SECT. 37.] 



Theory of the Average. 



501 



two commingled races were equal it would display a pair of 

 twin peaks. Again the question arises, ought we to in 

 volve the whole range within the scope of a single average ? 

 The answer is that the obligation depends upon the purpose 

 we have in view. If we want to compare that heterogeneous 

 race, as a whole, with some other, or with itself at some 

 other time, we shall do well to average without analysis. 

 All statistics of population, as we have already seen (v. p. 47), 

 are forced to neglect a multitude of discriminating charac 

 teristics of the kind in question. But if our object were to 

 interpret the causes of this abnormal error-curve we should 

 do well to break up the statistics into corresponding parts, 

 and subject these to analysis separately. 



Similarly with the measurements of the ancient buildings. 

 In this case if all our various errors were thrown together 

 into one group of statistics we should find that the resultant 

 curve of facility displayed, not two peaks only, but a suc 

 cession of them; and these of various magnitudes, corre 

 sponding to the frequency of occurrence of each particular 

 measurement. We might take an average of the whole, but 

 hardly any rational purpose could be subserved in so doing ; 

 whereas each separate point of maximum frequency of oc 

 currence has something significant to teach us. 



37. One other peculiar case may be noticed in con 

 clusion. Suppose a distinctly asymmetrical, or lopsided curve 

 of facility, such as this : 



ABC 



