An Introduction to the theory of statistics

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Monograph

Identifikator:: 881661368

URN:: urn:nbn:de:zbw-retromon-3236

Document type:: Monograph

Author:: Goldberger, Ludwig Max http://d-nb.info/gnd/117548804

Title:: Das Land der unbegrenzten Möglichkeiten

Edition:: Achte Auflage

Place of publication:: Berlin

Publisher:: F. Fontane & Co.

Year of publication:: 1911

Scope:: 1 Online-Ressource (299 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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

294 THEORY OF STATISTICS, p and ¢ may be interchanged without altering the value of any “term, and consequently terms equidistant from either end of the series are equal. If » and ¢ are unequal, on the other hand, the distribution is asymmetrical, and the more asymmetrical, for the same value of 7, the greater the inequality of the chances. The following table shows the calculated distributions for m=20 and values of p, proceeding by 0.1, from 0.1 to 0.5. When p=0.1, cases of two successes are the A. — Terms of the Binomial Series 10,000 (q+ p)? for Values of p from 0-1 to 0°5. (Ligures given to the nearest unit.) Number of p=0:1 p=0:2 »=0'3 p=0408 p=05 Successes. q=0°9 g=0-8 g=07 g=0'0lg=05 0 1216 115 8 — = 2702 576 68 5 — 92852 1369 278 s1 | 2 Bi 1901 2054 716 ol 11 §98 2182 1304 850 46 319 1746 1789 746 148 89 1091 1916 | 1244 370 20 545 1643 1659 739 4 222 1144 1797 1201 1 74 654 1597 1602 Y 0 308 1171 1762 120 710 1602 ’ 355 1201 146 739 19 370 Py he Nl 148 a 3 46 17 - — 11 13 - — 2 19 = = 20 = most frequent, but cases of one success almost equally frequent : even nine successes may, however, occur about once in 10,000 trials. As p is increased, the position of the maximum frequency gradually advances, and the two tails of the distribution become more nearly equal, until p=0.5, when the distribution is symmetrical. Of eourse, if the table were continued, the distribution for p=0.6 would be similar to that for ¢=0.6 but reversed end for end, and so on. Since the standard- deviation is (npg)! and the maximum value of pg is given by p=g¢q, the symmetrical distribution has the greatest dispersion. a.

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