An Introduction to the theory of statistics

Bibliographic data

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

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

XVIL.—SIMPLER CASES OF SAMPLING FOR VARIABLES. 337 in a very large sample,” the phrases “the standard-deviation of X in the original record,” “the form of the frequency-distribution in the original record”: but in very many, perhaps the majority of, practical cases the very question at issue is the nature of the relation between the distribution of the sample and the distribu- tion of the record from which it is drawn. As has already been emphasised in the passages to which reference is made above, no examination of samples drawn under the same conditions can give any evidence on this head. 3. Standard Error of a Percentile.—Let us consider first the fluctuations of sampling for a given percentile, as the problem is intimately related to that of Chaps. XIII.-XIV, Let X, be a value of X such that pN of the values of X in an indefinitely large sample drawn under the same conditions lie above it and ¢V below it. If we note the proportions of observations above X, in samples of » drawn from the record, we know that these observed values will tend to centre round p as mean, with a standard-deviation Vpg/n. If now at each drawing, as well as observing the pro- portion of X's above X,, say p +9, for the sample, we also proceed to note the adjustment e required in X, to make the proportion of observations above X,+e¢ in the sample p, the standard- deviation of e€ will bear to the standard-deviation of 8 the same ratio that e on an average bears to 4. But this ratio is quite simply determinable if the number of observations in the sample is sufficiently large to justify us in assuming that § is small—so small that we may regard the element of the frequency curve (for a very large sample) over which X, + e ranges as approximately a rectangle. If this assumption be made, and we denote the standard-deviation of X in a very large sample by o, and the ordinate of the frequency curve at X, when drawn with unit area and unit standard-deviation by z,, e=".3 2, Therefore for the standard-deviation of e or of the percentile corresponding to a proportion p we have A Iz, = > n a (1) 4. If the frequency-distribution for the very large sample be a normal curve, the values of y, for the principal percentiles may be taken from the published tables. A table calculated by Mr Sheppard (Table IIL, p. 9, in Zables for Statisticians and Biomet- Ory ah

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation