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 
the mean, M, = 2) where = indicates summation. 
For a series of groups of variates (classes), first multiply each class 
value (V) by the number of variates in the class or frequency (f) then 
summate and divide by n. Thus 
ne Ry 
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. 
Vv | f | pale The data are the same as in the 
| frequency table (Table II). 
TasLE II].—To Computrr THE MEAN 
ToraL YIELD or PLANT IN GRAMS 
0.5 A valuable short method of 
ae ty F920 computing the mean consists in the 
2.5 106 265.0 : 
3.5 109 381.5 use of an assumed mean which 
4.5 80 360.0 removes the necessity of multiply- 
5.5 42 231.0 ing the class values by their fre- 
6.5 7 45.5 quencies and hence greatly reduces 
7.9 2 15.0 ao . . 
Nee i ae the actual labor in dealing with 
‘ large numbers. For the same data 
= 400 = = 1383.0 the short method is shown in Table 
IV. The rule is as follows: To 
Ve 18 Bs 45g. 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 
“4007 — 0.0425 
M = 3.5 + (— 0.0425) = 3.458. 
Thus for the computation of the mean by the short method we have 
the formula 
Correction factor = w = - 
ST t( Vo 
M=G+w=G+ aut 
The mean is the best measure of type in organisms because it takes into 
account all the individuals measured. For this reason the swm of the 
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