Jan. 24, 1889] 



NA TURE 



297 



simple,but I cannotexplain it without using technicalterms. 

 In some cases this allowance is large ; thus the length of 

 the middle finger varies at so very different a rate from that 

 of the stature that i inch of difference of middle-finger 

 length is associated on the average with 8-4 inches of 

 stature. On the other hand, 10 inches of stature is 

 associated on the average with 06 inch of middle-finger 

 length. There is no reciprocity in these numerals ; yet, 

 for all that, when the scale of their respective variabilities 

 is taken into account as above mentioned, the values at 

 once become strictly reciprocal. I shall be able to explain 

 this better later on. 



In every pair of correlated variables the conditions that 

 were shown to characterize kinship will necessarily be 

 present— namely, that variation in one of the pair is on 

 the average associated with a proportionate variation in 

 the other, the proportion being the same whatever may 

 be the amount of the variation. Again, when allowance 

 is made for their respective scales of variability, the pro- 

 portion is strictly reciprocal, and it is always from i to 

 something less than I. In other words, there is always 

 regression. 



Variety.— T\i& principal topic of my further remarks 

 will be the claims of variety to more consideration from 

 anthropologists than it has hitherto received. They com- 

 monly devote their inquiries to the mean values of 

 different groups, while the variety of the individuals who 

 constitute those groups is too often passed over with 

 contented neglect. It seems to me a great loss of oppor- 

 tunity when, after observations have been laboriously 

 collected, and been subsequently discussed in order to 

 obtain mean values from them, the very little extra trouble 

 is not taken that would determine other values whereby to 

 express the var ety of the individuals in those groups. 

 Much experience some years back, and much new ex- 

 perience during the past year, has proved to me the ease 

 with which variety may be adequately expressed, and the 

 high importance of taking it into account. There are 

 numerous problems of especial interest to anthropo- 

 logists that deal solely with variety. 



There can be little doubt that most persons fail to have 

 an adequate conception of the orderliness of variability, 

 and think it useless to pay scientific attention to variety, 

 as being, in their view, a subject wholly beyond the powers 

 of definition. They forget that what is confessedly un- 

 defined in the individual may be definite in the group, 

 and that uncertainty as regards the one is in no way in- 

 compatible with statistical assurance as regards the other. 

 Almost everybody is familiar nowadays with the constancy 

 of the average in different samples of the same large 

 group, but they do not often realize the way in which 

 the same statistical constancy permeates the whole of 

 llie group. The Mean or the Average is practically 

 nothing more than the middlemost value in a marshaled 

 series. A constancy analogous to that of the Mean 

 characterizes the values that occupy any other fractional 

 position that we please to name, such as 'the loth per 

 cent., or the 20th per cent. ; it is not peculiar to the 

 50th per cent., or middlemost. 



Greater interest is usually attached to individuals who 

 occupy positions towards either of the ends of a marshaled 

 series, than to those who stand about its middle. For 

 example, an average man is morally and intellectually 

 a very uninteresting being. The class to which he belongs 

 is bulky, and no doubt serves to keep the course of social 

 life in action. It also affords, by its inertia, a regulator 

 that, like the fly-wheel to the steam-engine, resists sudden 

 and irregular changes. But the average man is of no 

 direct help towards evolution, which appears to our dim 

 vision to be the primary purpose, so to speak, of all living 

 existence. Evolution is an unresting progression ; the 

 nature of the average individual is essentially unpro- 

 gressive. His children tend to resemble him exactly, 

 whereas the children of exceptional persons tend to I 



regress towards mediocrity. Consider the interest at- 

 tached to variation in the moral and intellectual nature 

 of man, and the value of variability in those respects. 

 For example, in the Hebrew race, whose average worth 

 shows little that is worthy of note, but which is mainly 

 of interest on account of its variety. Its variability in 

 ancient and modern times seems to have been extra- 

 ordinarily great. It has been able to supply men, time 

 after time, who have towered high above their fellows, 

 and left enduring marks on the history of the world. 



Some thoroughgoing democrats may look with com- 

 placency on a mob of mediocrities, but to most other 

 persons they are the reverse of attractive. The 

 absence of heroic gifts is a heavy set-off against the 

 freedom from a corresponding number of very degraded 

 forms. The general standard of thought and morals 

 in a mob of mediocrities must be mediocre, and, what 

 is worse, contentedly so. The lack of living men to 

 afford lofty examples, and to educate the virtue of rever- 

 ence, would leave an irremediable blank. All men 

 would find themselves at nearly the same dead average 

 level, each as meanly endowed as his neighbour. 



These remarks apply with obvious modifications to 

 variety in the physical faculties. Peculiar gifts, moreover, 

 afford an especial justification for division of labour, each 

 man doing that which he can do best. 



The method I have myself usually adopted for express- 

 ing and dealing with the variety of the individuals in a 

 group, has been already explained on more than one 

 occasion. I should not have again alluded to it had I 

 not had much occasion of late to test and develop it, also 

 to devise an unpretentious little table of figures, that I 

 call a " table of normal distribution," which has been of 

 singular assistance to myself I trust it may be equally 

 useful to other anthropologists. It is appended to these 

 remarks, and I should like after a short necessary preface 

 to say something about it. The table and its origin, and 

 several uses to which it has been applied, will be found in 

 a book by myself, that will be published in a few days, 

 called " Natural Inheritance" (Macmillan and Co.). All the 

 data to which I shall refer will be found in that book also, 

 except such as concern correlation. These accompanied 

 a memoir read by me only a month ago before the Royal 

 Society, and will be published in due course in their 

 Proceedings.' 



It has already been said that the first step in the 

 problem of expressing variety among the individual 

 members of any sample, is to marshal their measures 

 in order, into a class. We begin with the smallest 

 measure and end with the greatest. The object of the 

 next step is to free ourselves from the embarrasment due 

 to the different numbers of individuals in different classes. 

 This is effected by dividing the class, whatever its size 

 may be, into 100 equal portions, caUing the lines that divide 

 the portions by the name of grades. The first of these 

 portions will therefore lie between grades 0° and 1°, and 

 the hundredth and last portion between grades 99° and 

 100". We have next to find by interpolation the values 

 that correspond to as many of these grades as we care to 

 deal with. It is of no consequence whether or no the 

 number in the class is evenly divisible by 100, because we 

 can interpolate and get the values we want, all the same. 

 This having been done, the value that corresponds with 

 the 50th grade will be the middlemost. It is practically 

 the same for ordinary purposes as the' mean value or the 

 average value ; but as it may not be strictly the same, it is 

 right to call it by a distinctive name, and none simpler or 

 more convenient occurs than the letter M. So I will 

 henceforth use M to denote the middlemost or median 

 value, or, in other words, that which corresponds to the 

 50th (centesimal) grade. 



The difference between the extreme ends of a marshaled 



' For abstract, see Nature, January 3. p. 238. For tables of percentiles, 

 see vol. xxxi. p. 223. For hereditary stature, see vol. xxxiii. p. 295. 



