Let in a series of 2n observations, half of them are equal to a and remaining half are equal to - a. Also by adding a constant b in each of these…

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to - a . Also by adding a constant b in each of these observations, the mean and standard deviation of new set become $\displaystyle 5$ and $\displaystyle 20$ , respectively. Then the value of $\displaystyle \mathrm{a}^2+\mathrm{b}^2$ is equal to :