Question

If a variable takes values 1,2,3,....n with frequencies $1^2,2^2,...n^2....$

Then the mean is

Answer 1

$Mean=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{1\times 1^2+2\times 2^2+3\times 3^2+-------n\times n^2}{1^2+2^2+3^2+---------n^2}$

$=\frac{\sum n^3}{\sum n^2}=\frac{n^2(n+1{)}^2\times 6}{4n(n+1)(2n+1)}$

$=\frac{3n(n+1)}{2(2n+1)}$