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:
“The present war having so long cut off all communication with Great-Britain, we are not able to make a fair estimate of the state of science in that country. The spirit in which she wages war is the only sample before our eyes, and that does not seem the legitimate offspring either of science or of civilization.”
—Thomas Jefferson (17431826)
“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 (18031873)