For a discrete frequency distribution with class mid-points and corresponding…

MATHEMATICS · Multi-part · CBSE · Mathematics · Statistics · Statistics

Problem

For a discrete frequency distribution with class mid-points

x_1, x_2, \ldots, x_k

and corresponding frequencies

f_1, f_2, \ldots, f_k

satisfying

N=\sum f_i

: (a) Prove that

\sum f_i (x_i - \bar{x}) = 0

. (b) Using the result in (a), write the formula for the population variance

\sigma^2

of the distribution in terms of

f_i

x_i

, and

\bar{x}