Difference between revisions of "Central limit theorem"
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The '''central limit theorem''' is a fundamental theorem in statistics. It states that: | The '''central limit theorem''' is a fundamental theorem in statistics. It states that: | ||
| − | :the distribution of an average of samples, taken from '''''any''''' type of underlying [[probability function]], will approach a [[Normal distribution]] as the sample size increases. | + | :the distribution of an average of samples, taken from '''''any''''' type of underlying [[probability function]] having a finite variance, will approach a [[Normal distribution]] as the sample size increases. |
If the sample size is only one, then the distribution of the average of samples will not approach a [[Normal distribution]], but will approach the distribution of the underlying probability function. But as the sample size increases, the distribution of their averages increasingly approaches a Normal distribution. | If the sample size is only one, then the distribution of the average of samples will not approach a [[Normal distribution]], but will approach the distribution of the underlying probability function. But as the sample size increases, the distribution of their averages increasingly approaches a Normal distribution. | ||
| − | [[ | + | [[Category:Probability and Statistics]] |
Latest revision as of 05:48, July 13, 2016
The central limit theorem is a fundamental theorem in statistics. It states that:
- the distribution of an average of samples, taken from any type of underlying probability function having a finite variance, will approach a Normal distribution as the sample size increases.
If the sample size is only one, then the distribution of the average of samples will not approach a Normal distribution, but will approach the distribution of the underlying probability function. But as the sample size increases, the distribution of their averages increasingly approaches a Normal distribution.