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

! 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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