VIII.—MEASURES OF DISPERSION, ETC. 151 
above it and 50 per cent. below, is the median: the two quartiles 
lie between the second and third and the seventh and eighth 
deciles respectively. 
28. The deciles, like the median and quartiles, may be 
determined either by arithmetical or by graphical interpolation, 
excluding the cases in which, like the former constants, they 
become indeterminate (¢f. § 24). It is hardly necessary to give 
an illustration of the former process, as the method is precisely 
the same as for median and quartiles (Chap. VII. § 15, and above, 
§ 22). Fig. 26 shows, of course on a very much reduced scale, the 
; 
SE 
= 
\ 
14 
a) 
3 
Percentage of the population 
in receipt of relief 
FiG. 26.—Curve showing the number of Districts of England and Wales in 
which the Pauperism on 1st January 1891 did not exceed any given per- 
centage of the population (same data as Fig. 10, p. 92): graphical 
determination of Deciles. 
curve used for obtaining the deciles by the graphical method in 
the case of the distribution of pauperism (Example ii. above). 
The figures of the original table are added up step by step from 
the top, so as to give the total frequency not exceeding the upper 
limit of each class-interval, and ordinates are then erected to a 
horizontal base to represent on some scale these integrated 
frequencies: a smooth curve is then drawn through the tops of 
the ordinates so obtained. This curve, as will be seen from the 
figure, rises slowly at first when the frequencies are small, then 
more rapidly as they increase, and finally turns over again and 
becomes quite flat as the frequencies tail off to zero. The deciles