An Introduction to the theory of statistics

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Monograph

Identifikator:: 1753210836

URN:: urn:nbn:de:zbw-retromon-128414

Document type:: Monograph

Author:: Nogaro, Bertrand http://d-nb.info/gnd/117039713

Title:: Modern monetary systems

Place of publication:: London

Publisher:: King

Year of publication:: 1927

Scope:: XII, 236 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The explanation of contemporary monetary phenomena and currency theory

Collection:: Economics Books

THEORY OF STATISTICS. 4. (a) In the first place, it almost goes without saying that an average should be rigidly defined, and not left to the mere estimation of the observer. An average that was merely estimated would depend too largely on the observer as well as the data. (b) An average should be based on all the observations made. If not, it is not really a characteristic of the whole distribution. (c) It is desirable that the average should possess some simple and obvious properties to render its general nature readily compre- hensible : an average should not be of too abstract a mathematical character. (d) It is, of course, desirable that an average should be calculated with reasonable ease and rapidity. Other things being equal, the easier calculated is the better of two forms of average. At the same time too great weight must not be attached to mere ease of calculation, to the neglect of other factors. (e) It is desirable that the average should be as little affected as may be possible by what we have termed fluctuations of sampling. If different samples be drawn from the same material, however carefully they may be taken, the averages of the different samples will rarely be quite the same, but one form of average may show much greater differences than another. Of the two forms, the more stable is the better. The full discussion of this condition must, however, be postponed ‘to a later section of this work (Chap. XVIL). (f) Finally, by far the most important desideratum is this, that the measure chosen shall lend itself readily to algebraical treatment. If, e.g., two or more series of observations on similar material are given, the average of the combined series should be readily expressed in terms of the averages of the component series : if a variable may be ‘expressed as the sum of two or more others, the average of the whole should be readily expressed in terms of the averages of its parts. A measure for which simple relations of this kind cannot be readily determined is likely to prove of somewhat limited application. 5. There are three forms of average in common use, the arithmetic mean, the median, and the mode, the first named being by far the most widely used in general statistical work. To these may be added the geometric mean and the harmonic mean, more rarely used, but of service in special cases. We will con- sider these in the order named. 6. The arithmetic mean.—The arithmetic mean of a series of values of a variable X;, X,, X;, . .. X,, & in number, is the quotient of the sum of the values by their number. That is to say, if M be the arithmetic mean, M= 3 (X; + Xt Xt itis: Fn) 108

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