Question

The mean of $n$ items is $\bar{X}$. If the first term is increased by 1 , second by 2 and so on, then the new mean is

(a) $\bar{X}+n$

(b) $\bar{X}+\frac{n}{2}$

(c) $\bar{X}+\frac{n+1}{2}$

(d) None of these

Answer 1

Let the terms are $x_1, x_2, x_3, \ldots x_n$

$\therefore \quad x_1+x_2+x_3+\ldots+x_n=n \bar{X}$

Now first term is increased by 1 , second by 2 and so on

$\therefore \quad x_1+1+x_2+2+\ldots+x_n+n=n \bar{X}+\frac{n(n+1)}{2}$

$\therefore \quad$ New mean $=\frac{n \bar{X}+\frac{n(n+1)}{2}}{n}=\bar{X}+\frac{(n+1)}{2}$

So, The correct option of this question will be (C).