THEORY OF STATISTICS. 
fication, considered in Chaps. I.-IV., is too crude: if the values are 
merely classified as A’s or o's according as they exceed or fall 
short of some fixed value, a large part of the information given 
by the original record is lost. A manifold classification, however 
(¢f- Chap. V.), avoids the crudity of the dichotomous form, since 
the classes may be made as numerous as we please, and numerical 
measurements lend themselves with peculiar readiness to a 
manifold classification, for the class limits can be conveniently 
and precisely defined by assigned values of the variable. For 
convenience, the values of the variable chosen to define the 
successive classes should be equidistant, so that the numbers of 
observations in the different classes (the class-frequencies) may be 
comparable. Thus for measurements of stature the interval 
chosen for classifying (the class-interval, as it may be termed) 
might be 1 inch, or 2 centimetres, the numbers of individuals 
being counted whose statures fall within each successive inch, or 
each successive 2 centimetres, of the scale; returns of birth- or 
death-rates might be grouped to the nearest unit per thousand 
of the population; returns of wages might be classified to the 
nearest shilling, or, if desired to obtain a more condensed table, 
by intervals of five shillings or ten shillings, and so on. When 
the variation is discontinuous, as for example in enumerations 
of numbers of children in families or of petals on flowers, the 
unit is naturally taken as the class-interval unless the range of 
variation is very great. The manner in which the observations 
are distributed over the successive equal intervals of the scale is 
spoken of as the frequency-distribution of the variable. 
3. A few illustrations will make clearer the nature of such 
frequency-distributions, and the service which they render in 
summarising a long and complex record :— 
(a) Table I. In this illustration the mean annual death-rates, 
expressed as proportions per thousand of the population per 
annum, of the 632 registration districts of England and Wales, 
for the decade 1881-90, have been classified to the nearest unit ; 
t.e. the numbers of districts have been counted in which the 
death-rate was over 12'5 but under 13:5, over 13'5 but under 
14'5, and so on. The frequency-distribution is shown by the 
following table. 
[TaBLE I. 
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