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

209 THEORY OF STATISTICS. rise from one year to the next when the other rises, and a fall when the other falls. The movement of both variables is, how- ever, of a much more regular kind than that of mortality, resembling a series of “waves” superposed on a steady general trend, and it is the “waves” in the two variables—the short-period movements, not the slower trends—which are so clearly related. 16. It is not difficult, moreover, to separate the short-period oscillations, more or less approximately, from the slower movement. Suppose the marriage-rate for each year replaced by the average of an odd number of years of which it is the centre, the number being as near as may be the same as the period of the “waves ”— e.g. nine years. If these short-period averages were plotted on the diagram instead of the rates of the individual years, we should evidently obtain a smoother curve which would clearly exhibit the trend and be practically free from the conspicuous waves. The excess or defect of each annual rate above or below the trend, if plotted separately, would therefore give the * waves?” apart from the slower changes. The figures for foreign trade may be treated in the same way as the marriagerate, and we can accordingly work out the correlation between the waves or rapid fluctuations, undisturbed by the movements of longer period, however great they may be. The arithmetic may be carried out in the form of the following table, and the correlation worked out in the ordinary way between the figures of columns 4 and 7. L 2. 3. 4. 5. 6. . Marriage-rate Nine Differ. Exports+Im- Nine Differ- . d Years’ ts, £ Years’ Zan lf Uridine Rei snr Ye GEES 1855 16-2 — - 9:36 - — 1856 167 — - 11-14 — -_ 1857 16' = 4 1185 — Z 1858 160 » 10-73 — LY 1859 17:0 16'6 +0'5 11-72 12°15 -043 1860 1:10 1 116 +05 13:03 12°94 +009 1861 16:3 167 “ut 13:01 13-52 -051 1862 1610 l163 — 1340 14°17 -077 1863 16:8 169 : 1513 14:31 40°32 1864 172 = 1643 g 1865 175 8 16°37 - 1866 176 - 1772 - 1867 165 : 16°47 - 17. Fig. 43 is drawn from the figures of columns 4 and 7, and shows very well how closely the oscillations of the marriage-rate are related to those of trade. For the period 1861-95 the correlation between the two oscillations (Hooker, ref. 5) is 0-86. The method may obviously be extended by correlating the devia

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