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

XV.—BINOMIAL DISTRIBUTION AND NORMAL CURVE. 295 If p=q the effect of increasing m is to raise the mean and increase the dispersion. If p is not equal to ¢, however, not only does an increase in mn raise the mean and increase the dispersion, but it also lessens the asymmetry; the greater n, for the same value of p and ¢, the less the asymmetry. Thus if we compare the first distribution of the above table with that given by »=100, we have the following :— B.—Terms of the Binomial Series 10,000 (0'9 + 0-1), (Figures given to the nearest unit.) Number Number Number 01 Frequency. of Frequency. of Frequency. Successes. Successes. Successes. y — : 1148 15 193 3 1304 17 106 16 1 1319 83 54 59 1 1199 | 13 2. IX E1508 [& £12 988 | 2) I 339 | 13 743 21 596 1% 513 24 ’29 £7 : The maximum frequencies now occur for 9 and 10 successes, and the two “tails” are much more nearly equal. If, on the other hand, n is reduced to 2, the distribution is— Number of Successes, Frequency. 8100 1800 100 and the maximum frequency is at one end of the range. What- ever the values of p and ¢, if » is only increased sufficiently, the distribution may be treated as sensibly symmetrical, the necessary condition being (we state this without proof) that p —¢ shall be small compared with the standard-deviation npg. It is left to the student to calculate as an exercise the theoretical distribu- tions corresponding to the experimental results cited in Chapter XIII. (Question 1). 4. The property of the binomial series used in the scheme of § 2 for deducing the series with exponent » from that with exponent n-1 leads to two interesting methods—graphical and mechanical — for constructing approximate representations of

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