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

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

264 THEORY OF STATISTICS. The student should note that in both cases the standard-devia- tions given are standard-deviations of the proportion of male births per 1000 of all births, that is, 1000 times the values given by equation (2). These values are given by simply substituting the proportions per 1000 for p and ¢ in the formula. Thus for the first column of Table I. the proportion of males is 508 per 1000 births, the mid-number of births 2000, and therefore— 508 x 492\} w=("go00) =112 11. In the above illustration the difficulty due to the wide variation in the number of births in different districts has been surmounted by grouping these districts in limited class intervals, and assuming that it would be sufficiently accurate for practical purposes to treat all the districts in one class as if the sex-ratios had been based on the mid-numbers of births. Given a sufficiently large number of observations, such a process does well enough, though it is not very good. But if the number of observations does not exceed, perhaps, 50 or 60 altogether, grouping is obviously out of the question, and some other procedure must be adopted. Suppose, then, that a series of samples have been taken from the same material, /; samples containing n, individuals or observa- tions each, f, containing n,, Js containing nm, and so on: What would be the standard-deviation of the observed proportions in these samples! Evidently the square of the standard-deviation in the first group would be pq/ny, in the second pg/n,, and so on: therefore, as the means tend to the same values in all the groups, we must have for the whole series— Fmpg(D4 Ler lay : 7 n,n, But if H be the harmonic mean of ny, Ny By eh Bale Zn, nyt, and accordingly g=t0, (5) That is to say, where the number of observations varies from one sample to another, the harmonic mean number of observations in a sample must be substituted for n in equation (2). Thus the following percentages (taken to the nearest unit) of

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