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

VIL.—AVERAGES. 121 on the choice of the scale of class-intervals. It is no use making the class-intervals very small to avoid error on that account, for the class-frequencies will then become small and the distribution irregular. What we want to arrive at is the mid-value of the interval for which the frequency would be a maximum, if the intervals could be made indefinitely small and at the same time the number of observations be so increased that the class-frequen- cies should run smoothly. As the observations cannot, in a practical case, be indefinitely increased, it is evident that some process of smoothing out the irregularities that occur in the actual distribution must be adopted, in order to ascertain the approximate value of the mode. But there is only one smoothing process that is really satisfactory, in so far as every observation can be taken into account in the determination, and that is the method of fitting an ideal frequency-curve of given equation to the actual figures. The value of the variable corresponding to the maximum of the fitted curve is then taken as the mode, in accordance with our definition. fo in fig. 21 is the value of the mode so determined for the distribution of pauperism, the value 2:99 being, as it happens, very nearly coincident with the centre of the interval in which the greatest frequency lies. The deter- mination of the mode by this—the only strictly satisfactory— method must, however, be left to the more advanced student. 20. At the same time there is an approximate relation between mean, median, and mode that appears to hold good with surprising closeness for moderately asymmetrical distributions, approaching the ideal type of fig. 9, and it is one that should be borne in mind as giving—roughly, at all events—the relative values of these three averages for a great many cases with which the student will have to deal. It is expressed by the equation— Mode = Mean — 3(Mean — Median). That is to say, the median lies one-third of the distance from the mean towards the mode (compare figs. 21 and 22). For the dis- tribution of pauperism we have, taking the mean to three places of decimals,— Mean . . 3289 Median 3-195 Difference 0-094 Hence approximate mode = 3:289 — 3 x 0-094 = 3-007, or 3-01 to the second place of decimals, which is sufficient accuracy for the final result, though three decimal places must be retained for the calculation. The true mode, found by fitting an ideal

Access restriction

Copyright

Contents: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation