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 III. Theory of sampling

Collection:: Economics Books

CHAPTER XVIL THE SIMPLER CASES OF SAMPLING FOR VARIABLES: PERCENTILES AND MEAN. 1-2. The problem of sampling for variables; the conditions assumed— 3. Standard error of a percentile—4. Special values for the percentiles of a normal distribution—5. Effect of the form of the distribution generally—6. Simplified formula for the case of a grouped frequency- distribution—7. Correlation between errors in two percentiles of the same distribution—8. Standard error of the interquartile range for the normal curve—9. Effect of removing the restrictions of simple sampling, and limitations of interpretation —10. Standard error of the arithmetic mean—11. Relative stability of mean and median in sampling—12. Standard error of the difference between two means—13. The tendency to normality of a distribution of means—14. Effect of removing the re- strictions of simple sampling—15. Statement of the standard errors of standard-deviation, coefficient of variation, correlation coefficient and regression, correlation-ratio and criterion for linearity of regression—186. Restatement of the limitations of interpretation if the sample be small. 1. Iv Chapters XIIL.-XVI. we have been concerned solely with the theory of sampling for the case of attributes and the frequency- distributions appropriate to that case. We now proceed to consider some of the simpler theorems for the case of variables (¢f. Chap. XIII § 2). Suppose that we have a bag containing a practically infinite number of tickets or cards bearing the recorded values of some variable X, and that we draw a ticket from this bag, note the value that it bears, draw another, and so on until we have drawn n cards (a number small compared with the whole number in the bag). Let us continue this process until we have & such samples of n cards each, and then work out the mean, standard-deviation, median, etc., for each of the samples. No one of these measures will prove to be absolutely the same for every sample, and our problem is to determine the standard-deviation that each such measure will exhibit. 2. In solving this problem, we must be careful to define precisely the conditions which are assumed to subsist, so as to realise the limitations of any solution obtained. These conditions 33H

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