442 Averages. [CHAP. xvm. 



but in which the commonest size was somewhat near the 

 largest or the smallest. If the men were in the habit of 

 selling their fish by weight, it is probable that they would 

 before long begin to acquire some kind of notion of what 

 is meant by the arithmetical mean or average, and would 

 perceive that this was the most appropriate test. But if the 

 fish were sorted into sizes, and sold by numbers in each of 

 these sizes, I suspect that this appeal to a maximum ordi- 

 nate would begin to take the place of the other. That is, 

 the most numerous class would come to be selected as a 

 sort of type by which to compare the same fishery at one 

 time and another, or one fishery with others. There is also, 

 as we shall see in the next chapter, some scientific ground 

 for the preference of this kind of mean in peculiar cases; 

 viz. where the quantities with which we deal are true 

 errors, in the estimate of some magnitude, and where also 

 it is of much more importance to be exactly right, or very 

 nearly right, than to have merely a low average of error. 



6. (4) The remaining kind of mean is that which is 

 now coming to be called the &quot;median.&quot; It is one with 

 which the writings of Mr Galton have done so much to 

 familiarize statisticians, and is best described as follows. 

 Conceive all the objects in question to be marshalled in the 

 order of their magnitude ; or, what comes to the same thing, 

 conceive them sorted into a number of equally numerous 

 classes ; then the middle one of the row, or the middle one 

 in the middle class, will be the median. I do not think 

 that this kind of mean is at all generally recognized at 

 present, but if Mr Galton s scheme of natural measurement 

 by what he calls &quot; per-centiles &quot; should come to be gener 

 ally adopted, such a test would become an important one. 

 There are some conspicuous advantages about this kind of 

 mean. For one thing, in most statistical enquiries, it is 



