VARIATION 45 



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 25, where the data are arranged in the form 

 of a so-called frequency polygon or curve. 



From such a polygon certain constants may be 

 computed which conveniently express in a single 

 number, for purposes of abstract comparison, dis- 

 tinctions that otherwise could be handled only in 

 the most indefinite way. 



Thus in this instance the arithmetical mean, ex- 

 pressed by the hypothetical number 4.915, a number 

 which of course does not actually occur in nature, 

 is simply the average number of rays in forty-seven 

 starfishes selected at random. 



The mode which represents the group containing 

 the largest number of individuals of a kind, namely, 

 thirty out of forty-seven, is five in this particular 

 polygon. 



The average deviation, which is an index of the 

 amount of variation going on among the starfishes in 

 question, is .52. In other words, .52 is the average 

 amount that each individual starfish deviates from 

 the arithmetical mean of 4.915. Although the one 

 seven-rayed starfish which happens to be in the 

 lot varies from the standard of 4.915 to the extent 

 of 2.085 (7 — 4.915) rays, there are thirty five-rayed 

 starfishes which vary only .085 (5 — 4.915) of a ray, 



