Mean + Variance

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.       

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