VIL—AVERAGES. 111 
in another column (4). The positive and negative products are 
totalled separately, giving totals — 776 and +509 respectively, 
whence 3(f.£) = —267. Dividing this by #, viz. 632, we have 
the difference of Jf from 4 in class-intervals, viz. 0-42 intervals, 
that is 0-21 per cent. Hence the mean is 35-021 =3-29 
per cent. 
CALCULATION OF THE MEAN: Example i.—Calculation of the Arithmetic 
Mean of the Percentages of the Population in receipt of Relief, from the 
Figures of Table VIII, Chap. VI., p. 93. 
(1) - (3) (4) 
Mid-values 
of the Deviation 
Class-intervals ~~ Frequency from Arbitrary Product 
{Percentage in Value 4 JE. 
receipt of 
Relief). 
1 18 - 9d 90 
5 48 - 4 192 
2 J 72 - & 216 
25 89 - 2 178 
3 100 - 1 100 
35 an =77sD 
1 75 
45 120 
5 120 
55 84 
Zz 5 ' 
65 : 
/ 
7°5 
85 
Total g = + 909 : 
=(f2)= +509 - 776 = — 267 
M-4=- - class-intervals= — 0°42 class-intervals 
= — 0°21 units 
-*. mean M=3'5-0'21= 3°29 per cent. 
It must always be remembered that 3(f.£)/N gives the value of 
M— 4 in class-intervals, and must not be added directly to 4 
unless the interval is also a unit. In the present illustration the 
(2) 
- 
43% .