In a series of 2 n observations, half of them equal a and remaining...

x_i=a$for$i=1,2, \ldots, n and x_i=-a$for$i=n, \ldots ., 2 n$S.D.$=\sqrt{\frac{1}{2 n} \sum_{i=1}^{2 n}\left(x_i-\bar{x}\right)^2} \Rightarrow 2=\sqrt{\frac{1}{2 n} \sum_{i=1}^{2 n} x_i^2} \quad\left(\right.$Since \left.\sum_{i=1}^{2 n} x_i=0\right) \Rightarrow 2=\sqrt{\frac{1}{2 n} \cdot 2 n a^2} \Rightarrow|a|=2$