Gesetz betreffend Kinderarbeit in gewerblichen Betrieben

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Monograph

Identifikator:: 882692321

URN:: urn:nbn:de:zbw-retromon-5020

Document type:: Monograph

Author:: Agahd, Konrad http://d-nb.info/gnd/116256575; Schulz, Max von http://d-nb.info/gnd/1033198951

Title:: Gesetz betreffend Kinderarbeit in gewerblichen Betrieben

Edition:: Zweite Auflage, neub bearbeitet

Place of publication:: Jena

Publisher:: Verlag von Gustav Fischer

Year of publication:: 1904

Scope:: 1 Online-Ressource (X, 168 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Zweiter Teil. Kommentar zum Reichsgesetz, betreffend Kinderarbeit in gewerblichen Betrieben vom 30. März 1903

Collection:: Economics Books

THEORY OF STATISTICS. Now let us approximate by assuming, as suggested in § 8, that k is very large, and indeed large compared with z, so that (x/k)® may be neglected compared with (x/k). This assumption does not involve any difficulty, for we need not consider values of x much greater than three times the standard-deviation or 3 JE2, and the ratio of this to % is 3/ ~ 2k, which is necessarily small if £ be large. On this assumption we may apply the logarithmic series S20 ST et log,(1+68)=20 TEE ad to every bracket in the fraction (3), and neglect all terms beyond the first. To this degree of approximation, z 2 re logle= -(1+2+3+ .. +o- 0-7 a=)» 5 Zk 22 Ro Therefore, finally, 22 2 Rr SEE Ry (4) Yo=Yl = =e where, in the last expression, the constant % has been replaced by the standard-deviation o, for o2="£%/2. The curve represented by this equation is symmetrical about the point = 0, which gives the greatest ordinate y=y, Mean, median, and mode therefore coincide, and the curve is, in fact, that drawn in fig. 5, p. 89, and taken as the ideal form of the symmetri- cal frequency-distribution in Chap. VI. The curve is generally known as the normal curve of errors or of frequency, or the law of error. 10. A normal curve is evidently defined completely by giving the values of y, and o and assigning the origin of x. If we desire to make a normal curve fit some given distribution as near as may be, the last two data are given by the standard-deviation and the mean respectively ; the value of g, will be given by the fact that the areas of the two distributions, or the numbers of observations which these areas represent, must be the same. This condition does not, however, lead in any simple and elementary algebraic way to an expression for y, though such a value could be found arithmetically to any desired degree of approximation. For it is evident that (1) any alteration in 302

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