An Introduction to the theory of statistics

Bibliographic data

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

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

9 THEORY OF STATISTICS. that, in a proportion (7, —r,)/r; of all the pairs, the bones do not really belong to the same skeleton, and have been virtually paired at random. (For a more general form of the theorem cf. again ref. 20.) 14. The Weighted Mean.—The arithmetic mean M of a series of values of a variable X was defined as the quotient of the sum of those values by their number #, or M=3(X)/N. If, on the other hand, we multiply each several observed value of X by some numerical coefficient or weight W, the quotient of the sum of such products by the sum of the weights is defined as a weighted mean of X, and may be denoted by 4", so that M=3(W.X)/3(D). The distinction between «weighted ” and ““ unweighted ” means is, it should be noted, very.often formal rather than essential, for the “weights” may be regarded as actual, estimated, or virtual frequencies. The weighted mean then becomes simply an arithmetic mean, in which some new quantity is regarded as the unit. Thus if we are given the means M;, My, MU, . . . . M, of r series of observations, but do not know the number of observations in every series, we may form a general average by taking the arithmetic mean of all the means, viz. 2(J/)/r, treating the series as the unit. But if we know the number of observations in every series it will be better to form the weighted mean Z(NM)/S(N), weighting each mean in proportion to the number of observations in the series on which it is based. The second form of average would be quite correctly spoken of as a weighted mean of the means of the several series: at the same time it is simply the arithmetic mean of all the series pooled together, z.e. the arithmetic mean obtained by treating the observation and not the series as the unit. (Chap. VIL § 13.) 15. To give an arithmetical illustration, if a commodity is sold at different prices in different markets, it will be better to form an average price, not by taking the arithmetic mean of the several market prices, treating the market as the unit, but by weighting each price in proportion to the quantity sold at that price, if known, 7.e. treating the unit of quantity as the unit of frequency. Thus if wheat has been sold in market 4 at an average price of 29s. 1d. per quarter, in market B at an average price of 27s. 7d., and in market C at an average price of 28s. 4d., we may, if no statement is made as to the quantities sold at these prices (as very Sa ay

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation