The agricultural output of England and Wales 1925

An Introduction to the theory of statistics

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Monograph

Identifikator:: 892769734

URN:: urn:nbn:de:zbw-retromon-76808

Document type:: Monograph

Author:: Maslov, Petr http://d-nb.info/gnd/123876184

Title:: Die Theorie der Volkswirtschaft

Place of publication:: Leipzig

Publisher:: Verlag von Arthur Kade

Year of publication:: 1912

Scope:: 1 Online-Ressource (VIII, 293 Seiten)

Collection:: Economics Books

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2 XV.—BINOMIAL DISTRIBUTION AND NORMAL CURVE. 307 1 ¥ Bibl] Lk Bc more general still, without introducing the concepti mot ina olek binomial at all, by founding the curve on more or less complex cases of the theory of sampling for variables instead of ¥ aftri- £5 butes. If a variable is the sum (or, within limits, some slightly(i~ > more complicated function) of a large number of other varia then the distribution of the compound or resultant variable is normal, provided that the elementary variables are independent, or nearly so (¢f. ref. 6). The forms of the frequency-distribu- tions of the elementary variables affect the final distribution less and less as their number is increased: only if their number is moderate, and the distributions all exhibit a comparatively high degree of asymmetry of uniform sign, will the same sign of asymmetry be sensibly evident in the distribution of the compound variable. On this sort of hypothesis, the expectation of normality in the case of stature may be based on the fact that it is a highly compound character--depending on the sizes of the bones of the head, the vertebral column, and the legs, the thickness of the intervening cartilage, and the curvature of the spine—the elements of which it is composed being at least to some extent independent, v.e. by no means perfectly correlated with each other, and their frequency-distributions exhibiting no very high degree of asym- metry of one and the same sign. The comparative rarity of normal distributions in economic statistics is probably due in part to the fact that in most cases, while the entire causation is certainly complex, relatively few causes have a largely predominant influence (hence also the frequent occurrence of irregular distributions in this field of work), and in part also to a high degree of asymmetry in the distributions of the elements on which the compound variable depends. Errors of observation may in general be regarded as compounded of a number of elements, due to various causes, and it was in this connection that the normal curve was first deduced, and received its name of the curve of errors, or law of error. 14. If it be desired to compare some actual distribution with the normal distribution, the two distributions should be superposed on one diagram, as in fig. 49, though, of course, on a much larger scale. When the mean and standard-deviation of the actual distribution have been determined, Y, 1s given by equation (5); the fit will probably be slightly closer if the standard-deviation is adjusted by Sheppard’s correction (Chap. XI. § 4). The normal curve is then most readily drawn by plot- ting a scale showing fifths of the standard-deviation along the base line of the frequency diagram, taking ‘the mean as origin, and marking over these points the ordinates given by the figures of the table on p. 303, multiplied in each case by ,- The curve

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