What is the arithmetic mean of 8^{2}, 9^{2}, 10^{2}, ..., 15^{2}?

Explanation

The sum of the squares from 8^2 to 15^2 is \sum_{n=1}^{15} n^2 - \sum_{n=1}^{7} n^2. Using the formula \frac{n(n+1)(2n+1)}{6}, we get \frac{15(16)(31)}{6} - \frac{7(8)(15)}{6} = 1240 - 140 = 1100. Since there are 8 terms, the mean is 1100 / 8 = 137.5.

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