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

XIIL—SIMPLE SAMPLING OF ATTRIBUTES. ) albinos were obtained in 121 litters from hybrids of Japanese waltzing mice by albinos, crossed inter se (A. D. Darbishire, Biometrika, iii. p. 30): — Percentage. Frequency. Percentage. Frequency. L 40 2 LE 43 2 WI 50 16 20 oi 22 60 25 - ul 29 &0 33 100 The distribution is very irregular owing to the small numbers in the litters, and the standard-deviation is 23-09 per cent. The numbers of litters of different sizes were given in § 27 of Chap. VII. p. 128, and the harmonic mean size of litter was found to be 3:03. The expected proportion of albinos is 25 per cent., and hence the standard-deviation of sampling is 25 x T5\! (S55) =205 in very close agreement with the actual value. The proportion of albinos amongst all the offspring together was 24-7 per cent. 12. If one of the two proportions » and ¢ become very small, equation (1) may be put into an approximate form that is very useful. Suppose p to be the proportion that becomes very small, so that we may neglect p2 compared with p: then Pq =p —p*=p approximately, and consequently we have approximately on= nnp= JM (4) That is to say, if the proportion of successes be small, the standard-deviation of the number of successes is the square root of the mean number of successes. Hence we can find the standard- deviation of sampling even though p be unknown, provided only we know that it is small. Thus (ref. 15) in 10 Prussian army corps in 20 years (1875- 1894) there were 122 men killed by the kick of a horse, or, on an average, there were 0-61 deaths from that cause in each army corps annually. From equation (4) we accordingly have for the standard-deviation of simple sampling o=(061)!=0178, 26%

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