THE CLASSES OF FREQUENCY POLYGONS. 



where the value of z corresponding to % is got from Table II I, 

 or from the formula 



The ratio of actual to probable discrepancy is next to be 

 calculated for each class. The probable limit (P.L.) of the 

 ratios varies with the number (A) of ratios found, according 

 to the following table : 



The foregoing method is from Sheppard (1898). 



The probable range of abscissae (2x t ) of a normal dis- 

 tribution, or that beyond which the theoretical frequency (y) 

 is less than 1, varies with the number of variates (n) as well 

 as with a, in accordance with the following formula derived 



by the transposition of y= 



by putting y=l: 



2^=2*7 



Example. For the ventricosity of 1000 shells of Lit- 

 tornea littorea from Tenby, Wales, A = 90.964% and a= 

 2.3775%. What is the probable range of ventricosity 

 expressed in per cent.? 



2zj=2X2.3775|/ .46051 7 X log x-^; 



1000 



= 15.2. 



'2.506628X2.3775 

 The observed range was 15 (Duncker, '98). See also the 



criterion of Chauvenet (' 

 variates (page 12). 



for the rejection of extreme 



THE NORMAL CURVE OF FREQUENCY AS A BINOMIAL 

 CURVE. 



The normal curve may also be expressed by the binomial 

 formula (pXgH where p=i, #=i, and A is the number of 



