COKRELATED VARIABILITY. 33 



A brief method of finding p is given by Duncker as follows: 



i -, p _ v .-/. ojXdev. .yx/) , 1 



p is composed of two factors: - - and - 



n cr,( 



To find -v~~/.gxclev. y X /), 



M 



Separate the deviation from the mean of each class into its 

 integral and its fractional parts ; the fractional parts for all 

 classes below the mean will be equal to the fractional part of 

 the mean ; of all classes above the mean, to the complement 

 of that number. Designate the integral parts of the variants 

 of the subject by X^; of the relatives by X^, and the frac- 

 tional complement parts of the means of subject or relative by 

 1, c 2 . Let /equal the frequency of any deviation in the com- 

 bination X.X 2 , as shown in the correlation table. Draw rect- 

 angular co-ordinates as shown on page 34 through the zero- 

 point of the correlation table. Number the N. W. quadrant, 

 which should include negative deviations of both subject and 

 relative variants, I ; the N. E. quadrant, II ; the S. "W. 

 quadrant containing solely positive deviations III ; and the 

 S. E. quadrant, IV. Then if 2i, 2 U , etc., indicate a summa- 

 tion for the quadrant I, II, etc., and having regard to signs : 



n n 



The numerator of this fraction consists entirely of whole 

 numbers ; of them the following are on their own account 



positive: 2 I (fX l XJ, ^nifX.X^, 2i(f), 2 n (fX,), 

 negative : 



Rule : (1) Find products of integral parts of deviations of 

 both subject and relative and the combination frequency, for 

 all four quadrants, and take their sum. 



(2) Subtract successively the sum. of the products of the sub- 

 ject deviations in the first quadrant multiplied by the fre- 

 quency, and the sum of the products of the relative deviations 



