I’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).

Reminds me of the distribution in salaries.

I read …, 1, 10, 30 but …, 1, 10^30 is far more dramatic.

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