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## Main Question or Discussion Point

I have seen that "the best estimate for the random error σ(X) in a single measurement is given by

σ(X)

I have two questions about this: firstly, how can this pertain to a "single measurement" if it requires the data from multiple measurements (x

σ(X)

^{2}≈ 1/(n-1) * ∑((x_{i}-μ)^{2}) where the sum is over all i"I have two questions about this: firstly, how can this pertain to a "single measurement" if it requires the data from multiple measurements (x

_{1}, x_{2}, x_{3}, ... x_{i})? Secondly, this seems to correspond to the sample variance - wouldn't it be a more accurate estimate of the value of X's random error to convert to the variance of the population of X as a whole?