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 III. Theory of sampling

Collection:: Economics Books

3323 THEORY OF STATISTICS. rucians, or Table IV., ref. 16, in Appendix I.) gives the values directly, and these have been utilised for tle following : the student can estimate the values roughly by a combined use of the area and ordinate tables for the normal curve given in Chapter XV., remembering to divide the ordinates given in that table by J/27 50 as to make the area unity— Value of 3, Median . . 0-3989423 Deciles 4 and 6 . 03863425 9. oand 7 : v ; 0:3476926 si and 8 : : 0-2799619 sit sliand 9 . . 01754983 Quartiles ; 03177766 Inserting these values of y, in equation (1), we have the following values for the standard errors of the median, deciles, etc., and the values given in the second column for their probable errors (Chap. XV. § 17), which the student may sometimes find useful :— Standard error is Probable error is o/Nn multiplied by o/Nn multiplied by Median : . 125331 084535 Deciles 4 and 6 . 1-26804 0-85528 ni 9 and THE . 1:31800 0-88897 yw £2 and 3H 1-42877 0:96369 yw Sl and 1-70942 1-15298 Quartiles . 1-36263 0-91908 It will be seen that the influence of fluctuations of sampling on the several percentiles increases as we depart from the median: the standard error of the quartiles is nearly one-tenth greater than that of the median, and the standard error of the first or ninth deciles more than one-third greater. 5. Consider further the influence of the form of the frequency- distribution on the standard error of the median, as this is an important form of average. For a distribution with a given number of observations and a given standard-deviation the standard error varies inversely as y,. Hence for a distribution in which y, is small, for example a U-shaped distribution like that of fig. 18 or fig. 19, the standard error of the median will be relatively high, and it will, in so far, be an undesirable form of average to employ. On the other hand, in the case of a distribu- tion which has a high peak in the centre, so as to exhibit a value of y, large compared with the standard-deviation, the standard error of the median will be relatively low. We can create such a . LN

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