VARIATION 



viations sometimes are plus and sometimes minus, and 

 consequently they may be termed fluctuating variations. 

 Pearson gives as a simple illustration of fluctuating 

 variation the number of ribs present in two sets of 

 beech-leaves, as shown below. These sets were taken 

 from two different trees, and each contains twenty-six 

 leaves. 



It will be seen that, while certain leaves might well 

 belong to either tree, as, for example, those with sixteen 

 ribs, the entire group of leaves from either tree is unlike 

 that of the other tree. In the first instance the number 

 of ribs fluctuates around eighteen as the commonest 

 kind ; in the second case, around fifteen. Such a differ- 

 ence could not easily be detected or expressed by any 

 other method than the statistical one. 



Again, in the case of forty-seven starfishes all of 

 which were collected from one locality the variation 

 in the number of rays proved to be, according to 

 Goldschmidt, an amount indicated graphically in 

 Figure 5, where the data are arranged in the form of 

 of a so-called frequency polygon or curve. 



From such a polygon certain constants may be com- 

 puted which conveniently express in a single number, 

 for purposes of abstract comparison, distinctions that 



