Question

$10$ is the mean of $25$ observations. If $1,3,5,...,49$ are added to corresponding observations, then the new mean is

• A. $32$
• B. $35$
• C. $39$
• D. $27$

Answer 1

The correct option is B $35$

We know that, $\overline{x}=\frac{1}{n}\sum _{i=1}^n{x}_i$
${\overline{x}}_{\text{new}}=\frac{(x_1+1)+(x_2+3)+(x_3+5)+...+(x_{25}+49)}{25}$
$=\frac{x_1+x_2+x_3+...+x_{25}}{25}+\frac{1+3+5+...+49}{25}$
$=10+\frac{{25}^2}{25}$
$=35$

Note:
$1+3+5+...+(2n-1)=n^2$