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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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Is mean absolute deviation smaller than standard deviation for $n\ge 3$?
I want to compare the mean absolute deviation with standard deviation in general case with this definition:
$$MAD = \frac{1}{n-1}\sum_1^n|x_i - \mu|, \qquad SD = \sqrt{\frac{\sum_1^n(x_i-\mu)^2}{n-1} …