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The Infinite Monkey Rule

I always learn things from listening to the radio. On 'The Infinite Monkey Cage', I heard Brian Cox rattle off a 'rule of thumb', which goes something like:

A number plus or minus the square root of the sample size is consistent with random sampling error. (listen from 20 minutes in)

I hadn't heard that one, but deploying those key research tools, the back of an envelope and a pencil, I could see where it comes from.