Difference between revisions of "Central limit theorem"
Jump to navigation
Jump to search
(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.) |
m (corrected punctuation typo, will address talk page next) |
||
| 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]], 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 20:31, November 26, 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, 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.