# Stats questions

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#1

Hi, what does 'unbiased' mean this in context for the population parameters? Also why is s^2 the point estimator of variance? Thanks
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3 years ago
#2
(Original post by coconut64)

Hi, what does 'unbiased' mean this in context for the population parameters? Also why is s^2 the point estimator of variance? Thanks
Unbiased means the expectation of the point estimator is equal to the population parameter.

If this is Edexcel (don't know about others), then s^2 is defined as which is an unbiased estimator of the variance.
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3 years ago
#3
(Original post by coconut64)

Hi, what does 'unbiased' mean this in context for the population parameters? Also why is s^2 the point estimator of variance? Thanks
"Unbiased" means that if you were to use a particular estimator many times, the errors would be evenly distributed about the respective true population parameter. In other words, there is no systematic loading of the errors in one direction or another.

The variance of a sample, calculated using the variance formula, is biased as an estimator pf the population variance because it is necessarily calculated with respect to its own mean rather than the population mean. The sample mean is naturally "in the middle" of the sample values and this tends to yield a variance on the low side, as compared to the population variance. S^2 fixes this low bias by using (n - 1) rather than n in the denominator.

Edit: beaten to it by ghostwalker
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