L' Allemagne économique ou histoire du Zollverein Allemand

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1014011027

URN:: urn:nbn:de:zbw-retromon-25942

Document type:: Monograph

Author:: Prion, Willi http://d-nb.info/gnd/101278861

Title:: Der Wirtschaftsbetrieb als Betrieb (Arbeit)

Place of publication:: Berlin

Publisher:: Verlag von Julius Springer

Year of publication:: 1936

Scope:: 1 Online-Ressource (VII, 240 Seiten)

Digitisation:: 2018

Collection:: Business and Management Classics

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: A. Die Grundlagen

Collection:: Business and Management Classics

VIIL.—MEASURES OF DISPERSION, ETC. 145 The new mean deviation is accordingly less than the old so long as m>31N. That is to say, if NV be even, the mean deviation is constant for all origins within the range between the &/2th and the (4/2 + 1)th observations, and this value is the least: if & be odd, the mean deviation is lowest when the origin coincides with the (& + 1)/2th observation. The mean deviation is therefore a minimum when deviations are measured from the median or, if the latter be indeterminate, from an origin within the range in which it lies. 15. The calculation of the mean deviation either from the mean or from the median for a series of ungrouped observations is very simple. Take the figures of Example i. (p. 137) as an illustration. We have already found the mean (15s. 11d. to the nearest penny), and the deviations from the mean are written down in column 3. Adding up this column without respect to the sign of the devi- ations we find a total of 590. The mean deviation from the mean is therefore 590/38=15'53d. The mean deviation from the median is calculated in precisely the same way, but the median replaces the mean as the origin from which deviations are measured. The median is 15s. 6d. The deviations in pence run 63, 57, 50, 36, and so on; their sum is 570; and, accordingly, the mean deviation from the median is 15d. exactly. 16. In the case of a grouped frequency-distribution, the sum of deviations should be calculated first from the centre of the class-interval in which the mean (or median) lies, and then reduced to the mean as origin. Thus in the case of Example ii. the mean is 3:29 per cent. and lies in the class-interval centring round 3-5 per cent. We have already found that the sum of deviations in defect of 3-5 per cent. is 776, and of deviations in excess 509: total (without regard to sign) 1285,—the unit of measurement being, of course, as it is necessary to remember, the class-interval. If the number of observations below the mean is N, and above the mean N,, and M — 4 =d, as before, we have to add X,.d to the sum found and subtract N,d. In the present case N,=327 and N,=305, while d= — 0-42 class-intervals, therefore dN, -Ny)= -042x22=-92, and the sum of deviations from the mean is 1285 — 9:2 = 12758. Hence the mean deviation from the mean is 1275-8/632 =2019 class-intervals, or 1-01 per cent. 17. The mean deviation from the median should be found in precisely similar fashion, but the mid-value of the interval in which the median (instead of the mean) lies should, for con- 10 a bu

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