VARIABILITY OF A SINGLE CHARACTER 



13 



comparison of the two standard deviations, because variability 

 in one case is expressed in terms of inches and in the other in 

 terms of ounces. 



If, however, each of the standard deviations be divided by its 

 mean as a base, then the quotients can be directly compared. 

 Thus 1 . 1 3 -=- 8 . 5 1 4 = o. 1 3 27, or, as it is more commonly written, 

 13.27, meaning thereby 13.27 per cent ; and 2.854 -j- 8.807 = 

 32.41, showing that the corn is much more variable with respect 

 to weight than it is with respect to length. Such a quotient — 

 standard deviation divided by its mean — is known as the coeffi- 

 cient of variability, and, being entirely an abstract number, it 

 serves as a basis on which the variabilities of any two distribu- 

 tions may be directly compared, whether dealing in terms of 

 inches or ounces, feet or pounds or numbers, and whether the 

 individuals involved are ears of corn, pounds of milk, bushels of 

 grain, or any other races or characters where differences can be 

 weighed, counted, or otherwise measured. The footnote 1 gives 

 a few coefficients of variability for human measurements. 



By the methods here outlined, any character or characters 

 may be accurately studied as to both type and variability, pro- 

 vided the character can be accurately measured in some way, and 

 provided also that sufficient numbers can be found to make the 

 distribution fairly smooth. 



It remains to offer suggestions as to certain details that are 

 encountered in studies of this sort, and on which the student 

 needs further information. 



Suggestions as to taking measurements. In the scale just 

 used, the measurements of corn were taken one half inch apart 

 and the weights in ounces. Why ? Why were not the lengths 



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