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An Introduction to the theory of statistics

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Monograph

Identifikator:: 870275321

URN:: urn:nbn:de:zbw-retromon-410

Document type:: Monograph

Author:: Sandmann, D.

Title:: Wie kann die heimische Cognacindustrie und der deutsche Weinbau gefördert werden?

Place of publication:: Berlin

Publisher:: H. S. Hermann

Year of publication:: 1905

Scope:: 1 Online-Ressource (43 Seiten)

Digitisation:: 2017

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

THEORY OF STATISTICS. giving the distribution of head-breadths for 1000 men, will serve as an example. TABLE Y.—Showing the Frequency-distribution of Head-breadths for Students at Cambridge. Measurements taken to the mearest tenth of am inch. (Cited from W. R. Macdonell, Biometrika, i., 1902, p. 220.) Number of Number of Ee Men with said Rng Men with said : Head-breadth. E Head-breadth. 55 3 6°3 99 56 12 6-4 37 5-7 43 65 15 58 80 66 12 59 131 67 3 60 236 6°8 2 61 185 RoC 62 142 Total 1000 Taking a piece of squared paper ruled, say, in inches and tenths, mark off along a horizontal base-line a scale representing class- intervals ; a half-inch to the class-interval would be suitable. Then choose a vertical scale for the class-frequencies, say 50 observations per interval to the inch, and mark off, on the verticals or ordinates through the points marked 55, 56, 5-7 . . . . at the centres of the class-intervals on the base-line, heights representing on this scale the class-frequencies 3, 12, 43. . . . The diagram may then be completed in one of two ways: (1) as a frequency-polygon, by joining up the marks on the ver- ticals by straight lines, the last points at each end being joined down to the base at the centre of the next class-interval (fig. 1); or (2) as a column diagram or histogram (to use a term sug- gested by Professor Pearson, ref. 1), short horizontals being drawn through the marks on the verticals (fig. 2), which now form the central axes of a series of rectangles representing the class- frequencies. The student should note that in any such diagram, of either form, a certain area represents a given number of observations. On the scales suggested, 1 inch on the horizontal represents 2 intervals, and 1 inch on the vertical represents 50 observations per interval: 1 square inch therefore represents 50x 2=100 observations. The diagrams are, however, con- ventional : the whole area of the figure is correct in either case, but the area over each interval is not correct in the case of the frequency-polygon, and the frequency of each fraction of any 84

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