Why is SD(X) unequal to MAD(X)?

MathJax.Hub.Config({ tex2jax: {inlineMath: [[‘$’,‘$’], [’\(‘,’\)‘]]} }); It may seem bewildering that the standard deviation (sd) of a vector X is (generally) unequal to the mean absolute deviation from the mean (MAD) of X, ie. $$sd(X) \ne MAD(X)$$. One could now argue this way: well, sd(X) involves computing the mean of the squared $$x_i$$, then taking the square root of this mean, thereby “coming back” to the initial size or dimension of x …