SECT. 2.] Averages. 437 



The grazier is thinking of his sheep : not in a merely general 

 sense, as sheep, and therefore under that name or con 

 ception, but as sheep of a certain approximate money value. 

 Some will be more, some less, but they are all near enough 

 to the assigned value to be conveniently classed together as 

 if by a name. Many of our rough quantitative designations 

 seem to be of this kind, as when we speak of eight-day 

 clocks or twelve-stone men/ &c. ; unless of course we in 

 tend (as we sometimes do in these cases) to assign a maximum 

 or minimum value. It is not indeed easy to see how else we 

 could readily convey a merely general notion of the quanti 

 tative aspect of things, except by selecting a type as above, 

 or by assigning certain limits within which the things are 

 supposed to lie. 



2. So far there is not necessarily any idea introduced 

 of comparison, of comparison, that is, of one group with 

 another, by aid of such an average. As soon as we begin 

 to think of this we have to be more precise in saying what 

 we mean by an average. We can easily see that the number 

 of possible kinds of average, in the sense of intermediate 

 values, is very great ; is, in fact, indefinitely great. Out of 

 the general conception of an intermediate value, obtained by 

 some treatment of the original magnitudes, we can elicit as 

 many subdivisions as we please, by various modes of treat 

 ment. There are however only three or four which for our 

 purposes need be taken into account. 



(1) In the first place there is the arithmetical average 

 )r mean. The rule for obtaining this is very simple : add 

 ill the magnitudes together, and divide the sum by their 

 lumber. This is the only kind of average with which the 

 inscientific mind is thoroughly familiar. But we must not 

 .et this simplicity and familiarity blind us to the fact that 

 ihere are definite reasons for the employment of this average, 



