436 Averages. [CHAP. xvm. 



The first vague notion of an average, as we now under 

 stand it, seems to me to involve little more than that of a 

 something intermediate to a number of objects. The objects 

 must of course resemble each other in certain respects, other 

 wise we should not think of classing them together ; and 

 they must also differ in certain respects, otherwise we should 

 not distinguish between them. What the average does for 

 us, under this primitive form, is to enable us conveniently to 

 retain the group together as a whole. That is, it furnishes a 

 sort of representative value of the quantitative aspect of the 

 things in question, which will serve for certain purposes to 

 take the place of any single member of the group. 



It would seem then that the first dawn of the conception 

 which science reduces to accuracy under the designation of 

 an average or mean, and then proceeds to subdivide into 

 various distinct species of means, presents itself as per 

 forming some of the functions of a general name. For what 

 is the main use of a general name ? It is to reduce a plu- 

 larity of objects to unity ; to group a number of things 

 together by reference to some qualities which they possess 

 in common. The ordinary general name rests upon a con 

 siderable variety of attributes, mostly of a qualitative 

 character, whereas the average, in so far as it serves the 

 same sort of purpose, rests rather upon a single quantitative 

 attribute. It directs attention to a certain kind and degree 

 of magnitude. When the grazier says of his sheep that one 

 with another they will fetch about 50 shillings, or the 

 farmer buys a lot of poles which run to about 10 feet, it is 

 true that they are not strictly using the equivalent of either 

 a general or a collective name. But they are coming very 

 near to such use, in picking out a sort of type or specimen of ] 

 the magnitude to which attention is to be directed, and in 

 classing the whole group by its resemblance to this type. 



