An Introduction to the theory of statistics

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Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

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

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