34 GENETICS IN RELATION TO AGRICULTURE 
principle has been expressed by King in terms, which fit well the imaginary 
case under discussion, as follows: ‘‘A moderately large number of items 
chosen at random from among a very. large group are almost sure, on 
the average, to have the characteristics of the large group.”” It must not 
be inferred that any partial group of individuals no matter how large, 
will give exactly the same results as would be obtained by the use of the 
entire mass. But the averages will be close and the probability of in- 
accuracy due to accidental error diminishes as the numbers increase 
because individual errors tend in the long run to counteract each other. 
Law of Deviations from the Average.—lIf, now, one lot of 500 beans 
be measured to the nearest millimeter and then arranged in columns from 
left to right according to width beginning with the narrowest beans, the 
result will be very similar to Fig. 14. It will be noticed first that the 
middle classes contain the most beans while the classes on the extreme 
left and right are very small. The black vertical line M indicates the 
average width or mean of all the beans and the column with the most 
beans in it represents the most frequent width of beans and is called 
the mode. The columns nearest the average value on either side contain 
the most beans and the further the column is from the average the fewer 
the beans in it. Thus we see that the majority of the beans show 
only slight deviations from the average while a few exhibit wide deviations 
therefrom. Statistical study has proved that it is a general rule with 
fluctuations that individuals showing extreme deviations in either 
direction for a given character are comparatively rare, while individuals 
exhibiting smaller deviations, and hence occupying a position inter- 
mediate between the two extremes are especially frequent. In other 
words, continuous variations usually appear in frequencies such that, 
if we represent these frequencies graphically, we obtain a polygon which 
resembles more or less the normal variability curve. Such a polygon 
is produced by connecting the ends of the columns in Fig. 14. 
The Normal Curve and its Significance-—The normal variability 
curve is a theoretical curve which pictures the result of expanding the 
binomial (a+ b)" when a=6=1 and n is assumed to be indefinitely 
great. By the binomial theorem 
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