An Introduction to the theory of statistics

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Monograph

Identifikator:: 1011193744

URN:: urn:nbn:de:zbw-retromon-34323

Document type:: Monograph

Title:: Die wirtschaftlichen Beziehungen zwischen Russisch-Polen und dem Deutschen Reiche und die sich daraus für den Friedensschluss ergebenden Folgerungen

Edition:: Als Handschrift gedruckt, streng vertaulich, nicht für die Presse

Place of publication:: Oppeln

Publisher:: Druck von Erdmann Raabe

Year of publication:: 1915

Scope:: 1 Online-Ressource (91 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Schlußfolgerungen

Collection:: Economics Books

! THEORY OF STATISTICS. (or median), in a grouped frequency-distribution, is found to be S. Find the correction to be applied to this sum, in order to reduce it to the mean (or median) as origin, on the assumption that the observations are evenly dis- tributed over each class-interval. Take the number of observations below the interval containing the mean (or median) to be n;, in that interval =, and above it my; and the distance of the mean (or median) from the arbitrary origin to be d. Show that the values of the mean deviation (from the mean and from the median respectively) for Example ii., found by the use of this formula, do not differ from the values found by the simpler method of §§ 16 and 17 in the second place of decimals. 8. (W. Scheibner, “Ueber Mittelwerthe,” Berichte der kgl. sdchsischen Gesellschaft d. Wissenschaften, 1873, p. 564, cited by Fechner, ref. 2 of Chap. VIL : the second form of the relation is given by G. Duncker (Die Methode der Variationsstatistik ; Leipzig, 1899) as an empirical one.) Show that if deviations are small compared with the mean, so that (2/2/)® may be neglected in comparison with z/J, we have approximately the relation a? e=1(1-1] 7): where @ is the geometric mean, J the arithmetic mean, and ¢ the standard deviation : and consequently to the same degree of approximation M2 - G2=42 9. (Scheibner, loc. cit., Qu. 8.) Similarly, show that if deviations are small compared with the mean, we have approximately . 2 eri) H being the harmonic mean. 156

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