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

CHAPTER VIL AVERAGES. 1. Necessity for quantitative definition of the characters of a frequency- distribution—2. Measures of position (averages) and of dispersion—s3. The dimensions of an average the same as those of the variable—4. Desirable properties for an average to possess—5. The commoner forms of average—6-13. Thearithmetic mean : its definition, calculation, and simpler properties—14-18. The median : its definition, calculation, and simpler properties—19-20. The mode: its definition and relation to mean and median—21. Summary comparison of the preceding forms of average—22-26. The geometric mean: its definition, simpler pro- perties, and the cases in which it is specially applicable—27. The harmonic mean : its definition and calculation, 1. IN § 2 of the last chapter it was pointed out that a classification of the observations in any long series is the first step necessary to make the observations comprehensible, and to render possible those comparisons with other series which are essential for any discussion of causation. Very little experience, however, would show that classification alone is not an adequate method, seeing that it only enables qualitative or verbal comparisons to be made. The next step that it is desirable to take is the quantitative definition of the characters of the frequency-distribution, so that quantitative comparisons may be made between the corresponding characters of two or more series. It might seem at first sight that very difficult cases of comparison could arise in which, for example, we had to contrast a symmetrical distribution with a “J- shaped ” distribution. As a matter of practice, however, we seldom have to deal with such a case; distributions drawn from similar material are, in general, of similar form. When we have to compare the frequency-distributions of stature in two races of man, of the death-rates in English registration districts in two successive decades, of the numbers of petals in two races of the same species of Ranunculus, we have only to compare with each other two distributions of the same or nearly the same type. 9. Confining our attention, then, to this simple case, there are two fundamental characteristics in which such distributions may 106

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