THEORY OF STATISTICS. 
Stature in Inches. wo FE 
57 and less than 58 2 
58 v Dy 4 
59 3st +00 14 
etc. etc. 
—the statement 57 and less than 58,” ete., being often abbreviated 
to 57—, 58, 59, etc. (¢f. Table VI, p. 88). The mode of grouping 
is, in effect, that described in the last paragraph as of service in 
avoiding intermediate observations, but it should be noted that the 
form of statement leaves the class-limits uncertain unless the degree 
of accuracy of the measurements is also given. Thus, if measure- 
ments were taken to the nearest eighth of an inch, the class- 
limits are really 5615-5715, 5712-5812 ete.; if they were 
only taken to the nearest quarter of an inch, the limits are 56 
57%, 57i-587, ete. With such a form of tabulation a state- 
ment as to the number of significant figures in the original 
record is therefore essential. It is better, perhaps, to state the 
true class-limits and avoid ambiguity. 
10. The rule that class-intervals should be all equal is one 
that is very frequently broken in official statistical publications, 
principally in order to condense an otherwise unwieldy table, 
thus not only saving space in printing but also considerable 
expense in compilation, or possibly, in the case of confidential 
figures, to avoid giving a class which would contain only one or 
two observations, the identity of which might be guessed. It 
would hardly be legitimate, for example, to give a return of 
incomes relating to a limited district in such a form that the 
income of the two or three wealthiest men in the district would 
be clear to any intelligent reader with local knowledge. If the 
intervals be made unequal, the application of many statistical 
methods is rendered awkward, or even impossible, and the 
relative values of the frequencies are at first sight misleading, so 
that the table is not perspicuous. Thus, consider the first two 
columns of Table IV., showing the numbers of dwelling-houses 
of different annual values, assessed to inhabited house duty. On 
running the eye down the column headed “number of houses” it 
is at once caught by the two striking irregularities at the classes 
“£60 and under £80,” and “£100 and under £150.” But these 
have no real significance ; they are merely due to changes from 
a £10 to a £20, and then to a £50 interval. Moreover, the 
intervals after £150 go on continuously increasing, but attention 
is not directed thereto by any marked changes in the frequencies. 
To make the latter really comparable inter se, they must first be 
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