The mean of 100 observations is 50 and their standard deviation is 5.The mean of the squares of all observations, is

Let $x_1,x_2,x_3,\dots ,x_{100}$ be 100 observations. Then

,$\begin{array}{l}\text{ Variance }=\frac{1}{100}\sum _{i=1}^{100} x_i^2-(\text{ Mean }{)}^2\\ \Rightarrow 25=\frac{1}{100}\sum _{i=1}^{100} x_i^2-2500\\ \Rightarrow \sum _{i=1}^n x_i^2=252500\Rightarrow \frac{1}{100}\sum _{i=1}^n x_i^2=2525\end{array}$