46 GENETICS 



and consequently the average of the entire forty- 

 seven amounts to .52 of a ray. In another collec- 

 tion of starfishes where either more seven-rayed or 

 two-rayed specimens might be present, the average 

 deviation would probably be greater. 



By computing the average deviation, therefore, 

 and using it as the criterion of variation, a compar- 

 ison of the variability of organisms that have been 

 taken from different localities or subjected to differ- 

 ent conditions can be definitely expressed. 



A measure of variability more commonly in use 

 by biometricians, since for mathematical reasons it 

 is more accurate, is the standard deviation. This is 

 the square root of the sum of all the deviations 

 squared and their frequencies divided by n, accord- 

 ing to the formula i v / 2 n 



/-*\? 'J) 



n 



in which x represents the deviation of each class from 

 the arithmetical mean ; /, the number of individuals 

 in each separate class ; 2, the sum of the classes ; and 

 n, the total number of individuals. 1 



In the present instance the standard deviation is 

 .846, an arbitrary number that has valuable sig- 

 nificance only when brought into comparison with 

 standard deviations similarly derived from other 

 groups of starfishes. 



Such a variation polygon as the above expresses 

 the law that the farther any single group is from the 



1 For directions explaining the use of such formulas see Davenport's 

 " Statistical Methods." 



