Sixty Sigma

Chebyshev's Inequality

A neglected fact is that a standard deviation provides a bound on the probability of samples lying away from the mean independent of the distribution. That is to say, you do not need to assume a normal distribution to say 75% of the samples lay within two standard deviations from the mean.

Pr(Xukσ)1k2 Pr(|X-u|\ge k\sigma) \le \frac{1}{k^2}


When you see 60 black swans in the same pond, run!