SECT. 5.] Averages. 441 



but when we are dealing with a symmetrical curve at all 

 resembling the binomial or exponential form they all three 

 coincide in giving the same result : as they obviously do in 

 the case in question. 



As soon, however, as we come to consider the case of 

 asymmetrical, or lop-sided curves, the indications given by 

 these three methods will be as a rule quite distinct; and 

 therefore the two former of these deserve brief notice as 

 representing different kinds of means from the arithmetical 

 or ordinary one. We shall see that there is something about 

 each of them which recommends it to common sense as being 

 in some way natural and appropriate. 



5. (3) The first of these selects from amongst the 

 various different magnitudes that particular one which is 

 most frequently represented. It has not acquired any tech 

 nical designation 1 , except in so far as it is referred to, by 

 its graphical representation, as the &quot;maximum ordinate&quot; 

 method. But I suspect that some appeal to such a mean 

 or standard is really far from uncommon, and that if we 

 could draw out into clearness the conceptions latent in the 

 judgments of the comparatively uncultivated, we should find 

 that there were various classes of cases in which this mean 

 was naturally employed. Suppose, for instance, that there 

 was a fishery in which the fish varied very much in size 



1 This kind of mean is called by tical average. 



Fechner and others the &quot; dichteste This mean ought to be called the 

 Werth.&quot; The most appropriate ap- probable value (a name however in 

 peal to it that I have seen is by Prof. possession of another) on the ground 

 Lexis (Massenerscheinungen, p. 42) that it indicates the point of likeliest 

 where he shows that it indicates occurrence ; i.e. if we compare all 

 clearly a sort of normal length of the indefinitely small and equal units 

 human life, of about 70 years ; a of variation, the one corresponding 

 result which is almost entirely mask- to this will tend to be most fre 

 ed when we appeal to the arithme- quently represented. 



