# Use of statistics in experiment

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

σ(X)2 ≈ 1/(n-1) * ∑((xi-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 (x1, x2, x3, ... xi)? 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?

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

Where did you see this?

If you look at your equation and plug in n = 1, is the variance defined?

Where did you see this?

If you look at your equation and plug in n = 1, is the variance defined?

http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation

No, but the variance need not (and perhaps should not) be defined for n=1 - a single measurement by definition cannot have a "spread".

Staff Emeritus