5 ms·
Someone has already explained why your example is wrong, but for a general proof, for dist X, let u = mean, m = median | u - m | = |E(X - m)| <= E(|X
by hhmc 4y ago
Someone has already explained why your example is wrong, but for a general proof, for dist X, let u = mean, m = median
| u - m | = |E(X - m)|
<= E(|X - m|)
<= E(|X - u|)
<= E(sqrt((X - u)^2))
<= stddev
mostly steps via Jensen's inequality
- mjburgess 4y agooops... I interpreted the claim, admittedly bizarrely, as something like: fit N(u, s) to {(x, y)...} then m will lie u+-s rather than, def. s^2 = E[X^2] - E[X]^2