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Sorry, my stats is rusty and I'm failing to find a quick answer to what is likely to be a very basic question.
If I take n measurements of a property that has an inherent mean mu and standard deviation s, I would estimate mu from the sample mean, and quantify the uncertainty in this estimate with the standard error. But what about the standard deviation? (I guess this is sort of a population s.d., though of a potentially infinite population) Presumably I'd estimate it from the sample standard deviation, but what is the right way to quantify its uncertainty? Clearly a value based upon 5 values is less reliable than one using 500.