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

XV.—BINOMIAL DISTRIBUTION AND NORMAL CURVE. 305 accumulate, but only the terms of the third order. There is only one second-order term that has been neglected, viz. that due to the last bracket in the denominator. Even for much lower values of n than that chosen for the illustration—e.g. 10 or 12 (cf. Qu. 4 at the end of this chapter)—the normal curve still gives a very fair approximation. TABLE showing (1) Ordinates of the Binomial Series 10,000 (3 + 3)% and 10,000 - 5 (2) Corresponding Ordinates of the Normal Curve Y=42r ef inomi al Binomial Normal Term, Pio ys Tera. Series. Curve. 32 993 997 24 and 40 196 135 31 and 33 963 967 23 ,, 41 ge 79 30 ,, 34 878 880 22, 42 a ad 29 ,, 3b 753 : 753 21 ,, 43 2:, 23 28 . 36 606 | cosh Cloo 41008 Ny : 3715 87 459 457 19° ,, 45 26 ,, 38 326 324 18 ,, 46 25 ,, 39 217 | 216 1, 4 13. But if the normal curve were limited in its application to distributions which were certainly of binomial type, its use in practice (apart from its theoretical applications to many cases of the theory of sampling) would be very restricted. As suggested, however, by the illustrations given in Chap. VI, a certain, though not a large, number of distributions—more particularly among those relating to measurements on man and other animals—are approximately of normal form, even although such distributions have not obviously originated in the same way as a binomial distribution. Take, for example, the distribution of statures in the United Kingdom (Chap. VI., Table VI.). The mean stature is 67-46 inches, the standard-deviation 2-57 inches (the values are worked out in the illustrations of Chaps. VII and VIIL), and the number of observations 8585. This gives y,=1333, and all the data necessary for plotting a normal curve of the same mean and standard-deviation (the process of fitting is dealt with at greater length in § 14 below). The two distributions are shown together in fig. 49, the continuous curve being the normal curve, and the small circles showing the observed frequencies. It is evident that they agree very closely. Other body measurements, e.g. skull measurements, etc., also follow the normal law ; it also applies to certain characters in plants (e.g. number of seeds per capsule in 20)

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