Question

The mean of $n$ numbers is $M$. If $1$ added to the first number, $2$ is added to the second number, n is added to the $n^{th}$ number then the new mean is

• A. $M+\frac{n+1}{2}$
• B. $M+\frac{n}{2}$
• C. $M+n$
• D. none of these

Answer 1

The correct option is A $M+\frac{n+1}{2}$

Let $x_1,x_2,.....X_n$ be the 'n' numbers
$\frac{x_1+x_2+...+x_n}{n}=M$

$\frac{x_1+1+x_2+2+.....+x_n+n}{n}=\frac{(1+2+....+n)+(x_1+x_2+...+x_n)}{n}$

$=M+\left[\frac{\frac{n}{2}(n+1)}{n}\right]=M+\frac{n+1}{2}$