Graf Georg Kankrin in nationalökonomischer und finanzwirtschaftlicher Beziehung

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Monograph

Identifikator:: 897653432

URN:: urn:nbn:de:zbw-retromon-12556

Document type:: Monograph

Author:: Schaulis, Georg

Title:: Graf Georg Kankrin in nationalökonomischer und finanzwirtschaftlicher Beziehung

Place of publication:: Tilsit

Publisher:: Buchdruckerei "Lituania"

Year of publication:: 1914

Scope:: 1 Online-Ressource (XII, 114 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: I. Abschnitt. Die Lehre Kankrins

Collection:: Economics Books

VIIL.—MEASURES OF DISPERSION, ETC. 135 But the sum of the deviations from the mean is zero, therefore the second term vanishes, and accordingly 2=c2+d2. (4) Hence the root-mean-square deviation is least when deviations are measured from the mean, 7.e. the standard deviation is the least possible root-mean-square deviation. 3(&2), or 3(f.&) if we are dealing with a grouped distribution and f is the frequency of & is sometimes termed the second moment of the distribution about 4, just as 3(¢) or 3(f.§) is termed the first moment (¢f. Chap. VII. § 8): we shall not make use of the term in the present work. Generally, 3(f.£") is termed the nth moment. 4. If o and d are the two sides of a right-angled triangle, s is a—— Fic. 2.. the hypotenuse. If, then, #/H be the vertical through the mean of a frequency-distribution (fig. 25), and AS be set off equal to the standard deviation (on the same scale in which the variable X is plotted along the base), S4 will be the root-mean- square deviation from the point 4. This construction gives a concrete idea of the way in which the root-mean-square deviation depends on the origin from which deviations are measured. It will be seen that for small values of d the difference of s from o will be very minute, since 4 will lie very nearly on the circle drawn through A/ with centre .S and radius SJ/: slight errors in the mean due to approximations in calculation will not, there- fore, appreciably affect the value of the standard deviation. 5. If we have to deal with relatively few, say thirty or forty, ungrouped observations, the method of calculating the standard deviation is perfectly straightforward. It is illustrated by the figures given below for the estimated average earnings of

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