THEORY OF STATISTICS.
4. The population itself,
in the metropolitan group of 32 unions, and the fundamental
constants (means, standard-deviations and correlations) are as
follows :—
TABLE I
! 2. 3.
- Sta 4 ion- mii
Rs So oon log VIR
104-7 29-2 12 +052 1-93154
906 417 13 +041 1:96003
107-7 5:5 | 14 -0°14 199570
i= ‘8 23 +0°49 164038
b24 +023 1:98820
34 +025 198598
It is seen that the average changes are not great; the per-
centages of the population in receipt of relief have increased on
an average by 4'7 per cent., the out-relief ratio has dropped by
9-4 per cent., and the percentage of old has increased by 7-7
per cent., at the same time as the population of the unions has
risen on the average by 11'3 per cent. At the same time the
standard-deviations of the first, second, and fourth variables are
very large. As a matter of fact, while in one union the
pauperism decreased by nearly 50 per cent. and in others by
20. per cent. in some there were increases of 60, 80, and 90
per cent. ; similarly, in the case of the out-relief, in several unions
the ratio was decreased by 40 to 60 per cent., a consistent
anti-out-relief policy having been enforced ; in others the ratio
was doubled, and more than doubled. As regards population,
the more central districts show decreases ranging up to 20 and
25 per cent., the circumferential districts increases of 45 to 80
per cent. The correlations of order zero are not large, the
changes in the rate of pauperism exhibiting the highest correlation
with changes in the out-relief ratio, slightly less with changes
in the proportion of old, and very little with changes in
population.
The correlations of the second order are obtained in two steps.
In the first place, the six coefficients of order zero are grouped in
four sets of three, corresponding to the four sets of three variables
formed by omitting each one of the four variables in turn (Table
IT. col. 1). Each of these sets of three coefficients is then
treated in the same manner as in the last example, and so the
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