Stock dividends

An Introduction to the theory of statistics

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Monograph

Identifikator:: 175754061X

URN:: urn:nbn:de:zbw-retromon-136496

Document type:: Monograph

Title:: Stock dividends

Place of publication:: Washington

Publisher:: U.S. Gov. Print. Off.

Year of publication:: 1927

Scope:: vii, 273 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: [Appendix]

Collection:: Economics Books

VIL—AVERAGES, 129 Whence, 1/7 =02831, //=3'532. The arithmetic mean is 4'587, or more than a unit greater, If the prices of a commodity at different places or times are stated in the form “so much for a unit of money,” and an average price obtained by taking the arithmetic mean of the quantities sold for a unit of money, the result is equivalent to the harmonic mean of prices stated in the ordinary way. Thus retail prices of eggs were quoted before the War as “so many to the shilling.” Supposing we had 100 returns of retail prices of eggs, 50 returns showing twelve eggs to the shilling, 30 fourteen to the shilling, and 20 ten to the shilling; then the mean number per shilling would be 12:2, equivalent to a price of 0-984d. per egg. But if the prices had been quoted in the form usual for other com- modities, we should have had 50 returns showing a price of 1d. per egg, 30 showing a price of 0-857d., and 20 a price of 1-2d.: arithmetic mean 0'997d., a slightly greater value than the har- monic mean of 0°984. The official returns of prices in India were, until 1907, given in the form of “Sers (2:057 Ibs.) per rupee.” The average annual price of a commodity was based on half- monthly prices stated in this form, and “index-numbers” were calculated from such annual averages. In the issues of Prices and Wages in India” for 1908 and later years the prices have been stated in terms of “rupees per maund (82286 1bs.).” The change, it will be seen, amounts to a replacement of the harmonic by the arithmetic mean price. The harmonic mean of a series of quantities is always lower than the geometric mean of the same quantities, and, & fortior, lower than the arithmetic mean, the amount of difference depend- ing largely on the magnitude of the dispersion relatively to the magnitude of the mean. (Cf. Question 9, Chap. VIIL) REFERENCES. General. (1) FEcENER, G. T. “Ueber den Ausgangswerth der kleinsten Abweich- ungssumme, dessen Bestimmung, Verwendung und Verallgemein- erung,” Abh. d. kgl. sdchsischen Gesellschaft d. Wissenschaften, vol. xviii, (also numbered xi. of the 4Abk. d. math.-phys. Classe); Leipzig (1878), p. 1. (The average defined as the origin from which the dispersion, measured in one way or another, is a minimum : geometric mean dealt with incidentally, pp. 13-16.) (2) FECHNER, G. T., Kollektivmasslehre, herausgegeben von G. F. Lipps; Engelmann, Leipzig, 1897. (Posthumously published: deals with frequency-distributions, their forms, averages, and measures of dis- persion in general : includes much of the matter of (1).) (8) Z1zER, FRANZ, Die statistischen Mittelwerthe; Dunckerund Humblot, Leipzig, 1908 : English translation, Statistical Averages, translated with addi- tional notes, etc., by W. M. Persons, Holt & Co., New York,1913. (Non- mathematical, but useful to the economic student for references cited.) J

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