In a set of 20 observations, each of the observation below the median of all observations is increased by 6 and each of the remaining observation is decreased by
2.Then the mean of the new set of observations

Arrange all observations in increasing or decreasing
order.

Let the observations be $x_1,x_2\dots x_{20}$ so that ${\frac{x_{10}+x_{11}}{2}}_{ }$.is the
median. The new set of observations will be  $x_1+6,\dots x_{10}+6,x_{11}-2,\dots ,x_{20}-2$

Their mean is equal to

                                $\begin{array}{r}\frac{1}{20}\left(\sum _{i=1}^{20} x_i+6\times 10-2\times 10\right)\\ =\frac{1}{20}\sum _{i=1}^{20} x_i+2\end{array}$