According to the formula,

The average of squares of first 'n' natural numbers =$\frac{(n+1)(n+2)}{6}$

Here, n=50

∴ Required average 

$$\begin{gathered} =\frac{\left(50+1\right)\left(2\times 50+1\right)}{6} \\ =\frac{51\times 101}{6} \\ =\frac{5151}{6}= 858.5 \end{gathered}$$

Hence, Option B is correct.