154 THE FIRST PRINCIPLES OF HEREDITY 



Some examples of the Index of Variability, according to 

 Galton, are : 



Man. Woman. 



Per Cent. Per Cent. 



Stature . . . . . . 2*50 . . 2*52 



Span of arms ,. .. 2*92 .. 2*92 



Weight 6-89 .. 8-89 



We see that weight is twice as variable as either stature or 

 span of arm, and is more variable in woman than in man. 



There are other methods of determining the variability 

 of a characteristic, which we cannot deal with here in 

 detail. One largely used by Karl Pearson is what has been 

 caUed the " Standard Deviation." Under " Deviation " 

 we understand the amount by which any individual differs 

 in a given character from the " type." The type may be 

 measured by the mode or the mean ; usually we take 

 deviations from the mean. For instance, if we have the 

 following series, where the frequencies represent the number 

 of leaves of a beech-tree showing a given number of veins : 



^, , , . ^ ^ r Mean number of 



IS umber of vems .. 15 16 17 18 19 20 | veins i7-i;=tvpe 



Frequencies . . i 4 7 9 4 i I Total number of 



^ -1- / :? T ^ mdividuals, 26, 



we get the deviation of each individual group by finding 

 the difference between its actual number of veins and the 

 mean number of veins of the whole series. The deviation for 

 the first group of individuals as given above is 17-5 - 15 =2-5, 

 that of the second 17-5 — 16 = 1-5, ^tc. We find the 

 standard deviation by multiplying the frequency of each 

 individual group by the square of its deviation from the 

 mean, adding all these products together, and dividing the 

 whole by the total number of individuals. The square root 

 of this total gives the standard deviation, or o-. In the 

 above instance we get 



•=n/ 



I X (2-5)2 + 4 X (i-sf-^ + y X ("5)^ + 9 X (•5)- + 4 X (i'5)^+ i x (2'5)^_^.^- 



_i 15. 



26 



