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.