64 GENETICS AND EUGENICS 



state whether the variation is symmetrical about the mode, 

 how extensive is its range, and whether the majority of the 

 variates cluster closely about the mode or are widely scat- 

 tered. To express these various features of the variation, 

 special statistical coefficients have been devised. It will 

 suffice for our purposes to discuss only the more important 

 of these. 



1 . The mean, or average, is in a case of symmetrical varia- 

 tion, identical with the mode. Thus the average height of 

 the thousand Harvard students (Table 1) is close to 174 mm., 

 the mode. But their average weight lies outside and above 

 the modal weight class, because their variation in weight 

 is decidedly skew, more men exceeding 66 kilos in weight 

 than fall below that weight. To find the average, multiply 

 the value of each class by the number of individuals contain- 

 ed in it, add the products, and divide by the entire number of 

 individuals. 



2. Average Deviation and Standard Deviation. Two sets of 

 variates having the same mode and mean may nevertheless 

 differ widely in their variability, one being more scattered 

 than the other. 



To express the greater spread of one curve as compared 

 with another, the average deviation, may be employed. That 

 is, we may estimate how far, on the average, an individual 

 taken at random differs from the mean. This is computed as 

 follows : Find the deviation of each class from the mean, multi- 

 ply this by the frequency of that class, add the products, and 

 divide by the entire number of variates. The quotient is the 



X D f . 



average deviation. Formula A D = in which S signi- 

 fies that the sum is to be taken of the products indicated, 

 D means the deviation of each class value from the mean of 

 all variates, / means the frequency (number of individuals) 

 of each class, and n means the total number of variates 

 (individuals). This measure of variability is improved, 

 mathematicians tell us, by the method of least squares, i. e., 

 by squaring the deviation of each class, and extracting the 



