Kritische Geschichte der Nationalökonomie und des Socialismus

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Monograph

Identifikator:: 83457490X

URN:: urn:nbn:de:zbw-retromon-77841

Document type:: Monograph

Author:: Dühring, Eugen http://d-nb.info/gnd/118527797

Title:: Kritische Geschichte der Nationalökonomie und des Socialismus

Edition:: 2., theilw. umgearb. Aufl.

Place of publication:: Berlin

Publisher:: Grieben

Year of publication:: 1875

Scope:: 1 Online-Ressource (XII, [1] Bl., 595 S.)

Collection:: Economics Books

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

Document type:: Monograph

Structure type:: Contents

Collection:: Economics Books

144 THEORY OF STATISTICS. sampling. On the other hand, it may be said that its general nature is not very readily comprehended, and that the process of squaring deviations and then taking the square root of the mean seems a little involved. The student will, however, soon surmount this feeling after a little practice in the calculation and use of the constant, and will realise, as he advances further, the advantages that it possesses. Such root-mean-square quantities, it may be added, frequently occur in other branches of science. The standard deviation should always be used as the measure of disper- sion, unless there is some very definite reason for preferring another measure, just as the arithmetic mean should be used as the measure of position. It may be added here that the student will meet with the standard deviation under many different names, of which we have adopted the most recent (due to Pearson, ref. 2): many of the earlier names are hardly adapted to general use, as they bear evidence of their derivation from the theory of errors of observation. Thus the terms “mean error” (Gauss), “error of mean square” (Airy), and “mean square error” have all been used in the same sense. The standard deviation multiplied by the square root of 2 has been termed the “modulus” (Airy),—the student will see later the reason for the adoption of the factor—-and the reciprocal of the modulus the “precision” (Lexis). For the square of the standard deviation, often required, R. A. Fisher has suggested the term variance.” 14. The Mean Deviation.—The mean deviation of a series of values of a variable is the arithmetic mean of their deviations from some average, taken without regard to their sign. The deviations may be measured either from the arithmetic mean or from the median, but the latter is the natural origin to use. Just as the root-mean-square deviation is least when deviations are measured from the arithmetic mean, so the mean deviation is least when deviations are measured from the median. For suppose that, for some origin exceeded by m values out of &, the mean deviation has a value A. Let the origin be displaced by an amount ¢ until it is just exceeded by m — 1 of the values only, t.e. until it coincides with the mth value from the upper end of the series. By this displacement of the origin the sum of devia- tions in excess of the origin is reduced by m.c, while the sum of deviations in defect of the mean is increased by (& —m)c. The new mean deviation is therefore N —m)c — me apliiopne =A ! N-2 =A + 7 - 2m)e.

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