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 



100<r 



^ = \7~' 



M 



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 + b) n where a = 6 = 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 set 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 % X M = M- 



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: 



head and 4 tails = 1(MY 



1 head and 3 tails = 4(H) 4 



2 heads and 2 tails = 



3 heads and 1 tail = 



4 heads and tail = 



