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

Te THEORY OF STATISTICS. Stirling (1730). If n be large, we have, to a high degree of approximation, |n= 20m se Applying Stirling’s theorem to the factorials in equation (1) we have Hy 5 heh ime 5) The complete expression for the normal curve is therefore FE 7 Nor. : (6) The exponent may be written 22/c2 where c= v2.0, and this is the origin of the use of 2 xo (the “modulus ”) as a measure of dispersion, of 1/ 2.0 as a measure of “precision,” and of 20? as “the fluctuation” (¢f. Chap. VIIL § 13). The use of the factor 2 or a/2 becomes meaningless if the distribution be not normal. Another rule cited in Chap. VIIL, viz. that the mean deviation is approximately 4/5 of the standard-deviation, is strictly true for the normal curve only. For this distribution the mean deviation =o N/2/r=0-79788 . . .. 0: the proof cannot be given within the limitations of the present work. The rule that a range of 6 times the standard-deviation includes the great majority of the observations and that the quartile deviation is about 2/3 of the standard-deviation were also suggested by the properties of this curve (see below §§ 16, 17). 12. In the proof of § 9 the assumption was made that % (the half of the exponent of the binomial) was very large compared with # (any deviation that had to be considered). In point of fact, however, the normal curve gives the terms of the symmetrical binomial surprisingly closely even for moderate values of n. Thus if »=064, k=32, and the standard-deviation is 4. Deviations # have therefore to be considered up to +12 or more, which is over 1/3 of k As will be seen, however, from the annexed table, the ordinates of the normal curve agree with those of the binomial to the nearest unit (in 10,000 observations) up to z= +15. The closeness of approximation is partly due to the fact that, in applying the logarithmic series to the fraction on the right of equation (3), the terms of the second order in expansions of corresponding brackets in numerator and denominator cancel each other: these terms, therefore, do not 304

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