494 Theory of the Average. [CHAP. xix. 



take the modulus as the measure of this superiority. In 

 fact we are quite safe in simply saying that the average of 

 those average results is better than that of the individual 

 ones. 



When however we proceed in what Hume calls &quot;the 

 sifting humour,&quot; and enquire why it is sufficient thus to 

 trust to the average ; we find, in addition to the considera 

 tions hitherto advanced, that some postulate was required as 

 to the consequences of the errors we incur. It involved an 

 estimate of what is sometimes called the detriment of an 

 error. It seemed to take for granted that large and small 

 errors all stand upon the same general footing of being mis 

 chievous in their consequences, but that their evil effects in 

 crease in a greater ratio than that of their own magnitude. 



30. Suppose, for comparison, a case in which the im 

 portance of an error is directly proportional to its magnitude 

 (of course we suppose positive and negative errors to balance 

 each other in the long run) : it does not appear that any 

 advantage would be gained by taking averages. Something 

 of this sort may be considered to prevail in cases of mere 

 purchase and sale. Suppose that any one had to buy a very 

 large number of yards of cloth at a constant price per yard : 

 that he had to do this, say, five times a day for many days in 

 succession. And conceive that the measurement of the 

 cloth was roughly estimated on each separate occasion, with 

 resultant errors which are as likely to be in excess as in 

 defect. Would it make the slightest difference to him 

 whether he paid separately for each piece; or whether 

 the five estimated lengths were added together, their average 

 taken, and he were charged with this average price for each 

 piece ? In the latter case the errors which will be made in 

 the estimation of each piece will of course be less in the long 

 run than they would be in the former : will this be of any 



