44 GENETICS IN RELATION TO AGRICULTURE 
consideration may be widely different in value. It may even happen 
that the characters to be compared were measured in different units, as 
inches and grams. Hence it is desirable to have an expression of vari- 
ability in relation to the mean. Such an expression is the coefficient of 
variability which is the ratio of the mean to the standard deviation ex- 
pressed in per cent. The formula for the coefficient of variability is 
1000 
MM 
In the case of total yield of plant in grams for Sixty Day oats in 1910 
substituting the values which have been calculated we have 
_ 100 X 1.323 
~ 3.458 
The coefficients for the other two years are: 1909, 55.779 and 1912, 
42.113. Thus the amount of relative variation in yield was much 
greater in 1909 than in 1912 and although the standard deviation for 
1910 is only a third as large as that for 1912, yet the amount of relative 
variation is almost as great. A measure of absolute variation is very 
useful but a relative measure is essential, especially when comparing 
different kinds of material such as total yield in grams and number of 
culms or milk production and butter fat production. 
The Theory of Error.—It has been said that the frequency curves of 
many biological measurements follow the curve made by plotting the points 
given by the expanded binomial (a + 6)” wherea = b = 1. The reasons 
why this should be true are not difficult to see. They depend upon the 
laws of probability or chance that have been generalized into the theory 
of error. The chance of an event happening in an infinite number of 
trials is expressed by a fraction of which the numerator is the number 
of ways it may occur and the denominator is the total number of ways 
it may occur or fail to occur, if each is equally likely. Thus in tossing a 
coin a great number of times, the chances that it falls heads is one-half. 
Further, the probability that all of a sét of independent events will 
occur on a single occasion in which all of them are in question is the product 
of the probabilities of each event. Hence, the probability that two coins 
tossed together will fall heads is 14 K 19 = 4. 
Now suppose four coins are tossed at random; what is the probability 
that any particular number m of them will be heads and the rest tails? 
The number m may be 0, 1, 2, 3, and 4, and the probabilities are as 
follows: 
C= 
Cc = 38.259. 
0 head and 4 tails = 1(15)4 
1 head and 3 tails = 4(1¢)1 
2 heads and 2 tails = 6(1)4 
3 heads and 1 tail = 4(19) 
4 heads and 0 tail = 1(14)4, 
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