68–95–99.7 Rule

Remember that a lot of data is not actually normally distributed, even though it looks so at first. The horror of &quot;risk management&quot; units of financial institutions, when they get a &quot;7-sigma&quot; event twice in a month.<p>Can you imagine there was a time when the entire US options market was running on flat volatility vs strike price (implying that financial asset prices are lognormal). Must have been cool to just buy the cheapest, most OTM options and collect big results every now and then.

I always like the inverse of this, which is that if you calculate that less than 68% is in the first standard deviation, you can guess that the data isn’t normally distributed.<p>It’s really a heuristic on where to start with analysis, though. Not a result in and of itself.

Memorizing a set of numbers doesn&#x27;t really feel like a shorthand way to remember those numbers. Did you know about the 3.14 rule? It&#x27;s a way to remember the first three digits of pi are 3.14.

The table of numerical values is pretty interesting for a layman. I&#x27;ve often heard scientists (such as Brian Cox) talk about x-sigma probabilities, but putting it the context in this table is much more meaningful for someone like me who only has self-study reading as scientific understanding.

Mentioned in the OP, but perhaps buried a bit, I am always partial to Chebyshev&#x27;s Inequality (<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Chebyshev%27s_inequality" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Chebyshev%27s_inequality</a>) since it describes all distributions not just Gaussian. While approximations, they are nice to have when you question the normality of the data and still want to estimate limits - more numbers to remember however, since they are estimates.

This is why also claims of IQs above 180 or so are almost always BS, at least on normed tests. 6sd is about the maximum

I like how they call this a &#x27;rule&#x27; instead just a list of three hard to remember numbers in a row.