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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

- THEORY OF STATISTICS. perimental verification of these results. The following will serve as illustrations, but the student is strongly recommended to carry out a few series of such experiments personally, in order to acquire confidence in the use of the theory. It may be as well to remark that if ordinary commercial dice are to be used for the trials, care should be taken to see that they are fairly true cubes, and the marks not cut very deeply. Cheap dice are generally very much out of truth, and if the marks are deeply cut the balance of the die may be sensibly affected. A convenient mode of throwing a number of dice, suggested, we believe, by the late Professor Weldon, is to roll them down an inclined gutter of corrugated paper, so that they roll across the corrugations. (1) (W. F. R. Weldon, cited by Professor F. Y. Edgeworth, Encycl. Brit., 11th edn., vol. xxii. p. 394. Totals of the columns in the table there given.) Twelve dice were thrown 4096 times ; a throw of 4, 5, or 6 points reckoned a success, therefore p=¢=0'5. Theoretical mean //=6 ; Pe value of the standard-deviation oj, = #/05 x 0:5 x 12 = 1-732. The following was the frequency-distribution observed :— Successes. Frequency. ! Successes. Frequency. 0 Ro 7 847 7 3 536 - 60 9 257 v 198 10 71 430 11 11 ae 731 12 —_ b a Total 4096 Mean M = 6-139, standard-deviation ¢=1-712. The proportion of successes is 6:139/12=0512 instead of 0-5. (2) (W. F. R. Weldon, loc. cit., p. 400. Totals of columns of the table given.) Twelve dice were thrown 4096 times; only a throw of 6 was counted a success, so p=1/6, ¢=>5/6. Theoretical mean M=2, standard-deviation o = /1/6 x 5/6 x 12 =1-291. The following was the observed frequency-distribution :— Successes. Frequency. Successes. Frequency. 0 447 5 115 1 1145 6 24 a 1181 ( 7 J 796 8 1 : 380 Total 4096 258

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