123 THEORY OF STATISTICS.
distribution, is 2:99. As further illustrations of the closeness
with which the relation may be expected to hold in different cases,
we give below the results for the distributions of pauperism in
the unions of England and Wales in the years 1850, 1860, 1870,
1881, and 1891 (the last being the illustration taken above),
and also the results for the distribution of barometer heights at
Southampton (Table XI., Chap. VI. § 14), and similar distribu-
tions at four other stations.
Comparison of the Approximate and True Modes in the Case of Ive Dis-
tributions of Pauperism (Percentages of the Population in receipt of
Relief) in the Unions of England and Wales. (Yule, Jour. Roy. Stat.
Soc., vol. lix., 1896.)
Year. Mean. Median. Approximate guy, Mode,
Mode.
1850 6508 6°261 5767 5-815
1860 5:195 5000 4610 4:657
1870 5451 5:380 5238 | 5-038
1881 | 3676 3-523 3-217 3-240
1891 3289 3195 3-007 2987
Comparison of the Approximate and True Modes in the Case of Five Dis-
tributions of the Height of the Barometer for Daily Observations at the
Stations named. (Distributions given by Karl Pearson and Alice Lee,
Phil. Trans., A, vol. cxe. (1897), p. 423.)
Station. Mean. Median. 2P prowiinate True Mode.
Southampton . 29-981 30°000 30°038 30089
Londonderry . 29891 29915 29963 29960
Carmarthen . 29:952 29974 30018 30-013
Glasgow . : 29-886 29906 29-946 29967
Dundee . : 29-870 29°890 29930 29-951
It will be seen that in the case of the pauperism figures the
approximate mode only diverges markedly from the true value
in the year 1870, a year in which the frequency-distribution was
very irregular. In all the other years the difference between the
true and approximate values of the mode is hardly greater than
the alteration that might be caused in the true mode itself by
slight variations in the method of fitting the curve to the actual
distribution. Similar remarks apply to the second series of illus-
trations ; the true and approximate values are extremely close,
except in the case of Dundee and Glasgow, where the divergence
reaches two-hundredths of an inch.
21. Summing up the preceding paragraphs, we may say that
the mean is the form of average to use for all general purposes;
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