Question

Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is

• A. $\frac{(n+1)d}{(2n+1)}$
• B. $\frac{(nd}{(2n+1)}$
• C. $\frac{n(n+1)d}{(2n+1)}$
• D. $\frac{2(n+1)d}{n(n+1)}$

Answer 1

The correct option is C $\frac{n(n+1)d}{(2n+1)}$

$\overline{x}=\frac{\frac{2n+1}{2}(a+a+2nd))}{(2n+1)}=a+nd\sum |x-\overline{x}|=2d(1+2+.....+n)=n(n+1)d\therefore M.D=\frac{n(n+1)d}{(2n+1)}$