ER THEORY OF STATISTICS. 
If we now compute the theoretical frequencies from (8), putting 
A="61, we have the following results :— 
Actual Frequency assigned 
Deaths: An, by Se Tomit, 
0 109 108-7 
1 65 66°38 
RB 2 202 
3 41 
1 *7 (4 and over) 
The agreement here is excellent, but such a concordance is not 
very common in actual statistics. Cases do, however, occur in 
which the method is of service, and the advanced student will find 
that the reasoning illustrated is of value in many theoretical 
investigations. 
IV. GOODNESS OF FIT. 
(Supplementary to Chapter XVII.) 
IN par. 15, Chapter XV. (p. 308), it was remarked that the general 
treatment of the problem, whether the discrepancies between 
any system of observed frequencies and those postulated by a 
theoretical law might have arisen by the operation of simple 
sampling, was beyond the scope of this work. As, however, the 
student will find in the course of his reading that a test of this 
character is often applied in practical problems, the following 
notes may be of service by way of comment on, or elucidation 
of, the highly technical papers in which the subject is fully 
discussed (see refs. 22 and 23, p. 315, and also additional 
refs. on p. 394). 
The student who has followed the argument leading up to 
the table on p. 310 will have perceived that, when the frequency 
distribution of a variable is known, the probability that a set of 
observations departing from the most likely value would occur 
can be evaluated by comparing the portion of area bounded by 
the ordinate corresponding to the observed deviation with the 
whole area of the theoretical curve, and the work is illustrated 
in Examples i.-iv. of pp. 311-313. In this case there is only a 
single variable, and the test for goodness of fit is reduced to its 
simplest terms. But a consideration of Chapter XVI., and the 
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