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APPENDIX 



SECTION III GRAPHIC REPRESENTATION OF 

 STATISTICS 



A mere tabulation of any considerable number of figures does not make 

 it possible, in general, for the mind to grasp the main facts which the 

 figures represent ; in fact, such a tabulation of, say a thousand figures, may 

 make no impression on the mind which is at all worth mentioning. By the 

 graphic method, however, the chief characteristics of a mass of figures are 

 presented to the eye by means of a picture or curve. The graph gives, 

 at a glance, important facts which may be overlooked, or which can be 

 obtained from the figures only by considerable labor. 



The use of graphic methods in statistics is very extensive, and has proved 

 to be of great service. In fact, everyone who has to deal with complicated 

 groups of figures comes to appreciate the graphic method, as it enables one 

 to perceive relations through the eye. 



It is the object of this section to show how graphs are formed from given 

 data. 



Frequency curves. Let us consider the graph of the following frequency 

 distribution, in which the first line of the table gives the marks of the 

 classes, and the second gives the number of variates in the classes : 



What we propose to do here is to present a significant picture of this 

 population. 



Draw two. lines, OX and OY, at right angles to each other (Fig. i). 

 These reference lines are called coordinate axes. The line OX is called 

 the ^--axis, and the line (9Fthe j-axis. The point (9, from which we meas- 

 ure, is called the origin, or zero point. Beginning at this point mark off 

 on the ;r-axis equal intervals upon a scale convenient to the problem at 

 hand. From the same zero point lay off equal intervals also on the j-axis. 

 These need not be on the same scale as those on the .r-axis, but should 

 be suited to best bring out the facts to be shown by the graph. Not all 

 graphs are drawn upon the same scale therefore, nor are the two axes of 

 the same graph alike as to spacing or scale. 



In the particular case in hand, let each interval along OX represent a 

 half inch. The question as to what each interval shall represent is a matter 

 of the scale used ; and the scale must be chosen to suit the particular data 

 in hand. Next, along OX lay off the class marks. Corresponding to each 

 class mark there is a frequency. From the various points on the ^r-axis 



1 This distribution is taken as a representative of any frequency distribution. It is not, 

 however, made up artificially, but actually represents the distribution of eight hundred ears 

 of corn with respect to length. 



