Let \sum_{i=1}^{9}x_{i}^{2}=855. If M is the mean and \sigma is the standard deviation of x_{1},x_{2},\dots,x_{9}, then what is the value of M^{2}+\sigma^{2}?

Explanation

The formula for variance is \sigma^2 = \frac{\sum x_i^2}{N} - M^2. Rearranging this gives M^2 + \sigma^2 = \frac{\sum x_i^2}{N}. Substituting the given values N=9 and \sum x_i^2 = 855, we get M^2 + \sigma^2 = \frac{855}{9} = 95.

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