TYPE AND VARIABILITY 



433 



own type or even from his standard of selection, as well as to 

 know how it deviates from its own mean. 



I have therefore recommended their use, calling the one 

 deviation from mode and the other deviation from standard, 

 and earnestly suggest their constant employment by the breeder 

 as a means of acquainting himself with the true nature of the 

 variety he is attempting to improve ; for improvement consists 

 often in changing the type as well as in bringing a larger propor- 

 tion of the population to conform either to the natural or to the 

 accepted standard. 1 To do this he should make these determina- 

 tions year by year, and keep the results as a history of the vari- 

 ety or breed as it behaves with him under selection. 



Practical meaning of standard deviation. Inasmuch as the 

 standard deviation is an index of variability whether from mean 

 or from type, it expresses accurately the tendency of the variety 

 to wander, so far as the character in question is concerned. It 

 affords, therefore, a basis of comparison of one variety with 

 another, or with itself at some future time. However, one 

 standard deviation ordinarily cannot be compared directly with 

 another for two reasons : first, one mean may be very much 

 larger than the other ; and second, the two may be of entirely 

 different units, as inches and pounds, in which case direct 

 comparison is impossible. 



Coefficient of variability. We seek, therefore, an abstract 

 expression combining the idea both of standard deviation and 

 of type. Such an expression is known as the " coefficient of vari- 

 ability," and is found as follows : Divide the standard deviation 

 by the mean as a base, and the result will be an excellent index 

 of variability appearing in the form of a rate per cent. 2 



Thus, for the case in question, we have 1.28 -s- 8.83 = 0.145, 

 indicating the variability of this population to be over 14.5 per 

 cent of its own mean. Here we have a mathematical expression 

 for comparing variability on a perfectly abstract basis, and by 

 this means we can compare the variability of this population 



1 " Standard," as here used, refers to the scale of points, or that which the 

 breeder is trying to establish. It is his standard for selection. 



standard deviation <r 



- The formula is C = or . 



mean M 



