28 STATISTICAL METHODS. 



_ oc fa-p) 5 + p 5 ~r(n-pY-p* w_ 

 -^ -*nn- ' 



31m*-101raM-28 

 2/m 



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

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



tn 

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



i/m 



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



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

 tion must be used. 



X-- (1 + ^ + ^+03+ ...) 



ym 



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

 series c lt 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 in units of o 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: 



