Solution

Bessel's Correction

Show the problem again

A sample consists of the values 2, 4, and 6. Compute the sample variance, using the n − 1 denominator.

Worked solution

The answer is 4. The sample mean is 4; squared deviations are 4, 0, 4, summing to 8, so s² = 8/(3 − 1) = 4. Dividing by n would be biased low because deviations are measured from the sample mean, which is fitted to the data and sits closer to the observations than the true mean does; n − 1 (the degrees of freedom) exactly corrects this, making E[s²] = σ².

Source: Standard correction attributed to Friedrich Bessel; textbook material in mathematical statistics. Statement written for AxiomIQ.