Question

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

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

Let, $x_1,x_2.......x_n$ be n items.
Then, $\overline{x}=\frac{1}{n}\sum x_i$
$Let{y}_1=x_1+1,y_2=x_2+2,y_3=x_3+3,.....,y_n=x_n+n$
Then the mean of the new series is
$\frac{1}{n}\sum y_i=\frac{1}{n}\sum _{i=1}^n(x_i+i)$
$=\frac{1}{n}\sum _{i=1}^n{x}_i+\frac{1}{n}(1+2+3+......+n)$
$=\overline{x}+\frac{1}{n}.\frac{n(n+1)}{2}=\overline{x}+\frac{n+1}{2}$