Chebychev’s Inequality

There is a neat theorem in statistics called Chebychev’s Inequality that states: for any distribution with a mean and standard deviation σ, at least 1 - (1/k^2) percent of the distribution is within ±kσ of the mean.  For normal distributions, the percent within ±kσ of the mean is exactly known. 

Percent of distribution that fall within ±kσ of the mean.

k	Any Distribution	Normal
1	-----	68.3%
1.415	50.0%	84.3%
2	75.0%	95.5%
3	88.9%	99.7%
4	93.8%	99.99%
5	96.0%	99.99994%
6	97.2%	99.9999998%

I think this is pretty useful.  You don't have to worry if the distribution is skewed, peaked, or flattened.  Chebychev's Inequality will always give you the minimum percent that falls within ±kσ.  It's a shame that this is not more widely used in engineering design or business decision making.