VIII.—MEASURES OF DISPERSION, ETC. 141 
CALCULATION OF THE STANDARD DEVIATION: Example iii.— Calculation 
of the Standard Deviation of Stature of Male Adults in the British Isles 
Jrom the figures of Table VI., p. 88. (Cf. p. 112 for the calculation of 
mean alone, ) 
(1) (2) (3) (4) (5) 
Deviation 
Height. Frequency. from Product. Product 
Inches. I Value 4. T= Fas 
ez 
57- 9 -10 20 200 
58- 4 - 9 36 324 
59- 14 - R 112 896 
€- 41 - 287 2,009 
ai. 83 - 498 2,988 
Or 169 =~ 13 845 4,225 
63— 394 - 1576 6,304 
64- 669 - 2007 6,021 
65— 990 = Bi 1980 3,960 
66 1223 = i 1223 1.223 
67- 1329 0 —- 8584 — 
68 1230 3] : 1230 1,230 
69- 1063 + 2 2126 4,252 
70- 646 + 3 1938 5,814 
71- 392 =f 1568 6,272 
72- 202 + 1 1010 5,050 
73- 79 + 474 2,844 
7— a! + 7 : 224 1,568 
yo— 1: : 128 1,024 
7h- 45 405 
» : 20 200 
Tin) EJ +8763 56,809 
From previous work, #/ — 4 =d= + ‘0209 class-intervals or inches, 
=(/.8) _ 56809 
= CER 66172. 
o2=6"6172 — (0209)2 
=66168. 
.*.  @=2'57 class-intervals or inches. 
ii. the standard deviation is 1-24 per cent. ; six times this is 7-44 
per cent., and a range from 0-75 to 8:19 per cent. includes all 
but one observation out of 632. In Example iii. the standard 
deviation 1s 2:57 in., six times this is 15°42 in, and a range from, 
say, 60 in. to 754 in. includes all but some 37 out of 8585 
individuals, z.e. about 99-6 per cent. This rough rule serves to 
a AEQE :