What is the mean deviation of the first 10 natural numbers?

Explanation

The mean of the first 10 natural numbers is \frac{1+10}{2} = 5.5. The mean deviation is given by \frac{1}{10}\sum |x_i - \bar{x}|. The deviations |x_i - 5.5| for x_i \in \{1, 2, \dots, 10\} are 4.5, 3.5, 2.5, 1.5, 0.5, each appearing twice (for values above and below the mean). The sum of deviations is 2(4.5 + 3.5 + 2.5 + 1.5 + 0.5) = 2(12.5) = 25. The mean deviation is \frac{25}{10} = 2.5.

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