Difference between revisions of "Central limit theorem"
Jump to navigation
Jump to search
m (corrected punctuation typo, will address talk page next) |
(qualification of having a finite variance added per talk page) |
||
| Line 1: | Line 1: | ||
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]] | [[category:Probability and Statistics]] | ||
Revision as of 03:36, November 27, 2015
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.