THE CLASSES OF FREQUENCY POLYGONS. 2? 



The extreme values are not calculated for the relations 

 indicated by the formula do not hold well there where the 

 frequencies are small and the proportionate values of y are 

 changing rapidly for small changes of x For the five values 

 considered the actual discrepancy is less than the probable 

 discrepancy in three cases and less than the probable limit 

 in all. 



To find the average difference between the 

 ptli and the (p + l)th individual in any seriation 

 (Galtoii's difference problem). Let x p be the aver- 

 age interval between the pth and (p+l)th individual; n the 

 total number of variates; and a their standard deviation. 



Then, (1) when n is large and p small: 



p p e~ p 

 ~ 



m can be found from Table IV by the use of the formula 



where the value of m sought is the argument correspond- 

 ing to the tabular entry ( -- -\ . 



. 833 



_. .. 



n(n-p)p n 2 y m n 3 \y m 



2 ) \y m 



