VI.—THE FREQUENCY-DISTRIBUTION. :
of decimals: if the rate stated to be 16:50 proves to be 16-502, it
will be sorted to the class 16:5-17°5; if 16498, to the class
155-165. Death-rates that work out to half-units exactly do
not occur in this example, and so there is no real difficulty. In
the case of Table II., again, there is no difficulty : if the year of
birth and death alone are given, the age at death is only calculable
 to the nearest unit; if the actual day of birth and death be
cited, half-years still cannot occur in the age at death, because
there is an odd number of days in the year. The difficulty may
always be avoided if it be borne in mind in fixing the limits
to class-intervals, these being carried to a further place of decimals,
or a smaller fraction, than the values in the original record. Thus
if statures are measured to the nearest centimetre, the classintervals
 may be taken as 1505-1515, 151'5-152°5, ete. ; if to
the nearest eighth of an inch, the intervals may be 5915-6013,
6015-6118, and so on.
If the difficulty is not evaded in any of these ways, it is
usual to assign one-half of an intermediate observation to each
adjacent class, with the result that half-units occur in the
class-frequencies (¢f. Tables VIL, p. 90, X,, p. 96, and XI.,
p. 96). The procedure is rough, but probably good enough for
practical purposes ; strict precision is usually unattainable, for in
point of fact the odd way in which different individuals read a
scale (¢/. Supplement I.) renders it impossible to assign exact
limits to intervals.
9. Tabulation.—As regards the actual drafting of the final
table, there is little to be said, except that care should be taken
to express the class-limits clearly, and, if necessary, to state the
manner in which the difficulty of intermediate values has been
met or evaded. The class-limits are perhaps best given as in
Tables I. and II, but may be more briefly indicated by the midvalues
 of the class-intervals. Thus Table I. might have been
given in the form—
Death-rate per 1000 Number of
per annum to the Districts with
Nearest Unit. said Death-rate,
13 5
14 16
15 61
15 112
eLc. ete.
A common mode of defining the class-intervals is to state the
limits in the form “az and less than .” In the case of measurements
 of stature, for example, the table micht run—

81
a