The other day I was thinking about the meaning of standard deviation:
$$\sigma = \frac{\sum_{i=1}^{N}(x_i - \bar{x})}{N-1}$$
What is it about? I think it is measuring the expectation of the deviation of a variable from its mean. Then why don’t we just measure the absolute deviation: $E|x_i - \bar{x}|$?
I saw this discussion on Stack Overflow and was taken aback by it. <a href=“https://stats.stackexchange.com/a/120" target=”_blank” rel=“noreferrer …