VIIL.—MEASURES OF DISPERSION, ETC. 149 
semi-interquartile range as a measure of dispersion is not to be 
recommended, unless simplicity of meaning is of primary im- 
portance, owing to the lack of algebraical convenience which 
it shares with the median. Further, it is obvious that the 
quartile, like the median, may become indeterminate, and that 
the use of this measure of dispersion is undesirable in cases of 
discontinuous variation: the student should refer again to the 
discussion of the similar disadvantage in the case of the median, 
Chap. VII. § 14. It has, however, been largely used in the past, 
particularly for anthropometric work. 
25. Measures of Relative Dispersion.—As was pointed out in 
Chapter VIL § 26, if relative size is regarded as influencing not only 
the average, but also deviations from the average, the geometric 
mean seems the natural form of average to use, and deviations 
should be measured by their ratios to the geometric mean. As 
already stated, however, this method of measuring deviations, with 
its accompanying employment of the geometric mean, has never 
come into general use. It is a much more simple matter to allow 
for the influence of size by taking the ratio of the measure of 
absolute dispersion (e.g. standard deviation, mean deviation, or 
quartile deviation) to the average (mean or median) from which 
the deviations were measured. Pearson has termed the quantity 
a 
ve. the percentage ratio of the standard deviation to the arithmetic 
mean, the coefficient of variation (ref. 7), and has used it, for 
example, in comparing the relative variations of corresponding 
organs or characters in the two sexes: the ratio of the quartile 
deviation to the median has also been suggested (Verschaeffelt, 
ref. 8). Such a measure of relative dispersion is evidently a mere 
number, and its magnitude is independent of the units of 
measurement emrloyed. 
26. Measures of Asymmetry or Skewness.—If we have to compare 
a series of distributions of varying degrees of asymmetry, or skew- 
ness, as Pearson has termed it, some numerical measure of this 
character is desirable. Such a measure of skewness should 
obviously be independent of the units in which we measure the 
variable—e.g. the skewness of the distribution of the weights of a 
given set of men should not be dependent on our choice of the 
pound, the stone, or the kilogramme as the unit of weight—and 
the measure should accordingly be a mere number. Thus the 
difference between the deviations of the two quartiles on either 
side of the median indicates the existence of skewness, but to 
measure the degree of skewness we should take the ratio of this