Estimating Variance (1 of 4)

The formula for the variance computed in the population, σ², is different from the formula for an unbiased estimate of variance, s², computed in a sample. The two formulas are shown below:

σ² = Σ(X-μ)²/N

s² = Σ(X-M)²/(N-1)

The unexpected difference between the two formulas is that the denominator is N for σ² and is N-1 for s². That there should be a difference in formulas is very counterintuitive. To understand the reason that N-1 rather than N is needed in the denominator of the formula for s², consider the problem of estimating σ² when the population mean, μ, is already known.

Assume that you knew that the mean amount of practice it takes student pilots to master a particular maneuver is 12 hours. If you sampled one pilot and found he or she took 14 hours to master the maneuver, what would be your estimate of σ²? The answer lies in considering the definition of variance: It is the average squared deviation of individual scores from μ.