VIII.—MEASURES OF DISPERSION, ETC. 
EXERCISES. 
1. Verify the following from the data of Table VI., Chap. VI, continuing 
ithe work from the stage reached for Qu. 1, Chap. VIL 
Stature in Inches for Adult Males born in— 
England. | Scotland. Wales. | Ireland. 
Standard deviation . : 256 250 2-35 2-17 
Mean deviation. 3 A 2-05 1-95 1-82 1-69 
Quartile deviation . 1780 1560 BB 1146 1:35 
Mean deviation / standard 0°80 0-78 0°78 0-78 
deviation 
Quartile deviation/standard 0°69 062 0-62 062 
deviation 
Lower quartile . : g 65°55 6692 65-06 66°39 
Upper ,, i 4 69°10 70°04 67°98 69°10 
2. (Continuing from Qu. 2, Chap. VIL.) Find the standard deviation, 
mean deviation, quartiles and quartile deviation (or semi-interquartile range) 
for the distribution of weights of adult males in the United Kingdom given in 
the last column of Table IX., Chap. VI. 
Compare the ratios of the mean and quartile deviations to the standard 
deviation with the ratios stated in §§ 19 and 23 to be usual. 
Find the value of the skewness (equation 12), using the approximate value 
of the mode. 
3. Using, or extending if necessary, your diagram for Question 4, Chap. VII. 
find the quartile values for houses assessed to inhabited house duty in 1885-6, 
from the data of Table IV., Chap. VI. 
Find also the 9th decile (the value exceeded by 10 per cent. of the houses 
only). 
4. Verify equation (9) by direct calculation of the standard deviation of the 
numbers 1 to 10. 
5. (Data from Sauerbeck, Jour. Roy. Stat. Soc., March 1909.) The 
following are the index-numbers (percentages) of prices of 45 commodities in 
1908 on their average prices in the years 1867-77 :—40, 43, 43, 46, 46, 46, 
54, 56, 59, 62, 64, 64, 66, 66, 67, 67, 68, 68, 69, 69, 69, 71, 75, 75, 76, 76, 
78, 80, 82, 82, 82, 82, 82, 83, 84, 86, 88, 90, 90, 91, 91, 92, 95, 102, 127. 
Find the mean and standard deviation (1) without further grouping ; (2) 
grouping the numbers by fives (40-, 45-, 50-, ete.); (3) grouping by tens (40-, 
50-, 60, etec.). 
6. (Continuing from Qu. 8, Chap. VIL) Supposing the frequencies of 
values 0, 1, 2, 3, . . . of a variable to be given by the terms of the binomial 
series 
qn, A Pu Link) J PY sininie 
1-2 
where p+¢=1, find the standard deviation. 
7. (Cf. the remarks at the end of § 17.) The sum of the deviations (with- 
out regard to sign) about the centre of the class-interval containing the mean 
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