VARIATION 27 



simply the average number of rays in forty-seven star- 

 fishes 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. If all individuals fell within the mode there 

 would be no variation and the polygon would become a 

 vertical line. 



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 c(5 4.915) of a ray, and conse- 

 quently the average of the entire forty-seven amounts 

 to .52 of a ray. In another collection 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 comparison 

 of the variability of organisms that have been taken 

 from different localities or subjected to different condi- 

 tions can be definitely expressed. 



A measure of variability more commonly in use by 

 biometricians, because of its relation to probable error, 

 is the standard deviation. This is the square root 

 of the sum of all the deviations squared and their 



