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 III. Theory of sampling

Collection:: Economics Books

CHAPTER XV. THE BINOMIAL DISTRIBUTION AND THE NORMAL CURVE. 1-2. Determination of the frequency-distribution for the number of successes in n events: the binomial distribution—3. Dependence of the form of the distribution on p, ¢ and n—4-5. Graphical and mechanical methods of forming representations of the binomial distribution— 6. Direct calculation of the mean and the standard-deviation from the distribution—7-8. Necessity of deducing, for use in many practical cases, a continuous curve giving approximately, for large values of n, the terms of the binomial series—9. Deduction of the normal curve as a limit to the symmetrical binomial—10-11. The value of the central ordinate—12. Comparison with a binomial dis- tribution for a moderate value of n—13. Outline of the more general conditions from which the curve can be deduced by advanced methods— 14. Fitting the curve to an actual series of observations—15, Difficulty ofa complete test of fit by elementary methods— 16. The table of areas of the normal curve and its use—17. The quartile deviation and the ‘“ probable error ”—18. Illustrations of the application of the normal curve and of the table of areas. 1. In Chapters XIII. and XIV. the standard-deviation of the number of successes in n events was determined for the several more important cases, and the applications of the results indicated. For the simpler cases of artificial chance it is possible, however, to go much further, and determine not merely the standard-deviation but the entire frequency-distribution of the number of successes.” This we propose to do for the case of “simple sampling,” in which all the events are completely independent, and the chances » and q the same for each event and constant throughout the trials. The case corresponds to the tossing of ideally perfect coins (homo- geneous circular discs), or the throwing of ideally perfect dice (homogeneous cubes). 2. If we deal with one event only, we expect in IV trials, Ng failures and Np successes. Suppose we how combine with the results of this first event the results of a second. The two events are quite independent, and therefore, according to the rule of 291

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