to have joined the rear of the line rather than to have come in at the front of the line.
1901
1912
World's Work
Fig. 43. Comparison in Size of Trainload on the Chicago, Burlington & Quincy Rail- road hi 1901 and hi 1912
Here one locomotive is above the other but both face in the wrong direction. Figures for the data are not given and the reader cannot tell whether the two lengths compared should include the locomotives or only the cars. Clearness could have been assured if the cars had been shown for comparison in solid black, with the locomotives included for pictorial effect, but only in outline
COMPARISONS INVOLVING- TIME
41
In Fig. 42 the idea is brought out that the railroads are now han- dling more freight. The drawing, however, should be reversed so as to have the two locomotives one above the other facing to the left, with the additional cars at the right-hand end. It would also be better if the dates for the two years and the figures representing tons had been placed at the extreme left in the manner shown in Fig. 41.
In Fig. 43, the two locomotives are placed neck and neck, but the whole chart reads backwards in that it reads to the left instead of to the right. Turn the page over and hold it up to the light. Through the back of the paper, the arrangement of the cars appears from left to right as it should.
1870
1880
1890
I9OO
PRODUCTION EXPORT
UPPER FIGURES
MILLIONS OF BALES LOWER FIGURES
MILLIONS OF DOLLARS
Fig. 44. Yearly Cotton Production and Export of the United States. The Figures with the Arrows Show the Number of Millions of Bales and also the Value in Millions of Dollars
If horizontal bars are used to represent years, the earliest year should be shown at the top as seen here
No data are given in Fig. 43, and it is impossible to tell whether the comparison' between 1901 and 1912 should be based on the ratios of the whole length, including engines, or whether it should be based on the lengths for cars only. A ratio without the engines would be much larger than with engines. This chart is accordingly unreliable. The difficulty in regard to engines being included in the drawing could be entirely overcome if the freight cars were made in solid black, with the engines shown in outline only, so that the eye could judge the ratio between the solid black bars representing freight cars without including the outline drawings of the engines.
Often in charting information like that given in Fig. 44, vertical bars instead of horizontal bars are used. However, the figures given in Fig. 44 in conjunction with the bars make it desirable that the bars should here be horizontal in order that the figures may be read easily.
GRAPHIC METHODS
$990
AVERAGE VALUE OF AMERICAN AUTO EXPORTS 1912 Q
Ian r $1.100
1910| $1,380 1909 1 $1.700 1908 F
$1,880
The arrangement of dimension marks with an arrow-head at each end is a convenient scheme worthy of wide use. Note that the per- centage figures in the illustration clearly refer to the value of the cotton rather than to the number of bales. The figures representing time, in this case years, read down- ward as they should do in every case in which horizontal bars are used to represent facts at different periods of time. If the horizontal bars are arranged with the earliest date at the top, any reader who wishes to do so may read the chart as a curve from the left-hand edge
THE RISE OF THE LOW-PRICED CAR
SHOWING HOW THE AVERAGE VALUE OF EXPORTED AMERICAN AUTOMOBILES HAS DROPPED IN FIVE YEARS
World's Wort
Fig. 45. The Illustration and the Titles are Shown Above Exactly as Origi- nally Printed
The reader is misled if he does not notice that the earliest year has been shown at the bottom instead of at the top. The wording of the two titles, when taken in conjunction with the chart, really adds to the general confusion
of the page and the dates will then appear in correct order from left
to right.
In Fig. 45 the latest date has been placed at the top of the chart.
This causes an impression absolutely the reverse of what it was in- tended to bring out by the drawing. Any one glancing at this chart is likely to suppose that the earlier year is indi- cated at the top and probably would not notice that the draftsman in this case, for some unjus-
PASSENGER AND FREIGHT REVENUES (Average for U. S.)
|
PER MILE OF ROAD |
Average |
Aver |
Av |
Ratio of |
||||
|
No. of |
No. of |
per |
Receipts |
Journey |
.Saul |
Expenses to |
||
|
D»te |
Net Operating |
Passengers Carried |
Tons Carried |
Passenger per Mile, |
per Ton per Mile, |
per Passenger, |
per Ton, Miles, |
Operating Revenues, |
|
Revenue |
1 Mile |
1 Mile |
Cents |
Cents |
Mites |
Per cent |
||
|
1908* |
$3171 |
130073 |
974654 |
1.937 |
.754 |
32.86 |
143.83 |
69.75 |
|
1907 |
36% |
123259 |
1 052 119 |
2.014 |
.759 |
31.72 |
131.71 |
67.53 |
|
1906 |
3548 |
114529 |
982401 |
2.003 |
.748 |
31.54 |
132.33 |
66.08 |
|
1905 |
3189 |
109949 |
8613% |
1.962 |
.766 |
32.21 |
130.60 |
66.78 |
|
1904 |
2998 |
104 198 |
829476 |
2.006 |
.780 |
30.64 |
133.23 |
67.79 |
|
1903 |
3133 |
103291 |
855 442 |
2 006 |
.763 |
30.10 |
132.80 |
66.16 |
|
1902 |
3048 |
99314 |
793351 |
1.986 |
.757 |
30.30 |
131.04 |
64.66 |
|
1901 |
2854 |
89721 |
760414 |
2.013 |
.750 |
28.58 |
135.03 |
64.86 |
|
1900 |
2729 |
83290 |
735352 |
2.003 |
.729 |
27.80 |
130.87 |
64.65 |
|
1899- |
2435 |
77821 |
659565 |
1.978 |
724 |
27.89 |
131.04 |
65.24 |
|
1898 |
2325 |
72462 |
617 810 |
1.973 |
'753 |
26.70 |
132.09 |
65.58 |
Fig. 46.
Courtesy of "Data," Chicago
Average Railroad Revenues from Passengers and from Freight in the United States
Here again the earliest year has been shown at the bottom instead of at the top. In tabulations of this sort there is less danger of erroneous reading if the earliest year is shown at the top. Years are usually grouped in fives, including in one group years ending from one to five inclusive, and in the next group years ending from six to ten inclusive
tifiable reason, has reversed the correct arrangement.
In Fig. 46 also,
the latest year has been placed at the top of the column instead of at the bottom of the column. Though some precedent could probably be found for such an arrangement, the arrangement nevertheless seems
COMPARISONS INVOLVING TIME
43
VALUE, AMERICAN EXPORTS 1906| [ $4,409,136 1911 1 $21,636,661 |
1 91 2 1 $28,300,139
VALUE, IMPORTS FROM ABROAD
1906 1 | 1911
an unfortunate one which should not be copied. Note that in Fig. 46 the figures have been arranged in groups of four with a blank space to assist the eye in reading across the page. In general, it is cus- tomary to have such figures not in groups of four but in groups of five, the groups including years ending in 1 to 5 inclusive and 6 to 10 inclusive.
A rapid reader seeing Fig. 47 is likely to get a much exaggerated idea of the increase in the Amer- ican exports of automobiles. The arrangement of the three hori- zontal bars for the three years is such that the reader is justified in assuming that the years are con- secutive. He is not likely to notice that the upper bar repre- sents the year 1906 and that four years are omitted between 1906 and the consecutive years 1911 and 1912. Since there is nothing to indicate that years have been left
out after 1906, the reader seeing the figure 1912 is apt to assume that the two earlier years are 1911 and 1910.
Fig. 48 is a redrawing of Fig. 47 with a change in scale to indi- cate to the reader that the earlier year shown for comparison must not be read as one of three con- secutive years. Though the space left between the bars for 1906 and
$4,910,208 $2,446,248 $2,000,000
A MARVEL OF EXPORT TRADE SHOWING THE AMAZING INCREASE IN OUR EXPORTS OF MOTOR CARS, AND THE STEADY DECREASE IN OUR IMPORTS, IN THE LAST SEVEN YEARS
World's Wort
Fig. 47. This Illustration was Originally Printed with Fig. 45 on the Same Page of a Magazine, yet in Fig. 45 the Earliest Year was Shown at the Bottom While Here the Earliest Year is Properly Shown at the Top
There is, however, danger, in this illustration, that the reader may assume that the three bars rep- resent consecutive years without noticing the jump from 1906 to 1911. Compare Fig. 48
VALUE, AMERICAN EXPORTS
1906 * 4, 409,1 36 ••
1911 1912
21,636,661 28.3OO.139
VALUE, IMPORTS FROM ABROAD
1906
1911 1912
4,910,208
2,446,248 2,000,000
Fig. 48. The Contrast of American Ex- ports and Imports of Automobiles
The data of Fig. 47 have here been redrawn. The values have been shown at the left of the bars, where they give the neatest and most convenient arrangement. Note that the bar for 1906 is somewhat separated from the bar for 1911, so as to indicate to the reader that the three bars do not represent consecutive years
1911 would not be sufficient for the four omitted years, if the whole chart were drawn to scale, the space is nevertheless large
44
GRAPHIC METHODS
enough to serve as a safeguard to the reader. A slight break could indicate in this manner a gap of any large number of years which it would not be feasible to denote by allowing space according to scale. In Fig. 48 the years and the figures for the chart are properly shown to the left much as they are shown in Fig. 24 and in Fig. 27.
1912
191!
1911
BU.
BU.
19U 1912 1911 1912
New York Times Annalist
Fig. 49. The Size and the Value of the Corn Crop of the United States in 1911 Com- pared with that of 1912
The object of the chart is to show that, though there were more bushels of corn in 1912, the producer re- ceived less total money than in 1911.
The left-hand illustration is incorrectly made as it shows the earlier year to the right. In the central illustration this error has been corrected and the years are named at the base instead of at the top. The arrangement still fails, however, to bring out the message clearly.
From the right-hand presentation it can be seen instantly that the number of bushels has increased while the total money received has actually decreased. The right-hand presentation is arranged in accord- ance with the working of the average person's mind and it gains in clearness accordingly
The left-hand group in Fig. 49 was used as an illustration in a business magazine. The purpose of the chart was to show that in 1912 the farmers of the country raised more bushels of corn than in 1911 but received less total money in return. Note that the earlier year is placed at the right instead of at the left, and that the dates •are given at the top rather than at the bottom. The middle group of bars corrects the error, but the information is still not as clearly brought out as it should be. The best way to bring out this informa- tion is to show that the number of bushels has increased while the number of dollars has decreased, and this is not clear from the middle drawing. In the right-hand presentation it is clearly seen that the bushels went up though the total value came down. The right-hand drawing follows the working of the average person's mind and it gains in clearness accordingly.
As a general rule dates should always be arranged to read from left to right, and columns of figures should be arranged with the col- umn for the earlier date at the left. A common exception is made, however, in the case of financial reports when it is desired to show the most recent year next to the various type-headings relating to
COMPARISONS INVOLVING TIME 45
earnings, expenses, etc., as in Fig. 50. In the case of financial reports it is always the latest year which is of chief interest, and for this reason the arrangement of Fig. 50 seems permissible in order that the figures and the account names may be side by side. The problem in Fig. 49 is so entirely different from that in Fig. 50, that the method of Fig. 50 cannot be held as a precedent to justify the reversed arrangement of dates shown at the left of Fig. 49. The fact that one needs an umbrella on a rainy day is not sufficient reason for carrying an um- brella at all times.
* * *
UNION BAG AND PAPER COMPANY— Reports for the year ended Jan. 31:
1913. 1912. 1911. 1910.
Net earnings $554,251 $1,017,835 $1,038,112 $1,055,400
Depr. and ext. fd. 122,585 122,2(55 120,987 149,925
Balance 431,666 895,570 917,125 905,475
Skg. fd. & bd. red. 134,025 114,095 110,745 107,603
Balance 296,741 781,475 806,380 797,870
Interest 253,748 202,480 197,135 204,611
Balance for divs.. 42,993 578,995 009,245 593,259
Preferred dividend 330,000 440,000 440,000 440,000
Deficit 287,007 *138,995 *169,245 "153,259
Prev. surp 1,921,788 2,020,471 1,851,226 1,697,968
Bond disc. & exp. 70,945 237,677
Profit and loss sur.1,563,836 1,921,788 2,020,471 1,851,220
# • •
New York Times Annalist
Fig. 50. Brief Financial Statement Regarding the Union Bag and Paper Company
In condensed statements of this sort there seems to be good reason for placing next to the headings at the left the column of figures for the latest fiscal year, since this information is of most vital interest to the reader. Columns -for other years are then printed to the right for comparative pur- poses. The earliest year is shown at the extreme right
Though this reversed arrangement of years seems permissible for the purpose of printed reports as here used, there is no justification for the use of the reversed arrangement in chart work. As a general rule material given by years should be shown with the earliest year at the left
Fig. 51 is an illustration photographed down from a large drawing used in a wall exhibit. It is a fair example showing what can be done to arouse interest by the judicious embellishment of charts, especially of those for wall exhibits intended to reach a miscellaneous audience having an average of rather limited education. Note the smoke- stacks in Fig. 51. The smoke-stack at the left is the same height as the bar for the year 1906-07, and the taller smoke-stack at the right the same height as the bar for 1912-13. As this drawing was made for a wall exhibit to show the co-operation of manufacturing companies with the college, the pictorial embellishment seems quite justifiable and useful to attract attention to this particular exhibit. A pictorial
46
GRAPHIC METHODS
CO-OPERATING WITH THE -• ENGINEERING COLLEGE
OF THE
UNIVERSITY OF CINCINNATI
HAS INCREASED 288
II
III
_^
effect also relieves monotony in a large exhibition which may have hundreds or even thousands of different charts and other wall exhibits. Fig. 52 was shown in conjunction with Fig. 51 with the idea of pointing out that the number of students in the University of Cin- cinnati had increased just as (according to Fig. 51) the number of firms co-operating in the engineering work of the University had
increased in the same time.
The bars in Fig. 51 and Fig. 52 are placed vertically, each bar representing a year. This vertical arrangement of bars permits reading the chart as if a curve had been made by drawing a line through the tops of all the bars. Curves are the common language of engineers and statisticians. In order that the bars may be read as curves, it is desir- able to have the bars placed in a vertical position, if they represent divisions of time, rather than entirely distinct subjects such as the separate cities compared as to the value of their output of manu- factured products, in the chart reproduced in Fig. 21. Lettering like that shown in Fig. 51 or Fig. 52 is conveniently made by using the gummed black-paper letters and figures which can be obtained in many good stationery stores. A thin pencil line as a guide at the bottom of the letters, and some judgment used in spacing, will assist greatly in getting a neat result from the gummed letters. Large bars like those shown in Fig. 51 and Fig. 52 can be made by cutting out strips of black paper and pasting them onto white card- board. Such work, however, must be very carefully done or the bars will curl on the edges and give an unpleasant effect. It is generally better to use India ink in making the bars if a good result is to be assured. The liquid drawing ink sold at most stationery stores is
Fig. 51. The Increasing Number of Business Firms Co-operating with the Engineering College of the University of Cincinnati
When the bars represent years or other divisions of time, a vertical arrangement of the bars is usually more desirable than the horizontal arrangement seen in Fig. 44. With the vertical arrangement a line may be imagined joining the tops of the bars so as to give a "curve".
Note, in this illustration of a wall chart, the popular touch given by the pictures of manufacturing plants with smoke-stacks of the same height as the first and the last vertical bars
COMPARISONS INVOLVING TIME
47
INCREASE IN STUDENTS CO-OPERATIVE COURSE ENGINEERING COLLEGE
INCREASE 1913 OVER 1907
1252
84
ill
available in many different colors. Some grades of the drawing ink are water-proof after drying. On elaborate charts the water-proof quality should always be used to make certain that a few rain drops, or handling with moist hands, will not ruin the finished work.
In the discussion of Fig. 51 and Fig. 52 it was mentioned that a line could be drawn through the tops of the vertical bars to give a curve. If the curve were actually drawn, the bars themselves would be omitted. In Fig. 53, instead of using bars, we have lines which may be considered as curves for each of the several items compared. In this case it would be impossible to use bars for each of the items shown because the bars would cover each other. The bars are entirely omitted and lines are simply drawn from the 100 per cent point in 1897 to the various points for different items in 1907. It is certain that the prices (that of pine lumber, for instance, shown by the upper curve) did not have the uniform rate of increase which the straight line from 1897 to 1907 would indicate. We are considering here, however, the changes over the period as a whole, and we can for simplicity draw a straight line and neglect all the fluctuations of intervening years. The general scheme of Fig. 53 is convenient, as the neglect of detail brings the main information out clearly. Fig. 53 has, unfortunately, been drawn in a misleading manner in that the reader is likely to interpret the curves as if zero were shown at the bottom of the chart. The general rule in charts of this kind is that zero should be shown as the bottom line, or, if not shown at the bottom, that the omission of zero should be clearly indicated. As Fig. 53 is shown on a per- centage basis, the 100 per cent line should be clearly indicated by drawing a broad line on the chart for the line opposite the figure 100 in the scale. It would have been better, perhaps, to have plotted the data so that zero would replace the figure 100. On a scale so made, pine lumber would go up 83 per cent, while railroad rates would be shown
American Review of Reviews
Fig. 52. The Increasing Number of Students in the Co-operative Course of the En- gineering College of the University of Cin- cinnati
This illustration was originally used as a companion piece to the chart of Fig. 51. For a popular exhibit the use of vertical bars brings out in- formation quite clearly. Though curves (such as are shown in later chapters) are superior to vertical bars, it is unfortunately true that most people do not know how to read even the sim- plest curves correctly.
Note the lettering at the upper portion of the chart. Letter- ing of this kind may be had by using separate gummed letters such as may be pur- chased ready for use
48
GRAPHIC METHODS
1897
1907
as decreasing 4 per cent. The scale would read upward from the zero line for increases, and downward from the zero line for decreases. By changing the scale and using a broad zero line, misinterpretation of the chart would be entirely prevented.
Fig. 54 is somewhat similar to Fig. 53 in that intervening years are neglected, and that lines drawn from left to right of the chart indicate the total movement rather than short-time fluctuations. Fig. 54 would be better if the lines around the outside of the drawing had been omitted. In general, lines of this kind around the outside of a chart are likely to be confusing. In this case, the double lines at the bottom of the chart draw too much attention to the bottom
and may cause a wrong interpre- tation of the chart. As charts of this type are usually made so as to have the bottom at zero, the reader of Fig. 54 may get an en- tirely erroneous idea of the actual increase in the rates of wages. This chart of Fig. 54 should have been drawn with J/g inch more room at the bottom so that the scale would begin at zero rather than at $1.00. A glance at the chart as it is shown here might convey to any but a careful reader that the wages of trackmen had more than doubled, within the period of ten years covered by the records thus graph- ically presented, though the ac- tual wage increase was only from about $1.12 to $1.50. Though Fig. 54 contains a good suggestion for presenting data in popular form, it is in itself misleading because it does not have its base line at zero. Fig. 55 is a commendable piece of work for popular presentation, as for instance in a magazine. Note the use of dimension marks in two independent horizontal rows so that the upper row indicates the material from which the ships are made while the lower row shows the
$100
Reproduced by Permission from Droege's "Freight Terminals and Trains", copyright, 1912, by the McGraw-Hill Book Company
Fig. 53. Changes after Ten Years in Costs of Railroad Materials and in Freight Rates for a Large Railroad System
A simple chart of this kind is often advantageous, as it neglects all temporary fluctuations and shows only the important changes over a period of time considered as a whole. The line for 100 on the scale should have been made a broad line to indicate the basis of comparison. A wavy line should have been put at the bottom of the chart to show that the scale does not begin at zero
COMPARISONS INVOLVING TIME
49
method of propulsion. Dimension lines used in this way are an ex- tremely valuable adjunct to chart work and should be used much more commonly than they are at present.
Tendencies for the future are frequently very accurately pre- dicted by drawing a smooth curve through known points and then continuing this curve for future years in the manner shown by the broad line in Fig. 55. The trend of this curve indicates that by 1925, we are likely to have ships about 1,200 feet long. Though the method of prediction by ex- tending a curve into the future is very valuable, care must always be used to apply the method with judgment. If in Fig. 55 a curve had been drawn from the data up to the year 1860 and extended from that point to show the prob- able length of vessels in succeeding years, the curve would have indi- cated a likelihood of 1,200-foot ships by 1870. We can see in the light of history that such a predic- tion would have been most errone- ous. It would have assumed the continuance of side-wheel steamers and would have been based chiefly on the length of the Great East- ern alone. The Great Eastern was too far in advance of the age and was in reality an engineering failure. Hence, we see the error which would result from basing a prediction curve on too limited an amount of data.
Periodic photographs of any kind of construction work are one of the most striking forms of graphic presentation. Many large contractors and machine manufacturers now make a practice of having photographs taken of each job at least once each week. The
THE RISING WAGE SCALE
SHOWING THAT THE PAY OF RAILROAD EMPLOYEES HAS INCREASED FROM 30 TO 50 PER CENT. IN TWELVE YEARS. NOTE THAT THE GENERAL OFFICE CLERKS NOW RECEIVE LESS THAN THE TRAINMEN.
World's Wort
Fig- 54- Wage-Scale Increase
This illustration is so drawn that wages appear to have increased much more rapidly than is proved by the actual data given in the chart it- self. The chart should have been extended to show the zero line of the vertical scale so as to assist the reader in getting a correct interpre- tation
50 GRAPHIC METHODS
photographs are carefully dated and filed for reference in case there should be any dispute later regarding the progress of the work and payment therefor. If a large card giving the date of the work is placed in front of the camera so that the date is photographed directly into the picture, the date is somewhat more easily proved than it would be otherwise. Putting the date card in front of the camera with the date upon the card gives a chance for any passer-by to check the hon- esty of the date on the picture, much as the "amount purchased" card at the front of a cash register checks the honesty of the clerk.
Progress photographs like those described above are particularly effective for use in advertising. A series of three or four pictures placed one below another, with the dates carefully stated on each, give the best possible demonstration of the rapidity with which con- struction work has been completed by the advertiser. A broad use for these progress photographs is found in the preparation of reports, catalogues, magazine advertising, etc. Thus a manufacturing plant, for instance, can be pictured in a series of photographs taken some years apart showing buildings which have been added to provide for increase in the business. In the case of machinery, a series of photo- graphs taken in different years are of value to show the increase in the size of the machines built or the successive improvements made in the design.
Moving-picture machines have opened up a whole field of possi- bilities in the rapid conveying of accurate information. Many com- panies are now using moving-picture films to show the technical operations involved in making up their manufactured product, or to show views in different parts of a factory. Moving-picture cameras have been used, also in a very striking way by Mr. Frank B. Gilbreth as an adjunct to methods of time and motion study. By placing in the camera field with the worker a clock with a large dial and a sweep- ing second hand, an automatic and permanent record may be secured both of the worker's movements and the corresponding elapsed time. The statistics thus graphically recorded are immeasurably more accurate and more conclusive than any that could be secured in any other way. Possibilities for the use of moving-picture machines in educational work in schools are only beginning to be grasped by a few of the world leaders in thought. When the moving-picture ma- chine becomes a feature of every school room the results will be as- tounding.
COMPARISONS INVOLVING TIME
1840 1950 1860 1870 1880 1890 1900 1910 1913
}< WOOD
PADDLE WHEELS
1 SCREW f— 2 SCREWS *-4 SCREWS TURBINES-J
Fig- 55- The Growth in the Length of Ocean Liners
World's Work
This is an excellent piece of presentation for reaching an average non- technical class of readers. A smooth curve line has been drawn through the ends of the pictured ships so as to approximate most closely the general law which seems to govern progress in ship building. The smooth curve has been extended into the future as a prediction of the length of the ships which will probably be built during the next ten years.
Note the excellent use of dimension-line arrows at the base of the chart showing the materials used in ship building and the methods of driving ships at different periods in history
Bars to represent different intervals of time as in Fig. 51 and Fig. 52 may be compared to the progress photographs mentioned above. Though the bars and progress photographs are valuable, they may be said to give information only in spots. A moving-picture machine shows pictures so rapidly that the pictures blend into a con- tinuous narrative in the eye and the brain of the observer. What the moving picture is to separate progress photographs, the curve is to detached bars representing time. In just so much as the moving picture is superior to separate pictures shown by lantern slides, in just that much is a curve superior to a series of horizontal or vertical bars for the same data. Unless a person knows thoroughly how to read and how to plot curves he cannot hope to understand the graphic presentation of facts. The use of curves will be covered in later chap- ters.
CHAPTER IV TIME CHARTS
THE horizontal-bar method used in Chapter I to show the com- ponent parts of any unit may be modified so as to represent various conditions at different hours, days, and other sub- divisions of time. Fig. 57 illustrates a convenient scheme to assist the arrangement of vacations for concerns having many employees, in which it is necessary to plan the vacations so that there shall always
VACATIONS FOR THE YEAR 1912
16 22 29 Sept.
Fig. 57. Chart for Assigning Vacation Periods in a Large Office
Vacations have here been phoned so that not more than two men are away at any one time
53
54
September-^
GRAPHIC METHODS
October- ->)< November
_S3aS_S^Q
\Bonus Earn eat, is Bonus Lost oc Day Work t3 Day Absent. Heavy vertical lines indicate Sundays.
CD |6
*!f e!4
o!2
Fig
The
V
zrs
Jlfr. /f. i. Gantt, in Journal Am. Soc. Mechanical Engineers
, 58. Chart Illustrating Bonus Work in a Factory where Bonus Work was Intro-
duced Too Rapidly at First
curve at the bottom shows the total number of workers earning a bonus each day. On November 22
all the workers earned a bonus
be a good man available to take charge of responsible work. A chart of this kind can be made quickly if co-ordinate paper is used, the hori- zontal lines being drawn in with lead pencil. Vacations are shifted around until an arrangement is found that is satisfactory to the man- ager and also to the various employees. After a final schedule has been decided upon, the time given each employee can be made suffi- ciently conspicuous by going over the lead-pencil marks with crayon or ink. A chart of this nature posted on the bulletin board of an office would serve as a convenient means of giving information to the employees as to their respective vacation periods.
Fig. 56 (page 52) illustrates a method regularly used by Mr. H. L. Gantt to indicate conditions in a manufacturing plant. This particular chart was drawn to show progress made in training the employees of a worsted mill under scientific management. Trained employees
TIME CHARTS 55
may earn a bonus by completing a certain quantity of work each day. It will be seen at a glance that the chart becomes blacker at the right hand, thus showing that two-months training had greatly in- creased the output of the employees. If a chart like this is made with different colored pencils, the facts can be grasped more quickly than when only one color is used.
Fig. 58, at the right-hand end, shows that the workers were earning a bonus practically every day, and it also shows clearly that some- thing was wrong during the middle part of October. The workers failed to earn a bonus at that time for the reason that the bonus work was introduced so rapidly that they did not get adequate instruction. The manager of a plant would realize such a situation at once if he had this kind of a chart before him.
At the bottom of Fig. 58 a curve is plotted to give the number of operators who earned a bonus every day. The horizontal scale for this curve is exactly the same as for the bar chart above, except that in the curve a day is represented by a line rather than by a space. In plotting curves, it is customary to represent time by lines rather than by spaces, and this curve is plotted in accordance with good practice. The scale at the left-hand edge of the lower part of the chart represents the number of workers who made the bonus. In order to plot the curve, one simply counts in the upper section of the chart the number of black blocks which are filled in for the particular day. Thus, for October 10, we see that there are seven black blocks. The point on the curve is then placed in the lower portion of the chart at the intersection of the horizontal line representing the number of workers earning a bonus and of the vertical line representing the day, October 10. The curve gives a convenient method of deter- mining the total number of operators who are earning a bonus. When it is desired to know only the number of employees earning bonus each day, the curve shows the matter more clearly than do the black blocks in the upper portion of the chart. The horizontal bars give the story for each worker, the curve gives the total for all the workers. 1 A chart like that shown in Fig. 59 would ordinarily be made on a long sheet of co-ordinate paper so that the co-ordinate ruling could be used for the vertical lines, indicating time. Co-ordinate paper in several different rulings can be purchased in rolls so that the desired ruling can often be had in continuous lengths. Sometimes, however, the desired ruling can be obtained only in flat sheets of limited size
56
GRAPHIC METHODS
TIME CHARTS 57
and it is then necessary to make a long sheet by pasting together several of the separate sheets. The original study from which Fig. 59 was prepared was made upon a built-up sheet seventeen inches wide and eight feet long, so that a full month of lighter operation could be shown on the one chart.
In a large working chart, such as is shown in Fig. 59, very little ruling is required except for the lines limiting the width of the hori- zontal bar representing each lighter. In the original chart, drawing inks of different colors were used to indicate the four different condi- tions— working north and working south, and idle north and idle south. Black was used to indicate towing. Solid red showed idle time in the north, and a red made up of red-ink strokes with white spaces showed idle time in the south. Thus all idle time may be indicated by red, the method of application determining whether the delay is at the north or at the south end of the trip. Working time may similarly be indicated by solid green and by green strokes with white spaces.
It is desirable in all chart work to have certain conventions by which colors would be understood to have certain definite meanings. Thus, following railroad practice, red could generally be used in chart work to indicate dangerous or unfavorable conditions, and green to indicate commended features or favorable conditions. Where neither commendation nor adverse criticism is intended, colors such as blue, yellow, brown, etc., could be used.
In Fig. 59, an ordinary atomizer filled with writing ink was used to fill in gray areas representing night hours. If a little care is used in regulating the spray, a good uniform and light shade of gray is obtained, on top of which colored crayons will show out clearly, as, for instance, in Fig. 59 where Lighter No. 7 is represented as working on the night of September 23. To prevent the ink spreading over the chart, a strip of cardboard should be laid carefully on each edge of the surface which it is desired to ink in by means of the spray.
In making up charts like that shown in Fig. 59, the data are usu- ally recorded on the chart day by day as reports come in. This in- volves a large amount of handling of the chart, and the chart is likely to be much smeared by the time the last reports are entered. If col- ored crayons with the color embodied in paraffin are used, very brilliant colors can be obtained, yet rubbing with the hands will not smear the colored areas. Unless a non-smearing crayon is used, it is better
58
GRAPHIC METHODS
Fig. 60. Operations of Three Tug-boats in New York for Twenty-four Hours. The Boat Represented by the Lower Bar is in Service for a Twelve-Hour Shift Only
A working chart of this kind would usually be made on a long strip of co-ordinate paper. The illustration was drawn entirely by hand to show the possibilities of hand cross-hatching for bringing out information ordinarily shown in several colors
to make up colored charts by using different colors of drawing ink. The ordinary crayons smear so badly that a chart made with them is sometimes unrecognizable before it is finished.
Fig. 60 is a further elaboration of the method used in Fig. 59. The actual chart from which this illustration was made was drawn on co-ordinate paper ruled in tenths of an inch. Each of these tenth- of-an-inch spaces was made to represent ten-minutes time, so that a much larger scale wras obtained than in Fig. 60. As the tug-boat captains regularly kept log-books in which their work was recorded to a five-minute interval the chart was made to the same interval by splitting the ten-minute squares to represent five-minute intervals. With a scale of this size it was feasible to use colored crayons, even though some of the divisions of time were very short.
Fig. 60 was drawn by hand and shows the possibilities in preparing an illustration of this kind when only one color of printing ink is available.
The chart from which Fig. 60 is taken was made to determine how much idle time there was in the operation of three tug-boats, and to ascertain whether the boats could be so run as to reduce the amount of idle time and give better service. The black in Fig. 60 shows the idle time vividly. By looking from bar to bar, it is possible to study all the work of the three tug-boats and to determine whether, if the work were differently assigned, there would be less waiting between jobs. Frequently the tug-boats had to tow two or more lighters or two or more car-floats, simultaneously, as will be seen from the extra
TIME CHARTS 59
bars placed below the main bar for each tug. The number of lighters and car-floats towed simultaneously is clearly shown in the chart, as well as the time at which each was picked up, and the time at which each was delivered by the tug. In the case of car-floats, a frequent break will be noticed at the end of the towing, one-half the width of the horizontal bar being marked with black. This convention was adopted to show that the idle time was occasioned by the necessity of waiting to obtain an unoccupied float bridge into which the car- float could be shifted. Though the tug-boat was standing idle it was not feasible for the dispatcher to take the tug away from the par- ticular car-float to which it was attached, for the tug would be neces- sary to place the car-float in the float bridge as soon as the float bridge became .free.
Charting of information frequently brings out points which would be entirely overlooked if charts were not made. The tug-boat chart from which Fig. 60 was taken at once calls attention to the time re- quired for the tugs to obtain water. As the service of tugs was valued at about $9.00 per hour, the time spent in taking water was a serious loss. As soon as the chart showed the extent of this loss, it was com- paratively simple to remedy the situation by providing different methods of getting boiler-feed water.
A time chart like Fig. 60 can often be used advantageously in conjunction with other time charts covering the same period of time. Thus, in studying tug-boats, the information on a chart for lighter operation such as is shown in Fig. 59, and on charts for the operation of car-floats or of float bridges, may be valuable. All the various kinds of equipment with which the tug-boats may be employed could be considered in the study, if it is to be determined whether or not the most effective use is being made of the tug-boats. If all the charts used in the study are drawn to the same horizontal scale, the charts can be placed immediately above each other so that the operations of all related equipment for every hour of the day and night can be instantly seen during the whole of a test period, of, say, a week or a month.
The charts thus far considered in this chapter have shown time in the horizontal direction only. In Fig. 61 we have time shown by days in the horizontal direction and by hours in the vertical direction. This type of chart is extremely valuable in determining whether or not schedules are maintained uniformly over any period of time.
60 GRAPHIC METHODS
By using different colors of ink a chart of this kind can be made so as to show all related operations without the drawing becoming too complex to read. Fig. 61 has purposely been made simpler than the ordinary chart of this kind to overcome the handicap of being limited to only one color of ink in the reproduction.
Charts in the form of Fig. 61 are valuable in that they show on one sheet all the operations occurring during a given period of time — in this case, twenty -four hours. Some conditions, such as the blizzard of January 7, affect all the deliveries to the different railroads. Study of the chart brings out in contrast conditions which are beyond the control of man and conditions which are the result of carelessness or poor management, which usually crop up first in connection with one railroad, then in connection with another, without being so gen- eral as to affect all of the curves, as did the blizzard of January 7.
Fig. 62 shows the possibility of simplification when so many dif- ferent horizontal curves must be shown that easy reading is impossible. The simplification is made in Fig. 62 by showing only one railroad on each sheet. All the figures for one railroad are shown in curves, placed one above the other. Ordinarily curves like those in Fig. 62 will be nearly parallel, for the time interval required to complete each of the steps of work remains about the same day after day. What Fig. 62 brings out most of all is not so much the time interval between the different steps as the information as to whether each of the dif- ferent steps was started promptly on schedule. Any one operation started late must delay all the following operations.
The paper on which Fig. 62 was drawn is in itself worthy of at- tention. This letter-sheet size of paper was carefully laid out so that a typewriter could be used for the lettering on the margins of the four sides of the sheet. The paper was purposely ruled in squares so that any of the common divisions of time might be shown. The possibilities in this direction are:
The days of the month may be used on the short edge of the paper as in Fig. 62.
Fifty -two weeks for one year can be shown by using the long edge of the paper.
Three years by months can be plotted by using the thirty-six squares on the short side of the paper.
One year by months can be shown by using every third line along the short edge of the paper.
TIME CHARTS
61
1AM 12
II P.M. 10
9
1 P.M. 12 M HAM 1O
9 8
7
\
\ \
«n. 1 2 3 4 5 6 7 8 9 1O 11 IE 13
NewYears Sunday (Blizzard) Sunday
is
Fig. 61 . Operation of Freight Car-Floats at a Railroad and Steamship Freight Terminal
Here we have time represented by days in the horizontal direction and by hours in the vertical direction.
The object of the chart is to record whether car-floats are loaded and dispatched at the same hour each
day. Dotted lines show the time at which cars are pushed onto car-floats by locomotives. Solid lines show
the time at which car-floats are towed away by tug-boats. Curves for any one car-float destination are
in pairs bearing the same letter. If the departure schedule is well maintained, all curve lines will be practically horizontal. Note that the
blizzard of January 7 affected the locomotives less than the tug-boats
GRAPHIC METHODS
ARRIVAL AffD BRIDGETS TIME
Of X Y 2 EAUHOAD GARPLOAT FOR MAY.
c
Sunday.
A
Arrived - tine D ---- Bridged - time
„ E - Waiting for bridge - hotirs, - Loaded - time ~R . Departure - time.
Fig. 62. Operation of Freight Car-Floats at a Railroad and Steamship Terminal
In Fig. 61 several different railroad connections were shown on one large sheet. Here, in Fig. 62, but one railroad is represented on one sheet, with the idea of using as many sheets as there are railroad connec-
tions.
This illustration is photographed down from a sheet of 8j^-inch by 11-inch co-ordinate paper specially designed for use with a typewriter. The zinc cut for this illustration was made directly from the type- written original
TIME CHARTS 63
Percentages up to 100 per cent can be indicated by using fifty of the fifty-two squares on the long dimension of the paper. This ruling gives a co-ordinate paper which is extremely convenient for general work. Other charts drawn on this same ruling of paper may be seen in Figs. 134, 130, 103, 156.
Fig. 63 was adapted from a chart shown in the United States Statistical Atlas for the Census of 1900. The Atlas illustration was printed in color, while Fig. 63 is in black ink. The scheme of this chart is one which could be used widely, for it is an extremely con- venient method of showing a frequently changing rank for a large number of units. The blocks for the various States are numbered according to the rank of each State at the first year shown at the left. The rise or fall in rank of each State at each census can be seen at once by following the lines joining the numbered blocks. The actual nu- merical rank at each census is seen by reading horizontally to the rank number at the right-hand margin or to the numbers in the left-hand column of blocks.
Sales managers publishing a house organ may find the method of Fig. 63 of great advantage in showing the status of each branch selling-house or the rank of each salesman. If every member of the selling organization is given a confidential number, the rank of each can be shown in the house organ sent out each month. Branch houses can be encouraged to compete with each other if their relative rank month after month is indicated on the chart. In the case of salesmen, if the numbers are kept confidential no one salesman can tell from the chart anything about any other salesman. He could, however, see very clearly that his own position in the sales force was getting better or worse, according to whether his relative-rank line pointed upward or downward. This comparison of selling units on a rank basis is in many respects fairer than any curve based on the value of sales. Good business conditions or bad business conditions affecting all alike do not show up in charts like Fig. 63. What is shown is the real progress or lack of progress made by every man or branch selling house as compared with all the others.
Printer's copy for a chart like Fig. 63 can very easily be made up if printed strips of the blocks shown in the chart are used. These, if desired, could be made from Fig. 63 itself. Simply photograph the chart, then take one vertical row of the blocks, as for the year 1900, and have a line engraving made of them, eliminating the figures
64 GRAPHIC METHODS
for numbers which appear in the middle of each block. Print from the zinc plate a number of strips of blocks. With shears and a paste- pot, another vertical row of blocks may be added at the right-hand edge of the chart copy each month to provide "copy" for the plate to print the succeeding month's illustration. The identification could be lettered by hand inside of the vertical row of blocks for the latest month. It then takes only a short time to draw lines joining blocks having corresponding numbers. The built-up "copy" is then ready for the engraver to make a zinc plate. Zinc plates cost so little that there is almost negligible expense required for the new line cut needed each month.
In Fig. 64 the general scheme of Fig. 63 is expanded so that the chart shows not only the rank, but also the comparative size of the units under consideration. This illustration shows also some inter- esting combinations of shading by means of which blocks of distinctly different appearance are obtained. Fig. 64 was photographed directly from a United States Government report. Otherwise, the years would not be shown here reading from right to left instead of from left to right. Though the right-to-left arrangement is unfortunate, the general scheme of Fig. 64 is excellent, as it gives a large amount of information in a small space. The convenience due to this method of double comparisons, either horizontal or vertical, gives it a decided advantage in clearness.
Train charts like that shown in Fig. 65 are very commonly used by railroads, rapid-transit subways, etc. Fig. 65 would not look so complex if colored ink were available to show in contrast the express passenger trains, the work trains, etc. It is suggested that the reader observe the key at the top of Fig. 65 and then follow a few of the various trains from one end of the line to the other, taking into con- sideration the fact that this is a single-track railroad and that trains must pass at the turnouts which are available. To schedule a pas- senger train such as that leaving Tyrone at 12:25 p. m. is no simple proposition on such a crowded railroad as this.
In rapid-transit work in large cities a time-distance chart in the general scheme of Fig. 65 is almost essential if methods of giving high-speed service to the people are to be studied. These time-distance charts can be made on so large a scale that two horizontal lines may be used to indicate the stations, with the lines spaced a distance apart to show to scale the actual length of each station platform. Time-
TIME CHARTS
65
I860
1870
1880
1890
1900
Montana.
Idaho
Dakota
Arizona.
Wyoming
RanK
1 New York
2 Penn.
3 Illinois
4 Ohio
5 Missouri
6 Texas
7 Mass.
8 Indiana
9 Michigan
10 Iowa
11 Georgia
12 Kentucky
13 Wisconsin
14 Tennessee
15 N.Carolina
16 New Jersey
17 Virginia
18 Alabama '9 Minnesota
20 Mississippi
21 California
22 Kansas
23 Louisiana 24*8. Carolina
25 Arkansas
26 Maryland
27 Nebraska
28 W. Virginia
29 Connecticut
30 Maine
31 Colorado
32 Florida
33 Washington
34 Rhode Isl'nd
35 Oregon 36N.Hampsh'e 378. Dakota
38 Oklahoma
39 Indian Ter.
40 Vermont
41 N. Dakota
42 Dist. of C.
43 Utah
44 Montana
45 N. Mexico
46 Delaware
47 Idaho
48 Hawaii
49 Arizona SOWyoming
51 Alaska
52 Nevada
Adapted from the United States Statistical Atlas
Fig. 63.
Rank of States and Territories in Population at Different Census Years from 1860 to 1900
Each State is represented by a block bearing an identifying number. The change in rank from census to census is indicated by the connecting lines. Actual rank at any census can be seen by referring horizon- tally to the figures at the right or to the figures at the left.
A. chart of this kind can be used for showing relative rank of salesmen or comparative sales of different branch sales-houses *
66
GRAPHIC METHODS
°^^ fl M «*- -g
<a y a
S B.2
*j •*• *j
,5 I
TIME CHARTS
6?
68 GRAPHIC METHODS
distance curves like those shown in Fig. 65 are then plotted, one for the rear end and another for the front end of each train. As the train remains constant in length throughout one whole journey it is obvious that the two curve lines must be a constant vertical distance apart throughout the length of the chart. At stations, subway trains must stop in such a way that the whole length of the train will be opposite the platform so that passengers may get in and out of every car. The trains follow each other very rapidly, and it is essential that sufficient room be left between two trains for safety. If two curves on a time- distance chart should touch each other, it would indicate a collision. The distance between different train curves on a chart gives informa- tion regarding the kind of signal and brake systems that must be used to give the desired degree of safety in operating the road.
CHAPTER V CURVE PLOTTING
INFORMATION may be charted in many different ways. Under present conditions, if six men were given a set of figures and asked
to chart these figures, the six resulting charts would be widely divergent in method. Though variety in method of charting is some- times desirable in large reports where numerous illustrations must follow each other closely, or in wall exhibits where there must be a great number of charts in rapid sequence, it is better in general to use a variety of effects simply to attract attention, and to present the data themselves according to standard well-known methods.
In Fig. 66 the attempt to give a spectacular scheme of presentation seems to have overshadowed everything else in the mind of the illus- trator. Though a striking architectural design has undoubtedly been obtained, the chart means nothing, for it is impossible of inter- pretation. No scale has been used in either the horizontal or the vertical direction, as can be seen by comparing the figures on the block for 1830 with the figures on the block for 1840. Even if some scale had been used in making up this chart, the general scheme is such that the reader would hopelessly flounder in trying to reach an accu- rate interpretation.
Fig. 67 puts the data given in Fig. 66 in the form of horizontal bars. Note that the values which the bars represent are given inside of the bars, for reference purposes. In order to make the shape of each bar stand out distinctly, gray dots were used which permit the figures representing the values to be read through the shading. This is an interesting attempt, but it is not satisfactory as a general scheme. Though Fig. 67 gives the data much more clearly and far more accu- rately than Fig. 66, the method is not satisfactory because it is diffi- cult for the eye to follow the ends of the different bars in order to judge the increase made from decade to decade. The best method
69
GRAPHIC METHODS
134
222
1830
1840
318
1850
687
I860
829
1870
1504-
!88O
164-7
1690
2224
I9OO
The Philadelphia Commercial Museum
Fig. 66. Commerce of the United States since 1830. The Sum of Annual Exports and Imports. Values are given in Millions of Dollars
Such a chart as this is worse than none. There is no scale in either direction. The block for 1830 is drawn with a larger area than the block for 1840 which represents a larger quantity. Compare with Fig. 67 and Fig. 68
CURVE PLOTTING
71
IB30 EJ3*I
IB9O I"'-- '-•'-..- .:.. '..•:•• -• ••- ; •-...•••' : IS47 : O ' - : . •' — :'-\/ •• 1
reoo [15 ••-••••'• -••••••• '.:••• ;zg-»a\ • -j
SB
Fig. 67. Values of Annual Exports and Imports of the United States. Figures are Given in Millions of Dollars
This chart is drawn to scale from the data given in Fig. 66, to show the use of horizontal bars for work of this nature
of the three is followed in Fig. 68, where the data from Fig. 67 are plotted in the form of a curve. The curve method brings out all the information in less space and in clearer form than does the block
system in Fig. 66.
An understanding of how to plot curves and of how to read them should be part of the equipment of every business man, just as it is of every engineer, physician, biologist, and statistician. The general scheme of curve plotting is so simple that instruction in it should be given as part of the work in elementary arithmetic in all public schools. Children over ten years of age can do plotting and can understand simple curves like that of Fig. 68. Curves are usually plotted on co-ordinate paper already ruled in squares, so that the person doing the plotting need not take the time necessary to rule the paper. For reports, for illustra- tions of magazine articles, or for advertising, it is ^ordinarily better to rule by hand a small area such as is shown in Fig. 68 so that the spacing of the ruling may suit ex- actly the data which it is desired to plot.
In Fig. 68 we have data avail- able only by decades, from 1830 to 1900 inclusive. Lines are drawn vertically for each decade. The scale need not run above 2,300, for the largest figure to plot is 2,244 millions. A suitable scale is secured by using one line for each 200 millions. After the background ruling has been drawn, the figures at each census are laid off to scale, on the proper vertical lines to represent census years, and a dot is placed on each vertical line at that vertical distance which represents
|
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\ N no f* 0> 0 5 ^ ) W £ 0 N S I 2d««>co;!:S?r |
|||||
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1830
'5O '6O '7O 'SO 'SO 19OO
Fig. 68. Value of Annual Exports and Imports of the United States. Fig- ures are Given in Millions of Dollars
This curve is drawn from the same data as Figures 66 and 67. The curve shows the changes from decade to decade more vividly than do the horizontal bars of Fig. 67
72 GRAPHIC METHODS
the data according to the scale chosen. Thus the figure 222 for the year 1840 would be indicated as a dot on the vertical line for 1840 slightly above the place where the horizontal scale line for 200 crosses the chart. After the dots for decade years have been placed on the vertical lines, the dots are joined with a heavy line and a curve appears.
The curve of Fig. 68 shows the changes from decade to decade much better than the bars of Fig. 67. It can be seen at once from the curve that the greatest gain in any decade was between 1870 and 1880 when the increase was three and a half divisions on the ver- tical scale. The bars in Fig. 67 have no horizontal scale to measure by and the comparison between census years is accordingly more difficult.
When plotting any curve the vertical scale should, if possible, be chosen so that the zero of the scale will appear on the chart. Other- wise, the reader may assume the bottom of the chart to be zero and so be grossly misled. Zero should always be indicated by a broad line much wider than the ordinary co-ordinate lines used for the background of the chart.
In Fig. 68, it will be noticed that figures are given at the top of the chart to represent the value for each point plotted on the curve. The use of figures at the top of the chart in this manner is very de- sirable. The figures are in plain sight, so that anyone desiring to know the value of any point on the curve can look above the point to get the actual figure wanted, without having to read from the? scale at the left-hand edge and then estimate roughly the value for any point which happens to fall in a space between two horizontal lines of the scale. Reading from the figures at the top of the chart permits any desired figure to be obtained more rapidly and much more accu- rately. In addition to this, the figures are recorded in such manner that they may be quoted for use elsewhere by anyone who may wish to make use of the data in a speech or in a written article in which the chart itself cannot be used.
It would be a desirable thing if in all curve charts the figures for the horizontal scale were placed at the bottom of the chart rather than at the top. Many illustrations in this book, taken from publications of excellent standing, show dates (such as years, months, etc.) at the top of the chart. If the horizontal scale were always placed at the bottom, the standard arrangement would be a convenience to the reader and would give the additional advantage that the top of the
CURVE PLOTTING
73
DOLLARS
4OOO
chart would be free for a numerical statement such as is found at the top of Fig. 68.
The scales of any curve chart should be so selected that the chart will not be exaggerated in either the horizontal or the vertical direc- tion. It is possible to cause a visual exaggeration of data by care- lessly or intentionally selecting a scale which unduly stretches the chart in either the horizontal or the vertical direction. Just as the English language can be used to exaggerate to the ear, so charts can exaggerate to the eye.
. p OgOSrHOSOOlMCSN^
A curve permits of finer e * S 1. I 1 • 1 1 i 1
interpretation than any other known method of presenting figures for anal- ysis. Fig. 69 gives some information which many persons might not fully grasp if only a column of figures were used to indicate the average yearly earnings of Princeton graduates. The fairly uniform slope of the curve for the first six years after graduation indicates that the men were receiving almost uniform raises in pay each year. It must be remembered that a straight-line curve simply indicates that the amounts of the increases year by year are uniform in numerical value. If a curve were started at the lower left-hand corner of the chart and drawn diagonally across each of the rectangles of the chart, it would be seen at once that there would be a straight line indicating an increase in salary of $500 per year. With such a straight line across the chart, the increase in salary for the first year would be $500. As compared with a zero beginning- wage there would be an increase of an infinite percentage at the end of the first year. The next year the increase would again be $500. Compared to the $500 salary, the increase would be 100 per cent. The third year the increase would be $500, and compared to a $1,000 salary the increase would be only 50 per cent. A curve of uniform slope on any chart of rectangular co-ordinate lines indicates only that there has been a uniform increase or decrease in actual numbers, not
Fig. 69. Average Income of 155 Princeton Grad- uates of the Class of 1901 for Ten Years After Graduation
Note the effect of the 1907 panic on incomes in 1908
74
GRAPHIC METHODS
VOtues given in Millions of DolUtt
•PRODUCTION
a uniform rate of change on a percentage basis. A plotted line repre- senting a uniform rate of increase from year to year on a percentage basis may be seen in the curve given in Fig. 121.
The untrained reader of curves will probably not be able to tell instantly what made the flat portion of the curve in Fig. 69 during the year 1907 to 1908. One of the chief advantages of the curve method of presenting information is that a curve forces one to think. A little thought here will at once bring out the fact that the flattening of the curve was caused by the 1907 panic. Though the panic started in October of the year 1907, the year 1907 was really one of the most prosperous years the coun- try has ever known. It would be more fitting if the panic were called the 1908 panic, since the main effect of the panic came in 1908 rather than in the year 1907. It can be seen that the Princeton men had their incomes reduced dur- ing the year 1908 so that the average fell below that of 1907. By looking along the curve it will be noticed
IMPORTS
as s
n
iflh
EXPORTS
Q Q o o o o S Sv (2 it o ft
Cotton Goods
The Philadelphia Commercial Museum
Fig. 70. Cotton Goods Production, Import and Export for the United States. Values are Given in Millions of Dollars
The order of years here reading from right to left gives the first impression that production is decreasing. Compare this illustration with Fig. 71
that though there was a larger yearly increase in salary after 1909, salaries at the end of 1911 had not attained the point which it would seem they would naturally have reached if no panic had occurred at a time so shortly preceding this date.
CURVE PLOTTING
Milllor
Dollar
36O
In Fig. 70 vertical bars have been placed touching each other, with the earlier years at the right. The whole arrangement of the chart is extremely poor and also misleading. In Fig. 71 the data of Fig. 70 have been replotted. The most striking thing about Fig. 71 is the falling off in the rate of increase of production in the decade between 1870 and 1880. The shape of the curve at once starts a train of thought in regard to tariff legislation and other conditions which may affect the manufacture of cotton goods.
- It will be noticed in Fig. 71 that we have four curves, while only three sets of bars were given in Fig. 70. It is evident that if we add production and imports and then deduct exports, we will have a fair indication ol consumption if the amounts remaining in warehouses, etc. (which are probably a negligible percentage of the whole con- sumption) are excepted. Note that the import and export curves follow each other in general form, though the export curve fluctuates on a percentage basis 'much more rapidly than does the import curve. Remember that in the fluct- uations of two curves like these, the change from year to year must be judged from the zero base line rather than from the slope of the curves themselves. The drop in the export line from 1860 to 1870 was almost one-half, while the drop in the import line for the same period was much less than one-half, even though the import line does show the greater slope downward.
In Fig. 72 we have an example of what not to do in charting. The main effect of the circles is to give one a headache without per- mitting any accurate comparison between the years. The eye does not easily see each circle as an area. The tendency is to see only rings
Fig. 71. Cotton Goods Production, Import and Export for the United States
These curves are plotted from the data of Fig. 70, and show the information in much clearer form
76
GRAPHIC METHODS
between the lines of the circles, rather than the whole area in- cluded inside of each circle line.
Fig. 73 gives the data of Fig. 72 in curve form. The heavy solid line curve shows the changes from decade to decade as they could never be interpreted from either the actual figures or the circles of Fig. 72. The tremendous increase in the world's commerce between 1900 and 1910 is of very great interest, showing the effect which better means of communication have brought about as a result of the splendid increase in scientific and engineering knowledge.
If one makes comparisons be- tween the circles of Fig. 72 on a
Billions ot Dollars
The Philadelphia Commercial Mvsevm
Fig. 72. Annual Commerce of the World, Imports and Exports Combined. Shown at Ten-year Periods, 1850- 1910
These circles, drawn on an area basis, are even more difficult to interpret than the circles of Fig. 38. The eye is likely to see the rings rather than the whole areas of the circles. Compare Fig. 73
185O I860 1870 I860 IO3O I9OO I91O The Philadelphia Commercial Museum
Fig. 73. Annual Commerce of the World, Imports and Exports Combined. Shown at Ten-year Periods, 1850- 1910
The solid line is plotted according to the figures given in Fig. 72. The dotted line shows the erroneous impression which would be obtained by the reader if he should interpret Fig. 72 by the diameters instead of by the areas of the circles
diameter basis rather than on the area basis to which the circles were drawn, one gets an interpretation like that indicated by the dotted line in Fig. 73. By comparing the dotted line with the solid curve the reader may see the extent of the error which arises if circles are compared on a diameter basis after being drawn on an area basis.
Fig. 74 gives a good idea of the utility of the curve method for showing concisely a large quantity of data. If the figures for the price of cement had been expressed in dollars and shown in a long numer- ical column, there would be very few readers who would take the
CURVE PLOTTING
77
trouble to follow the table of figures and notice the fluctuations from year to year. The curve, however, gives all the variations in price at a glance and shows in most striking manner the great reduction which occurred in the price of cement as manufacturing facilities im- proved and increased. A curve of this kind greatly stimulates thought, for one immediately wishes to know the cause of each of the peaks and of each of the valleys in the curve. One gets a vista of recurring periods of financial boom and of financial depression, and a glimpse of such factors as new developments in methods of manufacturing cement and the constantly increasing demand for the product.
If the reading of curves were understood by the average educated person, it would be possible to use, in almost any kind of magazine, advertising illustrations on the order of that shown in Fig. 75. Since, however, curves are not widely understood at present, this type of advertising must now be limited chiefly to the technical journals read by engineers and others who understand curve interpretation. It is really a calamity that curves are not more widely under- stood. Advertising men are now frequently un- able to convince people of their argument simply because they have no language by means of which figures can be made interesting or even intelligible when expressed in an advertisement of limited size. The author ventures to predict that it will be only a very few years until curves are so widely understood and used that they may be presented advantageously in any high-grade advertising pages.
It would be almost impossible to give a clear idea of the flood indicated in Fig. 76 if only columns of figures were used. With the curve it can be seen clearly that the stream rose very rapidly and subsided rapidly, so that the stream was down almost to normal level within forty-eight hours after the beginning of the flood. This curve was probably plotted from flood-gauge readings taken once an
|
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V |
V |
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Dt 111 |
i i * ita k |
! i 'c £ |
$ '. Mi it |
ago the |
Mill, from 1880 to 1910
Columns of printed figures or a series of vertical bars could not por- tray this information as vividly as it is brought out by the curve shown above
78
GRAPHIC METHODS
hour, or even more frequently. The curve, therefore, was plotted on much more numerous points than are indicated by the vertical lines of the horizontal scale. Frequent observations of the gauge height and the numerous points plotted on the curve in Fig. 76 ex- plain those fluctuations in the line of the curve which occur in the spaces between the vertical lines. Ordinarily a chart is sufficiently accurate if straight lines are drawn from point to point of the plotted data for a curve, without attempting to make a smooth, flowing line.
Fig- 75- Advertising Illustration used in a Technical Magazine, with a Heavy-type Statement Proclaiming that "3000 Central Stations hi the United States need a High Grade Gasoline-Electric Generating Set"
The black areas indicate the portion of the 24-hour power-house load for which the gasoline engine would be used
The curve looks smooth in this illustration simply because the gauge readings were taken so frequently that the nearness of the many points made the lines joining them appear curvilinear rather than angular. Such a smooth curve would not have resulted if gauge read- ings had been taken only every six hours and the chart made by con- necting with straight lines the points plotted for the data obtained at these longer intervals.
Another flood curve is shown in Fig. 77. The speed with which the water ran off the territory drained can be judged by the shape of the curve. It is not, however, safe to compare the shapes of the curves in Fig. 76 and Fig. 77 without noticing that in Fig. 77 we have one day represented by a space approximately the same as the space used in Fig. 76 for only six hours. If the curve of Fig. 76 were plotted on the same horizontal scale as the curve of Fig. 77, the flood would appear to be much more severe and rapid than it appears from Fig. 76.
CURVE PLOTTING
79
30
c
$20 g>
'o>
r
4)
g o
Noon Noon Noon
3ept.6th. Sept. 7th. Sept. 8th.
Time in Hours
Engineering Record
Fig. 76. Curve Showing Duration of a Flood, September 16, 1909, in the Canadian River, New Mexico
This curve was first plotted on a paper having co-ordinate lines close together. For ease of reading, the intermediate lines were omitted from the magazine illustration
In general, it is unwise to compare the shapes of two curves unless they are plotted to the same scales, both horizontal and vertical.
The curve of Fig. 77 is misleading because the scale does not begin at zero. Only the peak of the flood is shown, with no zero line from
which to judge the extent by which flood exceeded normal flow of
120000
100000
-25
80000
60000
40000
20000
-5
26 27 28 29 March. 1913
31
2
April Engineering Record
Fig. 77. Flood in the Hudson River at Mechanics- ville, N. Y., March, 1913
Note the different scales at the right and the left by which the curve may be interpreted. This chart is misleading because the scales do not begin at zero
the the the
river. If the co-ordi- nate lines were drawn so as to show the zero line, the base of the chart would be about ^8 inch lower than it appears in Fig. 77, and the whole curve would make a different im- pression. The omission of the zero line in charts of this kind is partic-
ularly irritating, yet it is a very common error made by persons drawing charts.
Note that in Fig. 77 the curve can be read from two distinct scales, one scale on the left side of the chart, and a different scale on the
80
GRAPHIC METHODS
right side of the chart. If only one scale is used, ft should be placed at the left-hand side of the chart. In very large charts it is some- times desirable to repeat the scale at the right-hand side as well. Where two different units of measurement are used in the scales, the units should be carefully named so that there will be no danger of the reader's using the right-hand and the left-hand scales inter- changeably as though they represented the same unit.
CITIES Charts like that shown in
Fig. 78 are quite frequently used in public health reports. It is difficult to see how such an unsatisfactory type of chart ever came into general use, unless it was because there are twelve months in a year and twelve hours on the face of a clock. If the death rates for the different months of the year were plotted in a curve, using rectangular co- ordinates, the data would be just as easy to read and to understand as when shown by the radial scheme (polar co- ordinates) of Fig. 78. There would be the additional ad- vantage that the rectangular
United Slates Statistical Atlas of the 1900 Census
Fig. 78. Death Rate from Consumption per 1000 Inhabitants for Each Month of the Year in Cities of the United States
This type of chart should be banished to the scrap heap. Charts on rectangular ruling are easier to draw and easier to understand
method would be more widely understood than the circular method of Fig. 78.
Though a chart in the form of Fig. 79 might be justified in the Sunday supplement of a newspaper where an untrained audience must be reached, it is much better to use a curve in the form of Fig. 80 whenever a trained audience is assured. The most interesting thing about Fig. 79 is the slanting line which gives an unusual optical illusion if observed under artificial light, especially with a bare gas flame. The slanting line then appears blue, although it is printed black like the horizontal bars of the chart.
The dotted line in Fig. 80 corresponds to the slanting line of Fig. 79, and represents a progressive average of all the points on the curve
CURVE PLOTTING
81
above. The dotted line, of course, coincides with the solid line at the first point where there is only one point to consider in the average. Figures for the dotted line are obtained by averaging the figures for the first two years, then the first three years, then the first four years, etc., until the last point on the dotted line represents an average for all the points on the solid line.
Fig. 80 is worthy of attention as a model of good practice which may be studied carefully by anyone just beginning to plot curves.
Pittsburgh and Lake Erie Railroad
Fig. 79. Yearly Average of Revenue Tons per Train Mile on the Pittsburgh and Lake Erie Railroad. The Slanting Line Shows a Progressive Average
If this illustration is observed with artificial light, an interesting optical illusion may be noticed in that the
slanting line appears blue in color The use of horizontal bars here gives a chart less easy to interpret than the curve shown in Fig. 80 for these
same data
82
GRAPHIC METHODS
^ «>
.^^U^io A*na<0a<'>aoa*tnnu>00f')<<)f*«-9--'N<0r»N<9Nr»0>(a ^ vrf> • • ~ «t • i $ 9 • 9 9 3 * • 9 9 • • 9 • * * • • * ~ ** * « * • 5 • • ^.^r 5'5 ii 5 ti • * ..il * Jl * 4 * *•• T * * * * si •». •» K i» • o o * g o 5-. • i
^W) 11,11 — i — iiiiiiiiiiiiiiiii777777777
Fig. 80. Yearly Average of Revenue Tons per Train Mile on the Pittsburgh and Lake Erie Railroad. The Slanting Line Shows a Progressive Average
Here we have the data of Fig. 79 plotted in a curve which can be interpreted easily and accurately This chart may be considered a model of good practice in curve plotting. All of the work, including the lettering, has been done by hand, thus insuring better results than can usually be obtained from printing
The following features of Fig. 80 are pointed out for the benefit of anyone who may have curves to plot:
1. The zero line is a much broader line than the co-ordinate lines.
2. Heavy lines are not used at the right- and left-hand edges, since the chart does not start or end at the beginning or end of time.
3. All lettering is so made that it can be read horizontally or from the right-hand edge of the sheet.
4. Years are given with four figures for every tenth year ending in zero. Other years are indicated with two figures so that they may be more quickly read.
CURVE PLOTTING 83
5. All letters and figures on this chart were made by hand, showing the perfection which may be attained by practice in lettering.
6. The curve itself stands out clearly from the co-ordinate lines.
7. Figures at various points along the curve indicate matters which are worthy of special notice. Foot notes are not given here, however, as they are only of highly technical interest.
8. Figures for the values of points on the main curve are given at the top of the chart immediately above each corresponding point on the curve. Values may be read correctly from the upper figures rather than guessed at by estimating them roughly on the left-hand scale.
9. The statement "Revenue Tons per Train Mile" at the upper left-hand corner is purposely printed diagonally so that it may serve as a heading for each of the two columns of figures, one at the left and the other at the top of the chart. The diagonal ar- rangement gives a neater effect than can be obtained otherwise.
10. Though figures for the dotted curve could be shown at the top of the chart the dotted line is of only minor interest here. It is accordingly best to avoid the two columns of figures at the top in order that the figures for the main curve may stand out more prominently.
CHAPTER VI CURVE PLOTTING CONTINUED
THERE are so many different applications of curves and such varied yet convenient methods of plotting curves, that it seems worth while to take up some of these in detail, and point out certain advantages and disadvantages of different curve-plotting schemes.
Practically all curves display relations existing between different sets of data which we may call " variables". One of the variables is used as a standard or measure by which to interpret the facts under consideration, and it may be called the "independent variable". The other variable, which is interpreted from the independent variable, is called the "dependent variable". For example, in a bacteriological examination of a pond at varying depths, distance below the surface would be the independent, and number of bacteria per cubic centimeter the dependent variable. In a seasonal gauging of a stream the dates of observation would be the independent and cubic feet per second of flow the dependent variable. Sometimes we consider more than two variables simultaneously, and we then have two or more independent variables from which to consider a dependent variable.
It is difficult to make a general rule for determining in any case which is the independent variable and which is the dependent variable. The decision depends entirely on how any set of data is approached and on the habits of mind of the investigator. When time is one of the variables it is usually, but not always, the independent variable. If we consider values or quantities at different dates, as in Fig. 80, time is very obviously the independent variable. If, however, we are interested in the length of time required to do different operations, as in Fig. 85, Fig. 86, and Fig. 87, our data are expressed in length of time and time is the dependent variable. This example is an excep- tional case and it is named here only to show that, although time is
84
CURVE PLOTTING 85
ordinarily the independent variable when it enters into curve plotting, nevertheless there may be occasions when time is the dependent variable, and charts should be plotted accordingly. It is important that the person drawing a chart should in each case distinguish be- tween the independent variable and the dependent variable, for this distinction affects the whole arrangement of the chart.
It should be a strict rule for all kinds of curve plotting that the horizontal scale must be used for the independent variable and the vertical scale for the dependent variable. When the curves are plotted by this rule the reader can instantly select a set of conditions from the horizontal scale and read the information from the vertical scale. If there were no rule relating to the arrangement of scales for the independent and dependent variables, the reader would never be able to tell whether he should approach a chart from the vertical
scale and read the information from the hori-
I7.00O , - - -
zontal scale, or the reverse. It charts are always plotted with the independent varia- ble as the horizontal scale, there need be no question in the reader's mind as to how he should interpret the chart. The rule for scale arrangement is not always followed, and a few examples are shown here to indicate the difficulty of interpretation which the reader may have just because a rather simple prin- ciple of curve plotting has been neglected, ^l^o' ,i0r.UIr,,t!^0rw In Fig. 81 the depth of the water has
rcrici per v/ u Die v/ciiii~
meter of Hudson River been plotted downward from the top of the
Water at New York at cnart so that the reader may get the impres- Different Depths below . „ -, ,.» p ..
the Surface ' Slon °* measurements taken at different dis-
tances below the surface of the water. In
making the tests which are represented in Fig. 81, different depths below the surfaces were selected and the bacteria determined from the water samples taken at these depths. The depth is here the in- dependent variable, and bacteria per cubic centimeter the dependent variable. The decision as to which is the independent variable and which is the dependent variable rests entirely on how the problem is approached. Numerous samples could have been taken at different depths, and then a curve plotted to determine the depth at which certain numbers of bacteria per cubic centimeter were found. In
i sston
86 GRAPHIC METHODS
such a case, bacteria per cubic centimeter would be the independent variable and depth would be the dependent variable. This sort of problem may be attacked from either one standpoint or the other, and it is just a question of convenience as to which method is used and which variable is made the independent variable. Though the problem can be stated in such manner that either one variable or the other can be made the independent variable, after the statement has been made the chart should be consistently drawn so that the inde- pendent variable will be used as the horizontal scale and the dependent variable as the vertical scale.
As Fig. 81 is shown it is necessary for the person interpreting the chart to select from the vertical scale some number of feet below the surface and then read the number of bacteria per cubic centi- meter by the horizontal distance to the right. It is only after some little puzzling that the reader will notice that the scales for the variables have been reversed and that the chart has been practically turned on its side. How this chart would appear if the horizontal scale were used for the independent variable may be judged by turning the book and looking at Fig. 81 from the left-hand side of the page. Though it is easy to see why the person making Fig. 81 happened to arrange the chart in the manner shown with the variables reversed, the gain due to showing depth below the surface in the vertical direc- tion does not make up for the possibility of misinterpretation which results because of the neglect to follow standard practice.
In Fig. 82 we again have depth plotted downward from the top of the chart. . As we wish to determine the velocity of the stream at different depths of water, depth is the independent variable and velocity is the dependent variable. The arrangement of Fig. 82 is not as objectionable as Fig. 81, for the upper half of the illustration shows quite clearly in pictorial form that the subject under considera- tion is a stream having a channel shaped as shown, with widths and depths as indicated by the two scales. In the bottom portion of the diagram the scale of depths downward relates very definitely to the upper portion of the illustration so that the reader cannot easily go astray. Notice that the curves for the velocity of the water are each plotted on a separate vertical line which serves as zero line. The curves for velocity begin at various points depending upon the thick- ness of the ice, as will be seen from the upper portion of the chart. There is, of course, no velocity in that portion of the stream which
CURVE PLOTTING
87
Distances in feet
40 50
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VERTICAL VELOCITY CURVES Note Numbers at totf of curves indicate measuring points Numbers at bottom of curves indicate mean velocity in toe vertical |
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Engineering News
Fig. 82. The Velocity of Water in Different Portions of a Stream Flowing under Ice
The horizontal scale at the top of the illustration shows points where velocity measurements were made through holes in the ice. Velocities at different depths are indicated by the curves in the lower half of the chart, each curve being plotted to the right of a vertical zero line which corresponds with some hole in the ice. Lines are drawn in the upper portion of the chart showing different points in the stream where velocities are the same
is frozen. The velocity curves end abruptly at the bottom of the stream. It will be seen by reading velocities horizontally from the different zero lines from which the curves are plotted that the velocities are considerably greater in the center of the stream than they are near the banks or the bottom. This is natural, as the friction of the earth bottom and sides, as well as the friction of the ice at the top, causes the water to be retarded and the velocity lessened. In the upper portion of the illustration lines are drawn through all those points in the stream cross-section which have the same velocities. The lines are similar to the well-known isothermal lines on a weather map show-
88
GRAPHIC METHODS
ing where the temperatures are the same. From these lines it can be seen instantly that the highest velocity is at the center of the stream, as far away as possible from retarding influences. Velocities gradually grow less as the sides, the bottom, or the ice at the top are approached.
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.50 3.OO .90 4.00 .90 5.0O JO
RELATIVE VALUE IN DOLLARS
Courtesy of Data, Chicago
Fig. 83. Relative Value of Different Coals as Compared to Anthracite Coal
The price of anthracite coal is here the "independent variable" since it is the standard or measure by which the other variable is judged. The price of anthracite coal should have been made the horizontal scale of the chart. See Fig. 84
Fig. 82 is an interesting piece of work and the method used in charting is justifiable, even though in this case, as in the preceding, the independent variable is plotted downward and the dependent variable is plotted horizontally.
2 34 5 6 T G 9
Price of Anthracite Coal — Dollars
10
it
Fig. 84. Relative Value of Different Coals as Compared to Anthracite Coai
With the arrangement shown here the curve lines for different coals appear in their correct position. Illinois coal is at the bottom instead of at the top. The heavy line here drawn for anthracite proves at a glance which fuels are better and which poorer than anthracite
CURVE PLOTTING 89
Fig. 83 is intended as a comparison between different kinds of coal from the standpoint of actual heating value. At the first glance at this chart the reader sees that the line for Illinois coal is above the other lines, and he is apt to draw the conclusion that Illinois coal is better than anthracite, coke, or Pocahontas coal. It is only after some puzzling over the chart that one notices that the whole chart has been drawn in reversed order. We are considering what the relative values of other coals may be if we know the value of anthracite coal. The whole scheme of reasoning begins with the "price of an- thracite coal." The "price of anthracite coal" is the independent variable and should be plotted horizontally, with the "relative value in dollars" plotted as the vertical scale. The reader may get a correct impression of the chart in Fig. 83 if he will turn over the page and read the chart by holding the page up to the light in such manner that the zeros of the two scales appear at the lower left-hand corner. When this is done, it will be seen that the relative value of Pocahontas coal exceeds each of the other fuels mentioned and that Illinois coal comes not at the top of the list, but at the bottom of the list in so far as fuel value is concerned.
Fig. 84 has been drawn with the "price of anthracite coal" as the horizontal scale, where it belongs because it is the independent vari- able. The lines for different fuels now appear in their correct order, and the reader sees at a glance that Pocahontas coal has more fuel value than anthracite coal. Notice that a heavy line has been used for the curve line drawn for anthracite coal. As this line is the standard by which the values are compared, it seems best to give it prominence on the chart. The position of other curve lines above or below this line shows instantly whether the fuels are better or worse than anthra- cite in relative value.
In Fig. 85 an effort has been made to show detail time-studies by the use of curves. There is an error here, however, in that the curve has been arranged in such manner that the independent variable is drawn vertically and the information desired as "time in seconds" must be read off from the horizontal scale. The reader wishes to know how many seconds are required for any one step or any series of steps in the whole work. The chart can be interpreted in the accus- tomed way if the page is turned over, and the diagram read by hold- ing the page in such manner that the zero on the scale of "time in seconds" appears at the lower left-hand corner of the chart when the
90
GRAPHIC METHODS
page is held up toward a light. The curve for operator No. 1 then appears below the curve for operator No. 2 and the chart shows cor- rectly the relative merits of the two operators. Fig. 86 is a re<
drawing of the data shown in Fig. 85'. Here the curves for the two operators appear in their cor- rect relative position, and it is seen at once that operator No. 1 is the more rapid worker, since he uses less time. With the independent v a r i - able made the hori- zontal scale, a chart can be interpreted quickly. If the de- pendent variable is used as the horizon- tal scale the reader is likely to draw a con- clusion the reverse of that the chart was intended to show.
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ations |
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label with — t i-~ giue :::j|:: / :^:::ji::::: Brings • --i £- brush to . --^- f label ?" r 7 wipes ::::L";!.: brush on *'» '- glue pot •-- sj!»"- - Reaches — ^ ! - — - - - — 1 for brush THj' ' Reaches '.it "- for label 1* 1 O 5 1O 15 20 2 Time in s |
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Fig. 85. Record of a Detailed Time-Suiuy of Two Operators Labeling Packages
We are here studying the time for different operations. The names of the operations constitute the independent variable while time is the dependent variable. The chart reverses the proper arrangement of scales and causes the curve for operator No. 1 to appear improperly above the curve for operator No. 2. Compare Fig. 86
Fig. 87 shows the data of Fig. 85 and Fig. 86 redrawn in the form of horizontal bars such as were seen in Chapter I and Chapter II. The relative times for the various operations are shown much more clearly by the horizontal bars than by the curves used in Fig. 85 and Fig. 86. The time in seconds required for each operation is given by detailed dimension lines above each section in the horizontal bar, and the comparative total time of the two different men can also be grasped instantly. The total time in seconds for the whole series of operations is shown by an over-all dimension line above each of the bars, and the reader, if he wishes, may make an accurate com- parison between operator No. 1 and operator No. 2 by using a numerical ratio. A chart of this kind can be very quickly made for ordinary office purposes if the horizontal bars are drawn on co-ordinate paper
CURVE PLOTTING
and the different areas made to stand out in contrast by the use of colored crayons. The actual differ- ences between the two operators would show more clearly, operation by operation, if lines were used join- ing the ends of the components in the two bars in a manner similar to that seen in Fig. 32. The data of Fig. 85 do not lend themselves well to presentation in curve form. In Fig. 85 and in Fig. 86 .the shape of the curves means nothing, since there is no numerical scale relating to the names of operations. Fig. 87 shows a much more satisfactory method for portraying the data.
In Fig. 88 we have an applica- tion of curves to advertising in pop- ular magazines. The curves de- pict the circulation of a newspaper,
Operations
Fig. 86. Record of a Detailed Time- Study of Two Operators Labeling Packages
Here the scales have been properly arranged and the two curves appear in their correct relative position on the chart. These data, however, are not well suited for curve presentation and they are more clearly brought out by the bar method used in Fig. 87
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Fig. 87. Record of a Detailed Time-Study of Two Operators Labeling Packages
By this method of presentation the reader may see clearly the relative 'ength of time for different operations as well as the comparison of total time taken by the two workers. Dimension marks and figures show conveniently the actual number of seconds required. The different operations have here been given numbers instead of names. The scale to which the chart is drawn is named
GRAPHIC METHODS
1905 1906
1907
1908
1909
1911
1913
150.000
150.000
The Plain Dealer'* circulation is by far the largest net paid morning and Sunday newspaper circulation between New York and Chicago: and in Cleveland and the retail trading area tributary to Cleveland — a radius of 75 miles at most- the Plain Dealer's net paid circulation is double the net paid circulation of any other Cleveland morning or Sunday newspaper. Every record bearing directly or indirectly upon figures above published or upon any other detail of Plain Dealer Circulation or Advertising is open to the most complete and searching investigation to anyone at any time and without further notice.
70000
EXPLANATION OF CHART
This chart shows the Cleveland Plain Dealer's circulation by months from February 1905 to June 1913. Each line up and down represents a month, each line across a thousand copies sold. Note how the top line indicating Sunday sales, and the lower line indi- cating daily sales move steadily upward. Observe the steady, healthy, sturdy growth from the first month to the last — no sudden mushroom-like gains, no unexplained losses, but a consistently increasing total affected only by the changing seasons and the bus- iness health of the whole country.
Cleveland Plain Dealer
Fig. 88. The Use of Curves in an Advertisement to Show the Growth in Circulation
of a Newspaper
It is unfortunate that this illustration was not made so as to show the zero line of the vertical scale. In advertising work it usually pays to avoid anything which might seem like exaggeration. Omitting the zero line makes the growth seem more rapid than it would if the zero line were included in a chart drawn to scale. Though the drafting on this chart might have been better, the application of curves to advertising deserves commendation
with the object of convincing advertising managers that this par- ticular newspaper is a desirable one in which to place advertisements because of the rapidly and steadily increasing circulation. It is sur- prising that circulation managers of newspapers have not more often used charts to show circulation, instead of the wordy typed state- ments so frequently seen claiming great growths in circulation over a period of months or years. Though Fig. 88 shows a commendable progressiveness on the part of this particular newspaper in adapting curves to circulation statements, it seems necessary to point out the fact that the chart may cause distrust in the minds of some readers. There is a chance that the man who has advertising to place may feel
CURVE PLOTTING
93
that the chart has been drawn in too optimistic a manner because it does not show zero at the bottom of the scale. It would have given a much more conservative impression if the excellent record of circu- lation growth had been plotted in curves having the zero line shown at the bottom of the chart, so that the relative growth could be accu- rately judged visually.
In Fig. 89 a large amount of information has been condensed into a small amount of space, yet the chart is fairly clear and easy of in- terpretation. Several ingenious combinations have been included as, for instance, the arrows that show the prevailing direction of the wind each day. The chart gives unusually complete information in a most convenient form for any ventilating engineer or power-plant manager who wishes to keep careful track of his cost of coal in different months of the year as dependent upon weather conditions.
DAY OF MONTH » 10 11 18 13 1< IS 16 17 18 19 80 21 82 83 84 25 26 «T 88 >» »0> »j
SRSCKRCPCSSCPCC PC.S PC /?/?/? PC PCSSSnS
Heating and Ventilating Magazine
Fig. 89. Record of the Weather in New York City for December, 1912
The heavy line indicates temperature in degrees Fahrenheit The light solid line shows wind velocity in miles per hour
The dotted line depicts relative humidity in percentage from readings taken at 8 a.m. and 8 p.m. Arrows portray the prevailing direction of the wind
Initials at the base of the chart show weather conditions as follows: S, clear; PC, partly cloudy; C, Cloudy; R, rain; Sn, snow
Fig. 90 shows an example of double co-ordinate ruling on the same sheet of paper. The scheme of using double co-ordinates is not very well known even to engineers and it seems worthy of atten- tion here. The solid line plotted in the general form of a curve with a flat space for each month shows the total water consumption in millions of gallons per day. The total water consumption is read from the scale of the horizontal lines as for any curve plotted by rectangular co-ordinates. The slanting lines are drawn after the total
94 GRAPHIC METHODS
number of gallons used per day has been divided by the number of inhabitants in the district so as to obtain a figure for the average daily consumption of water per capita. As the population figure used depends upon census records it may be necessary to get the rate of growth in the population from records as much as ten years apart. In Fig. 90 it can be observed that the slanting lines showing the rate of growth of the city are straight lines, indicating probably that the census figures were used in the drawing of these lines because yearly figures could not be obtained. If yearly figures were obtainable the slanting lines could be extended year by year until they reached completely across the chart. The rate of growth in population deter- mines the angle of the slanting lines, the more rapid the growth the greater the angle of the lines.
The slanting lines are located on the page so that a curve can be read from either the horizontal lines or from the slanting lines. The method of locating the slanting lines can be worked out by anyone who will experiment a little in making a chart of this type. When the population is known and the total consumption is known, it is only a matter of division to determine the consumption per capita. After the slanting lines are once placed upon the chart, the curve can be read either from the horizontal lines showing the total consumption or from the slanting lines showing gallons per capita.
Taking the peak for February, 1912, we see that the total con-