SERIATIOK AND PLOTTING OF DATA. 15 



figures. The determination of which it is the error should 

 be carried out to the same number of places as the probable 

 error and no more. 



The probable difference between two averages (A 1 and 

 A 2 ) of which the probable errors (E l and E 2 ) are known is 

 the square root of the sum of the squared probable errors, or 

 (Pearson, '02): 



Probable Difference ot A,-A 2 is \/E* + E*. 



The probable error of the menu is given by the 

 formula 



+ 0.fi74Sv stal ^ rd action [see below] = +a<t74fi * 

 A/number of variates Vn 



It will be seen that the probable error is less, that is, that 

 the result is more accurate, the greater the number of variates 

 measured, but the accuracy does not increase in the same ratio 

 as the number of individuals measured, but as the square root 

 of the number. The probable error of the mean decreases as 

 the standard deviation decreases. 



The_ probable error of the median is .84535(7 

 -7-Vn (Sheppard, '98). 



The geometric mean of a series of values (v) is the 

 number corresponding to the average of the logarithms of 

 the values. Thus, 



The index of the variability, a, of the variates when 

 they group themselves about one mode is found by adding 

 the products of the squared deviation-from-the-mean of each 

 class multiplied by its frequency, dividing by the total 

 number of variates, and extracting the square root of the 

 quotient, thus: 



sum of [(deviation of class from mean) 2 



X frequency of class] 



number of variates 



whore A is the number of units in the class range, frequently 

 unity. 



