SECT. 39.] Theory of the Average. 503 



modification of the common exponential form. Its charac 

 teristics have been discussed in the paper by Dr Macalister 

 already referred to, but any attempt to examine its properties 

 here would lead us into far too intricate details. 



39. The general conclusion from all this seems quite 

 in accordance with the nature and functions of an average as 

 pointed out in the last chapter. Every average, it was urged, 

 is but a single representative intermediate value substituted 

 for a plurality of actual values. It must accordingly let slip the 

 bulk of the information involved in these latter. Occasionally, 

 as in most ordinary measurements, the one thing which it 

 represents is obviously the thing we are in want of; and 

 then the only question can be, which mean will most accord 

 with the true value we are seeking. But when, as may 

 happen in most of the common applications of statistics, 

 there is really no true value of an objective kind behind 

 the phenomena, the problem may branch out in various 

 directions. We may have a variety of purposes to work out, 

 and these may demand some discrimination as regards the 

 average most appropriate for them. Whenever therefore we 

 have any doubt whether the familiar arithmetical average is 

 suitable for the purpose in hand we must first decide pre 

 cisely what that purpose is. 



