1 THEORY OF STATISTICS. 
The difference between median and mean in this case is 
therefore only about one-hundredth of an inch, the smallness 
of the difference arising from the approximate symmetry of 
the distribution. In an absolutely symmetrical distribution 
it is evident that mean and median must coincide. 
16. Graphical interpolation may, if desired, be substituted 
for arithmetical interpolation. Taking, again, the figures of 
Example i., the number of districts with pauperism not exceeding 
2:25 is 138 ; not exceeding 2:75, 227 ; not exceeding 3:25, 327 ; 
and not exceeding 3'75, 417. Plot the numbers of districts 
with pauperism not exceeding each value X to the corresponding 
Sh = 
% 400 - 200 
3 : 
3 
3 376 
8 JC —300 
as 
aS 
3 
Ho 
a 200- - 200 
08 
§ 100~~ —+}- 100 
2 3 5 2 
Percentage ¢- _ . ropulation 
wv receipt of relief 
F1a. 28. —Determination of the median by graphical interpolation. 
value of X on squared paper, to a good large scale, as in fig. 23, 
and draw a smooth curve through the points thus obtained, 
preferably with the aid of one of the “curves,” splines, or flexible 
curves sold by instrument-makers for the purpose. The point 
in which the smooth curve so obtained cuts the horizontal line 
corresponding to a total frequency N/2=316 gives the median. 
In general the curve is so flat that the value obtained by this 
graphical method does not differ appreciably from that calculated 
arithmetically (the arithmetical process assuming that the 
curve is a straight line between the points on either side of 
the median); if the curvature is considerable, the graphical 
value—assuming, of course, careful and accurate draughtsmanship 
—is to be preferred to the arithmetical value, as it does not 
y,