CHAPTER VIIL
MEASURES OF DISPERSION, ETC.
1. Inadequacy of the range as a measure of dispersion—2-13. The standard
deviation : its definition, calculation, and properties—14-19. The
mean deviation : its definition, calculation, and properties—20-24, The
quartile deviation or semi-interquartile range—25. Measures of
relative dispersion—26. Measures of asymmetry or skewness—27-30.
The method of grades or percentiles.
1. THE simplest possible measure of the dispersion of a series of
values of a variable is the actual range, i.e. the difference between
the greatest and least values observed. While this is frequently
quoted, it is as a rule the worst of all possible measures for any
serious purpose. There are seldom real upper and lower limits
to the possible values of the variable, very large or very small
values being only more or less infrequent : the range is therefore
subject to meaningless fluctuations of considerable magnitude
according as values of greater or less infrequency happen to
have been actually observed. Note, for instance, the figures of
Table IX., Chap. VL p. 95, showing the frequency distributions of
weights of adult males in the several parts of the United King-
dom. In Wales, one individual was observed with a weight of
over 280 lbs., the next heaviest being under 260 lbs. The
addition of the one very exceptional individual has increased th~
range by some 30 lbs., or about one-fifth. A measure subject to
erratic alterations by casual influences in this way is clearly not
of much use for comparative purposes. Moreover, the measure
takes no account of the form of the distribution within the limits
of the range; it might well happen that, of two distributions
covering precisely the same range of variation, the one showed
the observations for the most part closely clustered round the
average, while the other exhibited an almost even distribution of
frequency over the whole range. Clearly we should not regard
two such distributions as exhibiting the same dispersion, though
they exhibit the same range. Some sort of measure of dispersion
is therefore required, based, like the averages discussed in the last
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