Question

Calculate the mean deviation about the mean of the set of first $n$ natural numbers when $n$ is an even number.

Answer 1

Mean of first n natural no. where n is as

even no is $=\frac{1}{2}[\frac{n}{2}+\frac{n+1}{2}]=\frac{2n+1}{4}$

mean deviation$=\frac{1}{4n}[1+3+5+\mathrm{9...}\dots .n^{th}odd]$

sum of odd no$=n^2$

$=\frac{1}{4n}{n}^2=\frac{n}{4}$.