INTRODUCTION 



31 



than the mean balanced up with those that were less to the same amount, 

 yet it is probable that no single item of the entire list is the exact equiva- 

 lent of the mean itself, but that each one deviates from this ideal, by so 

 much more or by so much less. Now, it is important to know, in a given 

 list, how much the items vary from the mean, in order to compare lists of 

 different measurements, for the purpose of seeing how great the variation. 



Now, the amount of variation, that is, whether all the items of a given 

 list keep rather near the mean, or whether they swing away from it 

 considerably, and thus show a large range of variation, is important to 

 know. This cannot be done by selecting from the list the two extremes 

 and comparing these, for this gives simply the range of variation, in which 

 both extremes may be unusual while the rest vary but little from the mean. 

 One must instead find the exact amount of deviation from the mean shown 

 by each item on the list, add them all together, and divide by the number 

 of items, which gives us an average or mean of the deviations, the Aver- 

 age Deviation, which takes into consideration, not simply two items but 

 all of them. 



This may, of course, be done by comparing each individual item with 

 the mean, adding all together algebraically, and dividing this sum by the 

 number of items, but, in a long series of items, such a method would be 

 too laborious. This work may be materially shortened by using a method 

 similar to that employed for getting the mean. As an illustration the 

 average deviation of the preceding table of cristal breadths may be 

 calculated as follows : 



