# Definition of Central limit theorem

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**Central limit theorem**Definition from Business & Finance Dictionaries & Glossaries

Sean_Woo's Finance,GIS & Real Estate Glossary

for a large sample size, the sampling distribution of

**x mean**is approximately normal, irrespective of the shape of the population distribution. The sample size is usually considered to be large if**n>=30**.**Central limit theorem**Definition from Science & Technology Dictionaries & Glossaries

Common Concepts in Statistics

The means of a relatively large number of random samples from any population (not necessarily a normal distribution) will be approximately normally distributed with the population mean being their mean and variance being the (population variance / n). This tendency will increase as the sample size (the number of samples) increases. See Central Limit Theorem

**Central limit theorem**Definition from Encyclopedia Dictionaries & Glossaries

English Wikipedia - The Free Encyclopedia

In probability theory, the

**central limit theorem**(**CLT**) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. To illustrate what this means, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a "bell curve"). A simple example of this is that if one flips a coin many times, the probability of getting a given number of heads should follow a normal curve, with mean equal to half the total number of flips.See more at Wikipedia.org... |

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