688 



APPENDIX 



.r-axis, and the two end ordinates (in this case ordinates at 4 and 10) equal 

 to the sum of the areas of these rectangles. The area under the curve 

 then represents the total population. This is an important point, because 

 it presents to the eye how much of the population is included between any 

 two measurements. For instance, at a glance you could estimate approxi- 

 mately the portion of the population discussed in Fig. i, whose measure- 

 ments are between 5 and 8. The use of the area under the frequency curve 

 will be found helpful in our discussion of "probable error." 



Choice of scale. In drawing a graph the question always arises as to 

 what scale shall be used in plotting, but unfortunately no definite rule can 

 be laid down. It may, however, prove useful to call attention to a few 

 points. First, we should choose such a scale that we can plot all the points 

 on one page of the paper used; for it is a great advantage to have the 

 whole graph on one paper, thus making it visible to the eye in its entirety. 

 Second, if the point involved in the investigation is a question of rate of 

 increase or decrease, we should select such a scale as to make the curve 

 reasonably steep. Frequency curves are used a great deal in the study of the 

 social sciences, as well as in natural science. For instance, the sociologist 

 presents the population of a city or country for successive years by using 

 years as the marks of classes, laying these off along the .r-axis, and 

 the population for these years as ordinates. 



Negative values easily represented graphically. We often desire to plot 

 negative values as well as positive values, and this is easily accomplished 

 by a slight extension of what has already been done in connection with 

 Fig. i. With the data exhibited in Fig. I it might have been found con- 

 venient to use the mean as the origin and to plot the frequency with respect 

 to deviations from the mean. Since the mean is in this case 7.25, we have 

 the following set of deviations and corresponding frequencies to plot : 



We should now lay off the positive deviations toward the right from the 

 origin O (Fig. 2) and the negative deviations toward the left from O. The 

 frequencies should, of course, be plotted upward from X'X, just as in Fig. i. 

 The result of plotting this frequency distribution is shown in Fig. 2. This 

 should bring home to the reader, who is not very familiar with the use of 

 negative numbers, the fact that negative numbers may be just as u real " 

 and useful as positive numbers. 



The frequency polygon of Fig. 2 does not differ in form from that of 

 Fig. I. It is only differently related to the lines of reference OX and OY. 



Graphical meaning of median, mean, and mode. If in Fig. i we select on 

 the curve a point whose ordinate divides the area under the curve into two 

 equal parts, the abscissa of this point is the median of the population. The 



