40 



GENETICS IN RELATION TO AGRICULTURE 



The Mean, Calculation and Significance. To compute the mean of a 

 series of single variates summate the variates and divide by the number of 

 variates. Thus if x. = any variate and n = the number of variates, then 



S (re) 

 the mean, M t = where S indicates summation. 



n 



For a series of groups of variates (classes), first multiply each class 

 value (7) by the number of variates in the class or frequency (/) then 

 summate and divide by n. Thus 



TABLE III. To COMPUTE THE MEAN 

 TOTAL YIELD OF PLANT IN GRAMS 



n 



In the calculation of this and other constants it is important that the 



work be indicated in a systematic 

 manner. The form as indicated 

 in Table III is usually preferred. 

 The data are the same as in the 

 frequency table (Table II). 



A valuable short method of 

 computing the mean consists in the 

 use of an assumed mean which 

 removes the necessity of multiply- 

 ing the class values by their fre- 

 quencies and hence greatly reduces 

 the actual labor in dealing with 

 large numbers. For the same data 

 the short method is shown in Table 

 IV. The rule is as follows: To 

 compute the mean of a series of 

 classes of variates, write the fre- 

 quency of each class in a column on the right of the class values, then 

 the deviation of each class from an assumed mean, and lastly the product 

 of each deviation by its corresponding frequency. Summate the devia- 

 tion-by-frequency products, divide by n, and add algebraically the correc- 

 tion factor thus obtained to the assumed mean (in this case, 3.5). 



-17 



M = 



1383 

 400 



= 3.458. 



Correction factor = 



w = 



400 



= -0.0425 



M = 3.5 + (- 0.0425) = 3.458. 



Thus for the computation of the mean by the short method we have 

 the formula 



M = 



= G + 



n 



i !T/ie mean is the best measure of type in organisms because it takes into 

 account all the individuals measured. For this reason the sum of the 



