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

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CONTENTS, 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 disiribution—3. Dependence of the form of the distribution on p, ¢, and n— 4-5. Graphical and mechanical methods of forming re- presentations 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 approxi- mately, 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 distribution for a moderate value of n—18. 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 of a 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 . . 291-316 CHAPTER XVL NORMAL CORRELATION. 1-3. Deduction of the general expression for the normal correlation surface from the case of independence—4. Constancy of the standard-deviations of parallel arrays and linearity of the regression—5. The contour lines : a series of concentric and similar ellipses—6. The normal surface for two correlated variables regarded as a normal surface for uncorrelated vari- ables rotated with respect to the axes of measurement: arrays taken at any angle across the surface are normal distributions with constant standard-deviation : distribution of and correlation between linear functions of two normally correlated variables are normal : principal axes—7. Standard- deviations round the principal axes—8-11. Investigation of Table III., Chapter IX., to test normality: linearity of regression, constancy of standard-deviation of arrays, normality of distribution obtained by diagonal addition, contour lines—12-13. Isotropy of the normal distribution for two variables—14. Outline of the principal properties of the normal distribution for n variables . , 317-334 X1V PAGE

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