CHAPTER III 
FREQUENCY FUNCTIONS OF ONE VARIABLE 
15. Introduction. In Chapter I we have discussed very 
briefly three different methods of describing frequency 
distributions of one variable—the purely graphic method, 
the method of averages and measures of dispersion, and 
the method of theoretical frequency functions or curves. 
The weakness and inadequacy of the purely graphic meth- 
od lies in the fact that it fails to give a numerical descrip- 
tion of the distribution. While the method of averages 
and measures of dispersion gives a numerical description 
in the form of a summary characterization which is likely 
to be useful for many statistical purposes, particularly for 
purposes of comparison, the method is inadequate for 
some purposes because (1) it does not give a character- 
ization of the distribution in the neighborhood of each 
point x or in each small interval x to x~+dx of the variable, 
(2) it does not give a functional relation between the 
values of the variable x and the corresponding frequen- 
cies. 
To give a description of the distribution at each small 
interval x to x-+dx and to give a functional relation be- 
tween the variable x and the frequency or probability we 
require a third method, which may be described as the 
“analytical method of describing frequency distribu- 
tions.” This method uses theoretical frequency functions. 
That is, in this method of description we attempt to char- 
acterize the given observed frequency distribution by ap-