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

VII.—MEASURES OF DISPERSION, ETC. 147 We pointed out in § 10 that in distributions of the simple forms referred to, a range of six times the standard deviation contains over 99 per cent. of all the observations. If the mean deviation be employed as the measure of dispersion, we must substitute a range of 71 times this measure. 20. The Quartile Deviation or Semi-interquartile Range.—1If a value @, of the variable be determined of such magnitude that one-quarter of all the values observed are less than ¢, and three- quarters greater, then , is termed the lower quartile. Similarly, if a value ; be determined such that three-quarters of all the values observed are less than @, and one-quarter only greater, then (J), is termed the upper quartile. The two quartiles and the median divide the observed values of the variable into four classes of equal frequency. If M7 be the value of the median, in a symmetrical distribution Me —- Q,=Q, - I, and the difference may be taken as a measure of dispersion. But as no distribution is rigidly symmetrical, it is usual to take as the measure 0-924, and @ is termed the quartile deviation, or better, the semi- interquartile range—it is not a measure of the deviation from any particular average: the old name probable error should be confined to the theory of sampling (Chap. XV. § 17). 21. In the case of a short series of ungrouped observations the quartiles are determined, like the median, by inspection. In the wage statistics of Example i., for instance, there are 38 observations, and 38/4=9'5: What is the lower quartile ? The student may be tempted to take it halfway between the ninth and tenth observations from the bottom of the list; but this would be wrong, for then there would be nine observations only below the value chosen instead of 95. The quartile must be taken as given by the tenth observation itself, which may be regarded as divided by the quartile, and falling half above it and half below. Therefore Lower quartile @Q, = 14s. 10d. Upper quartile Q,= 16s. 11d. Q;-¢ and Q= Lgl = 12-54, 22. In the case of a grouped distribution, the quartiles, like the median, are determined by simple arithmetical or by -

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