An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

IX.—CORRELATION. 165 at the centre of every compartment of the correlation-table a vertical of length proportionate to the frequency in that com- partment, and joining up the tops of the verticals. If the compartments were made smaller and smaller while the class- frequencies remained finite, the irregular figure so obtained would approximate more and more closely towards a continuous curved surface—a frequency-surface — corresponding to the frequency- curves for single variables of Chapter VI. The volume of the frequency-solid over any area drawn on its base gives the frequency of pairs of values falling within that area, just as the area of the frequency-curve over any interval of the base-line gives the frequency of observations within that interval. Models of actual distributions may be constructed by drawing the frequency- distributions for all arrays of the one variable, to the same scale, on sheets of cardboard, and erecting the cards vertically on a base-board at equal distances apart, or by marking out a base- board in squares corresponding to the compartments of the correlation-table, and erecting on each square a rod of wood of height proportionate to the frequency. Such solid representations of frequency-distributions for two variables are sometimes termed stereograms. 5. It is impossible, however, to group the majority of frequency-surfaces, in the same way as the frequency-curves, under a few simple types: the forms are too varied. The simplest ideal type is one in which every section of the surface is a sym- metrical curve—the first type of Chap. VL (fig. 5, p. 89). Like the symmetrical distribution for the single variable, this is a very rare form of distribution in economic statistics, but approximate illustrations may be drawn from anthropometry. Fig. 29 shows the ideal form of the surface, somewhat truncated, and fig. 30 the distribution of Table III., which approximates to the same type,—the difference in steepness is, of course, merely a matter of scale. The maximum frequency occurs in the centre of the whole distribution, and the surface is symmetrical round the vertical through the maximum, equal frequencies occurring at equal distances from the mode on opposite sides. The next simplest type of surface corresponds to the second type of frequency-curve—the moderately asymmetrical. Most, if not all, of the distributions of arrays are asymmetrical, and like the dis- tribution of fig. 9, p. 92: the surface is consequently asymmetrical, and the maximum does not lie in the centre of the distribution. This form is fairly common, and illustrations might be drawn from a variety of Sources—economics, meteorology, anthropometry, ete. The data of Table IL. will serve as an example. The total distributions and the distributions of the majority of the arrays i:

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation