How come if we're given only one data point the sample standard deviation would be undefined because of n - 1?
2026-03-27 14:10:51.1774620651
Given one data point, why is the population standard deviation equal to zero but the sample standard deviation is undefined?
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Uncorrected (biased) sample variance is defined (and is $0$). Corrected (unbiased) sample variance is not defined.
It's because there is no unbiased estimator that takes only one sample. Indeed, would there be, it should be zero everywhere (as for random variable that is always $x$ it should give $0$), but zero isn't unbiased estimator of variance (it's expectation wrt any random variable is $0$, but there are variables with non-zero variance).