Posts Tagged ‘variance’
Mean + Variance Continued
February 25th, 2007
Estimating the Variance
and the unbiased estimator: 
Confidence interval for 
is 
At 95% confidence interval,
, and
Note that:
For example,
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Mean + Variance
January 14th, 2007
The mean and variance are some of the most used in math and statistics. Below are some Math Formulas of the mean and variance.
Estimating the mean – µ
is an unbiased estimator. You can prove this by using: 
If 
for all n > 1, then the Central Limit Theorem says that: 
(a Normal distribution).
| Confidence Interval for µ
You can prove this by using:
|
If the sample is small, to retain 95% CI, you have to widen the interval. To do that, you replace Z 0.025 by t 0.025. Then either:
and Z 0.025 = 1.96
OR
If you don’t know for certain, you can use t 0.025 instead of Z to compensate for S.