NATURE OF STATISTICAL KNOWLEDGE 81 



6. The degree of individual diversity comprised 

 in the group. This attribute, called the varia- 

 bility of the group, is again variously measured : 

 by standard deviations, coefficients of variation, 

 etc. 



c. The degree of symmetry of the distribution 

 of the individuals composing the group. This is 

 measured by the skewness or other related con- 

 stants. 



d. Various other attributes of distributions 

 might be here included, such as, for example, the 

 kurtosis, but for purposes of the present general 

 analysis this scarcely seems necessary. Though 

 some of these attributes involve very complex 

 mathematical expressions for their measurement, 

 the general fact remains clear that they are all 

 attributes of groups or masses which are described 

 by the statistical constants. 



One point here we must be quite clear about. 

 This is that the kind of knowledge discussed under 

 this heading 2 is just as definite and precise, and 

 involves as little approximation and indetermin- 

 ism, as does any piece of individualistic knowledge, 

 so long as we confine our attention solely to the par- 

 ticular group discussed in a particular single case. 

 We are accustomed to stating means, for example, 

 with probable errors. But this is only because it 

 is proposed to extend the conclusions beyond or 

 outside of the particular group and the particular 

 instance for which the mean was calculated. For 



