An Introduction to the theory of statistics

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Monograph

Identifikator:: 175994050X

URN:: urn:nbn:de:zbw-retromon-137069

Document type:: Monograph

Author:: Gorter, Herman http://d-nb.info/gnd/118718207

Title:: Der historische Materialismus

Edition:: 3., bedeutend verm. Ausg.

Place of publication:: Berlin

Publisher:: Buchh. für Arbeiterliteratur

Year of publication:: 1928

Scope:: 137 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: IV. [i.E. VI.] Schluß

Collection:: Economics Books

114 THEORY OF STATISTICS. interval. In distributions of such a type the intervals must be made very small indeed to secure an approximately accurate value for the mean. The student should test for himself the effect of different groupings in two or three different cases, so as to get some idea of the degree of inaccuracy to be expected. 12. If a diagram has been drawn representing the frequency- distribution, the position of the mean may conveniently be indicated by a vertical through the corresponding point on the base. Thus fig. 21 (a reproduction of fig. 10) shows the frequency- polygon for our first illustration, and the vertical MJ indicates the mean. In a moderately asymmetrical distribution at all of this form the mean lies, as in the present example, on the side of the greatest frequency towards the longer tail” of the distribu- Mo Mid Fie. 22.—Mean JM, Median M7, and Mode Mo, of the ideal moderately asymmetrical distribution. tion: Min fig. 22 shows similarly the position of the mean in an ideal distribution. In a symmetrical distribution the mean coincides with the centre of symmetry. The student should mark the position of the mean in the diagram of every frequency dis- tribution that he draws, and so accustom himself to thinking of the mean, not as an abstraction, but always in relation to the frequency-distribution of the variable concerned. 13. The following examples give important properties of the arithmetic mean, and at the same time illustrate the facility of its algebraic treatment :— (a) The sum of the deviations from the mean, taken with their proper signs, is zero. This follows at once from equation (4): for if M and 4 are identical, evidently =(7.£) must be zero,

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