What is the corrected sample standard deviation when there is only one sample?

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What do we say about the corrected sample standard deviation when the sample size is one? Do we just assume it is 0? Is it even meaningful?

The usual equation seems to fall apart here because N - 1 is 0 and results in an (apparent?) division by 0.

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Its undefined...the sample does not have an unbiased variance estimate, only a very biased estimate of 0.