Squared Deviations - Sample Variance

Sample Variance

The sum of squared deviations needed to calculate variance (before deciding whether to divide by n or n − 1) is most easily calculated as

From the two derived expectations above the expected value of this sum is

which implies

This effectively proves the use of the divisor n − 1 in the calculation of an unbiased sample estimate of σ2.

Read more about this topic:  Squared Deviations

Famous quotes containing the words sample and/or variance:

    All that a city will ever allow you is an angle on it—an oblique, indirect sample of what it contains, or what passes through it; a point of view.
    Peter Conrad (b. 1948)

    There is an untroubled harmony in everything, a full consonance in nature; only in our illusory freedom do we feel at variance with it.
    Fyodor Tyutchev (1803–1873)