Das Kapital: Der Produktionsprozeß des Kapitals

Der Produktionsprozeß des Kapitals (1.1928)

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Multivolume work

Identifikator:: 1780159447

Document type:: Multivolume work

Author:: Marx, Karl http://d-nb.info/gnd/118578537

Title:: Das Kapital

Place of publication:: Berlin

Publisher:: J. H. W. Dietz Nachf., G. m. b. H.

Year of publication:: 1926-

Collection:: Economics Books

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Identifikator:: 1780159595

URN:: urn:nbn:de:zbw-retromon-188277

Document type:: Volume

Author:: Marx, Karl http://d-nb.info/gnd/118578537

Title:: Der Produktionsprozeß des Kapitals

Volume count:: 1.1928

Place of publication:: Berlin

Publisher:: J. H. W. Dietz Nachf., G. m. b. H.

Year of publication:: 1928

Scope:: XLVIII, 768 Seiten

Digitisation:: 2022

Collection:: Economics Books

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Document type:: Multivolume work

Structure type:: Chapter

Title:: Siebter Abschnitt. Der Akkumulationsprozeß des Kapitals

Collection:: Economics Books

344 THEORY OF STATISTICS. to test whether we may treat the distribution as approximately normal (cf. also § 16 below). (As regards the theory of sampling for the median and per- centiles generally, cf. ref. 15, Laplace, Supplement II. (standard error of the median), Edgeworth, refs. 5, 6, 7, and Sheppard, ref. 27: the preceding sections have been based on the work of Edgeworth and Sheppard.) 10. Standard Error of the Arithmetic Mean.—Let us now pass to a fresh problem, and determine the standard error of the arithmetic mean. This is very readily obtained. Suppose we note separately at each drawing the value recorded on the first, second, third . . . . and nth card of our sample. The standard-deviation of the values on each separate card will tend in the long run to be the same, and identical with the standard-deviation o of « in an indefinitely large sample, drawn under the same conditions. Further, the value recorded on each card is (as we assume) uncorrelated with that on every other. The standard-deviation of the sum of the values recorded on the nm cards is therefore a/n.oc, and the standard-deviation of the mean of the sample is consequently 1/nth of this; or, o On ="In . (5) This is a most important and frequently cited formula, and the student should note that it has been obtained without any reference to the size of the sample or to the form of the frequency- distribution. It is therefore of perfectly general application, if oc be known. We can verify it against our formula for the standard-deviation of sampling in the case of attributes. The standard-deviation of the number of successes in a sample of m observations is a/m.pg: the standard-deviation of the total number of successes in n samples of m observations each is there- fore a/mm.pq: dividing by n we have the standard-deviation of the mean number of successes in the = samples, viz. mpg [n/n agreeing with equation (5). 11. For a normal curve the standard error of the mean is to the standard error of the median approximately as 100 to 125 (¢f. § 4), and in general the standard errors of the two stand in a somewhat similar ratio for a distribution not differing largely from the normal form. For the distribution of statures used as an illustration in § 6 the standard error of the median was found to be 0:0349: the standard error of the mean is only 0-0277. The distribution being very approximately normal, the ratio of

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