Let in a series of \(2 n\) observations, half of them are equal to \(a\) and remaining half are equal to \(-a\). Also by…

Let in a series of \(2 n\) 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 5 and 20 , respectively. Then the value of \(a^2+b^2\) is equal to: