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Standard deviation is the square root of the variance of a random variable, an estimator thereof, or a similar measure of the spread of a batch of data.

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They both measure the same concept, but are not equal. You are comparing $\frac{1}{n} \sum |x_i-\bar{x}|$ with $\sqrt{\frac{1}{n} \sum (x_i-\bar{x})^2}$. They aren't equal for two reasons: Firstly …
answered Jan 12 '14 by ltronneberg