452 Averages. [CHAP. xvm. 



the trouble and risk of measuring them all. &quot;A barbarian 

 chief might often be induced to marshall his men in the 

 order of their heights, or in that of the popular estimate of 

 their skill in any capacity; but it would require some ap 

 paratus and a great deal of time to measure each man 

 separately, even supposing it possible to overcome the usually 

 strong repugnance of uncivilized people to any such pro 

 ceeding&quot; (Phil. Mag. Jan. 1875). That is, it being known 

 from wide experience that the heights of any tolerably 

 homogeneous set of men are apt to group themselves sym 

 metrically, the condition for the coincidence of the three 

 principal kinds of mean, the middle man of a row thus 

 arranged in order will represent the mean or average man, 

 and him we may subject to measurement. Moreover, since 

 the intermediate heights are much more thickly represented 

 than the extreme ones, a moderate error in the selection of 

 the central man of a long row will only entail a very small 

 error in the selection of the corresponding height. 



16. We can now conveniently recur to a subject which 

 has been already noticed in a former chapter, viz. the at 

 tempt which is sometimes made to establish a distinction 

 between an average and a mean. It has been proposed to 

 confine the former term to the cases in which we are dealing 

 with a fictitious result of our own construction, that is, with 

 a mere arithmetical deduction from the observed magni 

 tudes, and to apply the latter to cases in which there is 

 supposed to be some objective magnitude peculiarly repre 

 sentative of the average. 



Recur to the three principal classes, of things appropriate 

 to Probability, which were sketched out in Ch. n. 4. The 

 first of these comprised the results of games of chance. Toss 

 a die ten times: the total number of pips on the upper 

 side may vary from ten up to sixty. Suppose it to be 



