3 ms·
...this isn't true: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,10^30
by mjburgess 4y ago
...this isn't true:
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,10^30
- zeristor 4y agoReminds me of the distribution in salaries. I read …, 1, 10, 30 but …, 1, 10^30 is far more dramatic.
- Chirono 4y agoI’d double check your working there because it certainly is true. In your example the standard deviation (2e29) is far bigger than the difference between the median and mean (5e28).
- hhmc 4y agoSomeone 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