iv.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 41 



position will be exactly Middlemost, after the Strengths 

 of all the men in the group have been marshalled in 

 the order of their magnitudes. In other words, he is 

 of mediocre strength. The accepted term to express 

 the value that occupies the Middlemost position is 

 "Median," which may be used either as an adjective or 

 as a substantive, but it will be usually replaced in this 

 book by the abbreviated form M. I also use the word 

 " Mid " in a few combinations, such as " Mid-Fraternity," 

 to express the same thing. The Median, M, has three 

 properties. The first follows immediately from its con- 

 struction, namely, that the chance is an equal one, of 

 any previously unknown measure in the group exceeding 

 or failing short of M. The second is, that the most 

 probable value of any previously unknown measure in 

 the group is M. Thus if N be any one of the measures, 

 and u be the value of the unit in which the measure is 

 recorded, such as an inch, tenth of an inch, &c, then 

 the number of measures that fall between (N - \u) and 

 (N + ^w), is greatest when N— M. Mediocrity is always 

 the commonest condition, for reasons that will become 

 apparent later on. The third property is that whenever 

 the curve of the Scheme is symmetrically disposed on 

 either side of M, except that one half of it is turned 

 upwards, and the other half downwards, then M is 

 identical with the ordinary Arithmetic Mean or Average. 

 This is closely the condition of all the curves I have to 

 discuss. The reader may look on the Median and on 

 the Mean as being practically the same things, throughout 

 this book. 



