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

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

i= THEORY OF STATISTICS. i.e. the geometric mean of the numbers given by the two censuses. This result must, however, be used with discretion. The rate of increase of population is not necessarily, or even usually, constant over any considerable period of time: if it were so, a curve representing the growth of population as in fig. 24 would be continuously convex to the base, whether the population were increasing or decreasing. In the diagram it will be seen that the curves are frequently concave towards the base, and similar results will often be found for districts in which the population is not increasing very rapidly, and from which there is much emigration. Further, the assumption is not self-consistent in any case in which the rate of increase is not uniform over the entire area—and almost any area can be analysed into parts which are not similar in this respect. For if in one part of the area considered the initial population is P, and the common ratio R, and in the remainder of the area the initial population is p, and the common ratio r, the population in year = is given by Pt p,= Po B+ por”. This does not represent a constant rate of increase unless B=. If then, for example, a constant percentage rate of increase be assumed for England and Wales as a whole, it cannot be assumed for the Counties: if it be assumed for the Counties, it cannot be assumed for the country as a whole. The student is referred to refs. 14, 15 for a discussion of methods that may be used for the consistent estimation of populations under such circumstances. - 25. The property of the geometric mean illustrated by equation (13) renders it, in some respects, a peculiarly convenient form of average in dealing with ratios, 7.e. “index-numbers,” as they are termed, of prices. Let Kon wo i val EX i te Xn ) denote the prices of &/ commodities in the years 0,1, 2 . . . Further, let ¥,,=X,/X,, and so on, so that Y' 10 Yi Y 4 dele TT, Yop Yop Yop + + + + Yn represent the ratios of the prices of the several commodities in years 1, 2, . . . to their prices in year 0. These ratios, in practice multiplied by 100, are termed index-numbers of the prices of the several commodities, on the year 0 as base. Evidently some +26

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