Die Theorie der Volkswirtschaft

An Introduction to the theory of statistics

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Monograph

Identifikator:: 892769734

URN:: urn:nbn:de:zbw-retromon-76808

Document type:: Monograph

Author:: Maslov, Petr http://d-nb.info/gnd/123876184

Title:: Die Theorie der Volkswirtschaft

Place of publication:: Leipzig

Publisher:: Verlag von Arthur Kade

Year of publication:: 1912

Scope:: 1 Online-Ressource (VIII, 293 Seiten)

Collection:: Economics Books

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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 129

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