28 STATISTICAL METHODS. 



o 57 -- r~^ 41 -O 77 -- \ ' 



n\n-p) 2 p 2 n\n-p)p y 



2 



2 / \y m 



The solution of the equations for c lt c 2 , and c 3 will be facili- 

 tated by finding, once for all, the logarithms of n, (n p), 



(n 2p), (np)p, and . 



(2). When n and p are both large and not nearly equal: 



(3). When n is small the unsimplified form of the equa- 

 tion must be used. 



|n means the products of all integers from 1 to n. The 

 series c lf c 2 , c 3 is not complete, but the values of c with higher 

 subscripts are so small that they may be neglected. 



Let Ip'p" be the difference measured m units of a between 

 the p'th and the p"th individual, then 



The foregoing method is that of Pearson (1902 k ) based 

 upon some considerations of Galton (1902). 



To find the best fitting normal frequency dis- 

 tribution when only a portion of an empirical 

 distribution is given. 



First apply the following parabola of the second order: 



