VIL—AVERAGES, 1 
purpose of investigating the best methods of ascertaining and measuring 
Variations in the Value of the Monetary Standard,” British Association 
Beports, 1887 (p, 247), 1888 (p. 181), 1859 (p. 133), and 1890 (p. 485). 
(17) EvcrwortH, F. Y., Article ‘‘ Index-numbers” in Palgrave’s Dictionary 
of Political Economy, vol. ii.; Macmillan, 1896. 
(18) Founralx, H., “Memorandum on the Construction of Index-numbers 
of Prices,” in the Board of Trade Report on Wholesale and Retail 
Prices in the United Kingdom, 1903. 
EXERCISES. 
1. Verify the following means and medians from the data of Table YI., 
Chap. VI., p. 88. 
Stature in Inches for Adult Males in— 
England. Scotland. Wales. Ireland. 
Mean : . 67-31 68°55 66°62 6778 
Median . : . 67-35 68°48 66°56 67°69 
In the calculation of the means, use the same arbitrary origin as in Example 
ii., and check your work by the method of § 13 (d). 
2. Find the mean weight of adult males in the United Kingdom from the 
data in the last column of Table IX., Chap VI, p- 95. Also find the median 
weight, and hence the approximate mode, by the method of § 20. 
3. Similarly, find the mean, median, and approximate value of the mode 
for the distribution of fecundity in race-horses, Table X., Chap. VL, p. 96. 
4. Using a graphical method, find the median annual value of houses 
assessed to inhabited house duty in the financial year 1885-6 from the data 
of Table IV., Chap. VL., p. 83. 
5. (Data from Sauerbeck, Jour. Roy. Stat. Soc., March 1909.) The figures 
in columns 1 and 2 of the small table below show the index-numbers (or per- 
centages) of prices of certain animal foods in the years 1898 and 1908, on 
their average prices during the years 1867-77. In column 3 have been added 
the ratios of the index-numbers in 1908 to the index-numbers in 1898, the 
latter being taken as 100. 
Find the average ratio of prices in 1908 to prices in 1898, taken as 100 :— 
(1) From the arithmetic mean of the ratios in col, 8. 
(2) From the ratio of the arithmetic means of cols, 1 and 2, 
(3) From the ratio of the geometric means of cols. 1 and 2, 
(4) From the geometric mean of the ratios in col. 3. 
Note that, by § 25, the last two methods must give the same result, 
Index- number of price in Ratio 
Commodity. 1898. ns, 08/98. 
1. 2, 3. 
*. Beef, prime . : ' 78 88 112-8 
Beef, middling . ; . 72 | 90 1250 
. Mutton, prime . : . 84 92 1095 
“» Mutton, middling . CC 9 141-8 
. Pork . : ; : & 954 
. Bacon me 1077 
/. Butter 1197 
13: 
19u