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

140 THEORY OF STATISTICS. Means and Standard Deviations of the Distributions of Pauperism (Percentage of the Population in receipt of Poor-law Relief) in the Unions of England and Wales since 1850. (From Yule, Jour. Roy. Stat. Soc., vol. lix., 1896, figures slightly amended.) Percentage of the Population in receipt of Relief. Foor. Arithmetic Standard Mean. Deviation. 1850 6°51 2:50 1860 5:20 2:07 1870 5°45 2:02 1881 3:68 1-36 1891 3°29 1:24 8. In the table given on p. 141 (Example iii.), the calculation of the standard deviation is similarly shown for the distribution of the statures of adult males in the British Isles, the work being continued from the stage which it reached for the calculation of the mean in Example ii. of Chap. VII. The steps of the arith- metic hardly call for further explanation, but it may be noted that the class-interval being a unit in this case, no conversion of the standard deviation from class-intervals to units is required. 9. The student must remember, as in the case of the calculation of the mean, that the treatment of all values within each class- interval as if they were identical with the mid-value of the interval is an approximation and no more (¢f. Chap. VII. § 11), though, for a distribution of the symmetrical or moderately asymmetrical type with a class-interval not greater than one-twentieth or so of the range, the approximation may be a very close one. But while the value of the arithmetic mean may be either increased or decreased by grouping, in the case of distributions which are not more than slightly asymmetrical, the standard deviation of such distributions tends to be increased, and the increase is the greater the cruder the grouping. We give an approximate correction for this effect later (Chap. XI. § 4). The student is recommended to test for himself the effect of grouping in two or three cases. 10. Tt is a useful empirical rule to remember that a range of six times the standard deviation usually includes 99 per cent. or more of all the observations in the case of distributions of the symmetrical or moderately asymmetrical type. Thus in Example ~ No of L Uwe

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