Difference between variance & unbiased estimate of population variance?

[moneyfaery]

Is there any rule that states when I should find the 'unbiased' estimate vs. 'biased'? And what is that n/n-1 thing crammed right before the formula? :X

[Eyas]

The variance of the sample refers to the normal variance (the "biased" as you call it, which uses n as the denominator).

Only use the unbiased variance formula if you are asked for an "unbiased estimate for the variance" or "an estimate of the variance of the population". In other cases where you are just asked for the "variance" or "the variance of the sample", the /n is used.

The whole "n/n-1"is because:

Variance = (SUM[f_i(x-mean)^2]) /n

Unbiased variance = (SUM[f_i(x-mean)^2])/(n-1)

So if you already have the value of the variance and you want to convert it to an unbiased estimate, multiply it by n and then divide it by n-1 so that the denominator becomes n-1.

Not sure if I was clear enough.. but thats basically it

edit: also.. note that sometimes you'll get questions like "find the standard deviation of the sample" vs "find an unbiased estimate of the standard deviation of the population" each one is the square root of its respected variance (so unbiased S.D is sqrt(unbiased V) ..)

Edited May 2, 2009 by Eyas

[moneyfaery]

So they tell you when to find the biased/unbiased estimates.

That makes perfect sense. Thank you.