Question

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

• A. $\overline{X}+\frac{n+1}{2}$
• B. $\overline{X}+\frac{n}{2}$
• C. $\overline{X}+n$
• D. $\overline{X}+\frac{n-1}{2}$

Answer 1

Answer: (A)

$\overline{X}+\frac{n+1}{2}$

Mean of n items $=\overline{X}$

sum of n items $=n.\overline{X}$

New sum $=n\overline{X}+1+2+3+...+n$

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

Hence New mean equals

$\frac{n\overline{X}+\frac{n+1}{2}}{n}$

$=\overline{X}+\frac{n+1}{2}$