VIIL—MEASURES OF DISPERSION, ETC. 153 
arrange them in order of merit as regards this character: if the 
boys are then “numbered up” in order, the number of each boy, 
or his rank, serves as some sort of index to his capacity (cf. the 
remarks in § 12. It should be noted that rank in this sense is 
not quite the same as grade; if a boy is tenth, say, from the 
bottom in a class of a hundred his grade is 9:5, but the method 
is in principle the same with that of grades or percentiles). 
The method of ranks, grades, or percentiles in such a case may 
be a very serviceable auxiliary, though, of course, it is better if 
possible to obtain a numerical measure. But if, in the case of a 
measurable character, the percentiles are used not merely as 
20 29 40 50 £0 Ld 2 
4 
3. ; 
v 
3649 — 2 
~ 
“ep .. 2 
60- — 60 
v vo <9 30 40 50 60 70 80 90 100 
Stature corres onding to 7 
Por adele males in the Britian reer. 
F16. 28. —Ogive Curve for Stature, same data as Fig. 6, p. 89. 
constants illustrative of certain aspects of the frequency-distribu- 
tion, but entirely to replace the table giving the frequency- 
distribution, serious inconvenience may be caused, as the 
application of other methods to the data is barred. Given the 
table showing the frequency-distribution, the reader can calculate 
not only the percentiles, but any form of average or measure of 
dispersion that has yet been proposed, to a sufficiently high 
degree of approximation. But given only the percentiles, or at 
least so few of them as the nine deciles, he cannot pass back to 
the frequency-distribution, and thence to other constants, with any 
degree of accuracy. In all cases of published work, therefore, 
the figures of the frequency-distribution should be given ; they 
are absolutely fundamental.