An Introduction to the theory of statistics

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Monograph

Identifikator:: 890892032

URN:: urn:nbn:de:zbw-retromon-34137

Document type:: Monograph

Author:: Waha, Raymund de http://d-nb.info/gnd/117560855

Title:: Die Nationalökonomie in Frankreich

Place of publication:: Stuttgart

Publisher:: Verlag von Ferdinand Enke

Year of publication:: 1910

Scope:: 1 Online-Ressource (XIX, 540 Seiten)

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Buch II Die katholischen und verwandten Richtungen

Collection:: Economics Books

XVIL—SIMPLER CASES OF SAMPLING FOR VARIABLES. 341 But this gives at once for the standard error expressed in terms of the class-interval as unit n, ym 22 (2) As an example in which we can compare the results given by the two different formule (1) and (2), take the distribution of stature used as an illustration in Chaps. VII. and VIIL and in $$ 13, 14 of Chap. XV. The number of observations is 8585, and the standard-deviation 2:57 in., the distribution being approximately normal : o/,/n=0027737, and, multiplying by the factor 1-253 . . . . given in the table in § 4, this gives 00348 as the standard error of the median, on the assumption of normality of the distribution. Using the direct method of equation (2), we find the median to be 67:47 (Chap. VII. § 15), which is very nearly at the centre of the interval with a frequency 1329. Taking this as being, with sufficient accuracy for our present purpose, the frequency per interval at the median, the standard error is J8585 1399 =00349. As we should expect, the value is practically the same as that obtained from the value of the standard-deviation on the assump- tion of normality. Let us find the standard error of the first and ninth deciles as another illustration. On the assumption that the distribu- tion is normal, these standard errors are the same, and equal to 0:027737 x 1'70942=00474. Using the direct method, we find by simple interpolation the approximate frequencies per interval at the first and ninth deciles respectively to be 590 and 570, giving standard errors of 00471 and 00488, mean 0-0479, slightly in excess of that found on the assumption that the fre- quency is given by the normal curve. The student should notice that the class-interval is, in this case, identical with the unit of measurement, and consequently the answer given by equation (2) does not require to be multiplied by the magnitude of the interval. In the case of the distribution of panperism (Chap. VIL, Example i.), the fact that the class-interval is not a unit must be remembered. The frequency at the median (3-195 per cent.) is approximately 96, and this gives for the standard error of the median by (2) (the number of observations being 632) 0:1309 intervals, that is 0:0655 per cent. 7. In finding the standard error of the difference between two

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