434 



THE GRAMMAR OF SCIENCE 



e : from the consideration that the total number of 



4 ' 



wives in the [a) group is in^ we also find ^^ = ^3 

 the scheme becomes, if e = e^ + e^ = e^ + ^^ : — 



Husbands. 



Thus 



> 



71,. X 7)la 



N 



+ e 



Hg X nib 



N 



111 X m„ 



N ■ 



«6 X ;«6 



+ e 



Now we can simplify this still a stage further. We 

 chose our boundary between the classes a and ^ to be 

 the limit between hazel and light brown. But this limit 

 was purely arbitrary ; our reasoning is equally applicable 

 wherever this limit be taken. Now we might take this 

 limit at the man and woman with the median eye tint 

 instead of between hazel and light brown. By the 

 median individual we are to understand the individual 

 who would occupy the middle position if the whole group 

 of individuals were arranged in line according to the in- 

 tensity of the character in each. For example, if looi 

 husbands were arranged according to ascending darkness 

 of eye-colour, the man who occupied the 501st place would 

 have the median tint. If we took 1000 husbands, the 

 median husband must be considered as coming between 

 the 500th and 501st husbands in line, i.e. for practical 

 purposes he would be identical in tint with either of 

 them. When deviations in excess and defect of like in- 

 tensity are equally frequent, then the median coincides 

 with the mode and the mean, but for skew frequency the 

 median falls between the mode and the mean.^ 



Adopting the median as our division for the groups 



1 For nearly all cases which occur in practice it will be found that the 

 distance from the mean to the mode is sensibly three times the distance from 

 the mean to the median. By this rule, since the mean and median are easily 

 determined, we can get a good approximation to the true mode. 



