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 calcul- 
able 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 class- 
intervals 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 mid- 
values 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 measure- 
ments of stature, for example, the table micht run— 
81 
a