An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1779816413

URN:: urn:nbn:de:zbw-retromon-167099

Document type:: Monograph

Author:: Michels, Robert http://d-nb.info/gnd/118733737

Title:: Sittlichkeit in Ziffern?

Place of publication:: München [u.a.]

Publisher:: Duncker & Humblot

Year of publication:: 1928

Scope:: VIII, 229 Seiten

Digitisation:: 2021

Collection:: Economics Books

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Schlußbemerkung

Collection:: Economics Books

VIL.—AVERAGES. 117 such that the frequencies in excess and defect are equal. In the case of the buttercups of Table XIV. (Chap. VI. § 15) there is no number of petals that even remotely fulfils the required condition. An analogous difficulty may arise, it may be remarked, even in the case of an odd number of observations of a continuous variable if the number of observations be small and several of the observed values identical. The median is therefore a form of average of most uncertain meaning in cases of strictly discontinuous variation, for it may be exceeded by 5, 10, 15, or 20 per cent. only of the observed values, instead of by 50 per cent.: its use in such cases is to be deprecated, and is perhaps best avoided in any case, whether the variation be continuous or discontinuous, in which small series of observations have to be dealt with. 15. When a table showing the frequency-distribution for a long series of observations of a continuous variable is given, no difficulty arises, as a sufficiently approximate value of the median can be readily determined by simple interpolation on the hypo- thesis that the values in each class are uniformly distributed throughout the interval. Thus, taking the figures in our first illustration of the method of calculating the mean, the total number of observations (registration districts) is 632, of which the half is 316. Looking down the table, we see that there are 227 districts with not more than 2-75 per cent. of the population in receipt of relief, and 100 more with between 2-75 and 3-25 per cent. But only 89 are required to make up the total of 316 : bence the value of the median is taken as 276 + on. §=2T5 + 0-445 +100 2= + =3'195 per cent. The mean being 3:29, the median is slightly less ; its position is indicated by M7 in fig. 21. The value of the median stature of males may be similarly calculated from the data of the second illustration. The work may be indicated thus: — Half the total number of observations (8585) =4292'5 Total frequency under 661% inches . . =3589 Difference . = 7035 Frequency in next interval . =1329 a Miguniass Therefore median = 6615 + 1399 = 6747 inches.

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