An Introduction to the theory of statistics

Gesetz betreffend Kinderarbeit in gewerblichen Betrieben

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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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

XI.—CORRELATION : MISCELLANEOUS THEOREMS. 223 For the birth-rate, on the other hand, assuming that o,/@ is approximately the same for the decade 1881-90 as in 1891, we have, o, being 4:08, 32-34 — 30:34 459 ol 50d = 4 40, The closeness of the numerical values of # in the two cases is, of course, accidental. 18. The principle of weighting finds one very important application in the treatment of such rates as death-rates, which are largely affected by the age and sex-composition of the popula- tion. Neglecting, for simplicity, the question of sex, suppose the numbers of deaths are noted in a certain district for, say, the age-groups 0-, 10-, 20, ete., in which the fractions of the whole population are pg, p,, p,, etc, where 2(p)=1. Let the death- rates for the corresponding age-groups be dy, d,, dy, ete. Then the ordinary or crude death-rate for the district is D=3(d.p) i (16) For some other district taken as a basis of comparison, perhaps the country as a whole, the death-rates and fractions of the population in the several age-groups may be 6, 8,8; . . . , m 7, ms « « + , and the crude death-rate A=3(5.7) x (17) Now D and A may differ either because the @’s and &'s differ or because the p’s and =’s differ, or both. It may happen that really both districts are about equally healthy, and the death- rates approximately the same for all age-classes, but, owing to a difference of weighting, the first average may be markedly higher than the second, or wvice vers. If the first district be a rural district and the second urban, for instance, there will be a larger proportion of the old in the former, and it may possibly have a higher crude death-rate that the second, in spite of lower death- rates in every class. The comparison of crude death-rates is therefore liable to lead to erroneous conclusions. The difficulty may be got over by averaging the age-class death-rates in the district not with the weights Py Po pp - - . . given by its own population, but with the weights, mT, Ty Ty . . . . given by the population of, the standard district. The standardised death rate for the district will then be D' =3(d.w) 18)

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