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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

He THEORY OF STATISTICS. deviation @/r will be regarded as the equivalent of a deviation .@, instead of a deviation —a as the equivalent of a deviation +=. If a distribution take the simplest possible form when relative deviations are regarded as equivalents, the frequency of deviations between @/s and G/r will be equal to the frequency of deviations between 7.G and s.@. The frequency-curve will then be sym- metrical round log @ if plotted to log X as base, and if there be a single mode, log @ will be that mode—a logarithmic or geometric mode, as it might be termed : @ will not be the mode if the distri- bution be plotted in the ordinary way to values of X as base. The theory of such a distribution has been discussed by more than one author (refs. 2, 8,9). The general applicability of the assump- tion made does not, however, appear to have been very widely tested, and the reasons assigned have not sufficed to bring the geometric mean into common use. It may be noted that, as the geometric mean is always less than the arithmetic mean, the fundamental assumption which would justify the use of the former clearly does not hold where the (arithmetic) mode is greater than the arithmetic mean, as in Tables X. and XI. of the last chapter. 97. The Harmonic Mean.—The harmonic mean of a series of quantities is the reciprocal of the arithmetic mean of their reciprocals, that is, if A be the harmonic mean, LL 1-131) SE = 1%) The following illustration, the result of which is required for an example in a later chapter (Chap. XIIL § 11), will serve to show the method of calculation. The table gives the number of litters of mice, in certain breeding experiments, with given numbers (X) in the litter. (Data from A. D. Darbishire, Biometrika, iii. pp. 30, 31.) Number in | Number of Litter. Litters. f1X. xX. 7: 7 7:000 1 5:500 16 5333 17 4250 26 | 5200 31 57167 11 1-571 v 0125 0-111 i 84207 .28 qn

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