Let in a series of \( 2 \mathrm{n} \) observations, half of them are equal to \(a\) and remaining half are equal to \(-a…

Let in a series of \( 2 \mathrm{n} \) 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: