He THEORY OF STATISTICS. 
deviation @/r will be regarded as the equivalent of a deviation .@, 
instead of a deviation —a as the equivalent of a deviation +=. 
If a distribution take the simplest possible form when relative 
deviations are regarded as equivalents, the frequency of deviations 
between @/s and G/r will be equal to the frequency of deviations 
between 7.G and s.@. The frequency-curve will then be sym- 
metrical round log @ if plotted to log X as base, and if there be 
a single mode, log @ will be that mode—a logarithmic or geometric 
mode, as it might be termed : @ will not be the mode if the distri- 
bution be plotted in the ordinary way to values of X as base. 
The theory of such a distribution has been discussed by more than 
one author (refs. 2, 8,9). The general applicability of the assump- 
tion made does not, however, appear to have been very widely 
tested, and the reasons assigned have not sufficed to bring the 
geometric mean into common use. It may be noted that, as the 
geometric mean is always less than the arithmetic mean, the 
fundamental assumption which would justify the use of the former 
clearly does not hold where the (arithmetic) mode is greater than 
the arithmetic mean, as in Tables X. and XI. of the last chapter. 
97. The Harmonic Mean.—The harmonic mean of a series of 
quantities is the reciprocal of the arithmetic mean of their 
reciprocals, that is, if A be the harmonic mean, 
LL 
1-131) SE = 1%) 
The following illustration, the result of which is required for an 
example in a later chapter (Chap. XIIL § 11), will serve to show 
the method of calculation. 
The table gives the number of litters of mice, in certain 
breeding experiments, with given numbers (X) in the litter. (Data 
from A. D. Darbishire, Biometrika, iii. pp. 30, 31.) 
Number in | Number of 
Litter. Litters. f1X. 
xX. 7: 
7 7:000 
1 5:500 
16 5333 
17 4250 
26 | 5200 
31 57167 
11 1-571 
v 0125 
0-111 
i 84207 
.28 
qn