Theory of the Average. [CHAP. xix. 



Laws of error, of which this is a graphical representation, 

 are, I apprehend, far from uncommon. The curve in question, 

 is, in fact, but a slight exaggeration of that of barometrical 

 heights as referred to in the last chapter; when it was 

 explained that in such cases the mean, the median, and the 

 maximum ordinate would show a mutual divergence. The 

 doubt here is not, as in the preceding instances, whether or 

 not a single average should be taken, but rather what kind 

 of average should be selected. As before, the answer must 

 depend upon the special purpose we have in view. For all 

 ordinary purposes of comparison between one time or place 

 and another, any average will answer, and we should there 

 fore naturally take the. arithmetical, as the most familiar, or 

 the median, as the simplest. 



38. Cases might however arise under which other 

 kinds of average could justify themselves, with a momentary 

 notice of which we may now conclude. Suppose, for instance, 

 that the question involved here were one of desirability of 

 climate. The ordinary mean, depending as it does so largely 

 upon the number and magnitude of extreme values, might 

 very reasonably be considered a less appropriate test than 

 that of judging simply by the relatively most frequent value : 

 in other words, by the maximum ordinate. And various 

 other points of view can be suggested in respect of which 

 this particular value would be the most suitable and sig 

 nificant. 



In the foregoing case, viz. that of the weather curve, 

 there was no objective or true value aimed at. But a 

 curve closely resembling this would be representative of 

 that particular class of estimates indicated by Mr Galton, 

 and for which, as he has pointed out, the geometrical mean 

 becomes the only appropriate one. In this case the curve of 

 facility ends abruptly at : it resembles a much foreshortened 



