a) Calculate the mean absolute deviation E(|X-μ|) for X, the number on a six-sided die.
b) Use the fact that Var(|X-μ|)0 to show that SD(X)E(|X-μ|), with equality if and only if |X-μ| is a constant.

that is to say, unless |X-μ| is a constant, the standard deviation of a random variable is always strictly larger than the mean absolute deviation. If X is a constant, then both measures of spread are zero.