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Also, doesn't the +/- sigma rule only apply to a normal (gaussian) distributions?
by jorge-fundido 10y ago
Also, doesn't the +/- sigma rule only apply to a normal (gaussian) distributions?
- FabHK 10y agoYes, that rule: 31% outside +/- 1 standard deviation ("2 sigma"), 5% outside +/- 2 standard deviations ("4 sigma"), 0.3% outside +/- 3 standard deviations ("6 sigma"), etc. However, the more general Chebyshev inequality states that for any distribution, you have at most 1/k^2 outside +/- k standard deviations, so (at most): 100% outside +/- 1 standard deviation, 25% outside +/- 2 standard deviations, 9% outside +/- 3 standard deviations, etc. https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality