TYPE AND VARIABILITY 



427 



DEVIATION OF 327 EARS 

 OF CORN FROM THEIR 

 MEAN LENGTH OF 

 8.83 INCHES 



Again the concrete serves well as a medium for teaching a 

 principle. In this connection we refer once more to our distri- 

 bution of 327 ears, and note that every ear in the lot deviates 

 somewhat from the mean of 8.83 inches. The range and extent 

 of this deviation are shown in the following table, column D, 



The practical question now is to reduce 

 this column of deviations to a single ex- 

 pression denoting the variability of the 

 population of which this distribution is 

 representative. Manifestly, when this is 

 done, the variability of this distribution 

 can be compared directly and exactly with 

 that of any other, and at the present or 

 any future time. Two methods of pro- 

 cedure are possible in thus securing a kind 

 of general expression for the average 

 amount of deviation, giving rise to two 

 similar but slightly different values, 

 namely, the average deviation and the 

 standard deviation. 



The average deviation. If each devi- 

 ation (column D) represented an equal 

 number of ears, this single expression 

 could be readily derived by adding the 

 deviations and dividing by the total 

 number. But these deviations do not 

 represent equal numbers of ears. The 

 deviation 5.83, for example, represents but one ear, while no 

 less than twelve ears deviated 1.83 inches below the mean and 

 two deviated 2.67 inches above, with others unevenly distributed. 



Manifestly each deviation should first be multiplied by the 

 number of ears involved, as in the succeeding table : x 



(Biometrikd) is devoted to the reports of statistical studies in evolution, technically 

 known as " biometry." 



1 When the deviation is to be obtained in this way the minus sign is disregarded. 



* D indicates the deviation of the several groups from the common mean of 

 the race, 8.83 inches. Thus, for example, the first ear deviates the difference 

 between 3 inches and 8.83 inches, or 5.83, which, being below the mean, is written 

 with the negative sign ; also the 21 ears 10.5 inches long deviate 10.58.83, or 1.67 

 inches from the mean, and being above the mean, we write it positive. 



