# Central Limit Theorem

The central limit theorem states that any set of variates with a distribution having a finite mean and variance tends to the normal distribution. This allows statisticians to approximate sets of data with unknown distributions as being normal.

Central limit theorem is a college-level concept that would be first encountered in a probability and statistics course. It is an Advanced Placement Statistics topic and is listed in the California State Standards for Probability and Statistics.

### Prerequisites

Moment: | In statistics, a moment is a measure of the expected deviation from the mean. The most important example of a moment is the variance. |

Normal Distribution: | The normal distribution is a probability distribution associated with many sets of real-world data. Due to the shape of this distribution, it is also famously called the "bell curve." |

Standard Deviation: | The standard deviation is a statistic defined as the square root of the variance that measures how spread out a set of data is. |

Variance: | In statistics, variance is the measure of the expected deviation from the mean. The square root of the variance is the standard deviation. |