# Download e-book for kindle: Fundamentals of Mathematical Statistics (A Modern Approach), by S.C. Gupta, V.K. Kapoor

By S.C. Gupta, V.K. Kapoor

ISBN-10: 8170147913

ISBN-13: 9788170147916

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Extra resources for Fundamentals of Mathematical Statistics (A Modern Approach), 10th Edition

Sample text

In such cases median (discussed later) is the only average to be used. (iii) Arithmetic mean cannot be obtained if a single observation is missing or lost or is illegible unless we drop it out and compute the arithmetic mean of the remaining values. , (iv) Arithmetic mean is affected very much by extreme values. In case of extreme items, arithmetic mean gives a distorted picture of the distribution and no longer remains representative of the distribution. (v) Arithmetic mean may lead to wrong conclusions if the details of the ~ql from which it is computed are not given.

Xt2 ... ~t i-I I G2 = (X2t. X22 ... X2N2) tI"2 . I log G2 = - => n2 l: 10gX2; n2 j-l The geometric mean G of the combined series is given by G = (Xtt. X\2 ... Xt"t . X2t . X22 ... _ 1 log Xli n2] X2j + l: log i -1 = _1_ [nl log G t + n2 log G 2 '] nl + n2 The result can be easily generalised to more than two series. (iv) It is not affected much by fluctuations of sampling. (v) It gives comparatively more weight to small items. Demerits. (i) Because of its abstract mathematical character, geometric mean is not easy to understand and to calculate for a non-mathematics.

X; ;= 1 - - - N1· 1:f;Xi. II II {= l' 1:f; ;= 1 1:f;=N ] [" i= 1 ... (2·1) -- In case of grouped or continuous frequency distributioo. X is taken as the mid. value of the corresponding class. Remark. The symbol 1: is the leUer capital sigma of the Greek alphabet and is used in mathematics to denote the sum of values. Frequency Distributions And Measures Of Central Tendency 2· 7 Example 2·1. from thefollowing table: Marks : 0-10 10-20 20-30 30-40 40-50 50-60 No. of students : 12 18 27 20 17 6 Solution ..