Appendix E 



407 



above is a long and laborious process, in which the liability to 

 error is great. A much shorter, simpler, and at the same time 

 more accurate method has been devised. This consists in mak- 

 ing a guess at the mean (designated by G), and indicating the 

 difference between each class value and this guess in a column 

 marked (F-G). Each of these differences is then multiplied by 

 the corresponding frequency and the algebraic sum of the total 

 negative differences and the total positive differences is found. 

 This is the total amount by which our guess missed the mean 

 for the whole population, and hence we should divide this 

 quantity by n to find the average amount by which we missed 

 our guess. If this amount, which is called the "correction," is 

 positive, then our guess has been too low by that amount, and it 

 is to be added to the guess. On the other hand, if it is negative, 

 then our guess has been too high, and it is to be diminished by 

 this amount. The formula for this procedure is : 



x ft ~\r /~i\ 



correction (c) = (Algebraic) 4 ^ < 



n 



M = G c. 



V 



5-14 

 15-24 

 25-34 

 35-44 

 45-54 

 55-64 

 65-74 

 75-84 

 85-94 



- 780 

 500 



= - 1.56 



c 2 = 2.4336 



