The Measurement of Variation 47 



as to which should be used in each case, the mean or the 

 mode. 



Mathematical expression of variability. After the 

 average or mean of any group of plants has been deter- 

 mined, it is desirable to know the amount of deviation of 

 the different individuals from the mean. This determina- 

 tion gives a concrete expression which is an index of the 

 amount of variability exhibited. This variability is ex- 

 pressed as the average deviation or the standard deviation. 

 The latter is ordinarily employed by mathematicians. 



Average deviation. The average deviation is deter- 

 mined by obtaining, first of all, the amount which each 

 class varies from the mean and multiplying each deviation 

 by the number of individuals concerned. For example, 

 the column D is obtained by finding the difference between 

 the mean, 15.5, and the variations in column V : thus 

 in the first case the difference between 5.8 and 15.5 is 9.7 

 while farther down column V we find 16.3, which is greater 

 than the mean, giving us a value of 0.8 in column D. 



Now, if there were the same number of individuals in 

 each class, the average deviation could be found by adding 

 up the deviations in column D, and dividing by the total 

 number of individuals in column /, but there is one indi- 

 vidual deviating - 9.7 while there are 43 deviating 0.8 

 and 18 deviating 5.3, and so forth. In order to overcome 

 this the deviations are multiplied by the number of in- 

 dividuals giving the column /D. The sum of this column 

 divided by the total number of individuals gives the 

 average deviation. This is an index of variability. 

 The average deviation is expressed by the following 

 formula : 



