Question

In a set of $2n$ distinct observation, each of the observation below the median of all the observations is increased by $5$ and each of the remaining observations is decreased by $3$. Then the mean of the new set of observations :

• A. Increases by $1$.
• B. Decreases by $1$.
• C. Decreases by $2$.
• D. Increases by $2$.

Answer 1

The correct option is A Increases by $1$.

$Mean=\frac{x_1+x_2+......+x_n+x_{n+1}+......+x_{2n}}{2n}$
$Median=\frac{x_n+x_{n+1}}{2}$
New mean $=\frac{x_1+x_2+......+x_n+5n+x_{n+1}+......+x_{2n}-3n}{2n}$
$\frac{x_1+x_2+......+x_n+x_{n+1}+......+x_{2n}}{2n}+\frac{2n}{2n}$
$Newmean=Originalmean+1$