BIOMETRICS 



157 



height of all the sons together is 65-5 inches. We now 

 construct the arrays of sons for each class of fathers of 

 all given heights from 62 inches up to 76 inches. For 

 instance, the array of sons for fathers of 63 inches is : 



Heierhts of sons "^ ^ ^ ^ ^^ ^ ^o c /"Mean height of 



il inches r^ 64 65 66 67 68 69 70 71 7^\^o^^,^^ilz\v^^. 



Frequency 



4 10 16 9 3 3 I 



/Total number 

 i. of sons, 51. 



Arranging all these arrays one underneath the other, we 

 get a " Correlation Table," as given in Fig. 71. Here we 

 see the different classes of fathers arranged in the first 

 vertical column, and the arrays of sons for each class of 

 fathers in the horizontal lines. Contrariwise, the arrays 

 of fathers belonging to each class of sons having the same 

 height are represented in the vertical columns, the different 

 classes of sons being arranged in the first horizontal line. 

 The mean height of each array of sons we find in the last 

 right-hand column, while the mean height of the arrays of 

 fathers, each belonging to a given class of sons, is found 

 in the lowest bottom line. The mean of all the arrays 

 together is given in the right-hand corner : it is 69 inches. 

 This is the average or mean height of the whole population, 

 and is designated by P. 



If we now compare the height of each class of fathers 

 with the mean height of their sons — i.e., the mean of the 

 array of sons belonging to each class of fathers — we can 

 formulate a definite law, viz. : 



