# Python – Central Limit Theorem

Here is an explanation of the Central Limit Theorem (CLT) in a few simple points:

• Explanation:
• The Central Limit Theorem states that the distribution of the sample means (averages) of a large number of samples from any population will be approximately normally distributed.
• Or with other words – the mean of samples of random values have a bell curve distribution.
• Independence:
• Each sample must be independent of the others.
• This means the samples are drawn randomly and each one does not influence the others.
• Sample Size:
• The theorem holds true as the sample size (number of observations in each sample) becomes large.
• Typically, a sample size of 31 is considered sufficient.
• Population Distribution:
• The shape of the population distribution does not matter.
• Whether the population is normal, skewed, or has any other shape, the distribution of the sample means will tend to be normal.
• Mean and Variance:
• The mean of the sample means will be equal to the population mean.
• The variance of the sample means will be equal to the population variance divided by the sample size, indicating that larger samples provide more precise estimates of the population mean.

In summary, the Central Limit Theorem is a fundamental principle in statistics that allows us to make inferences about population parameters based on sample statistics, regardless of the population’s distribution shape, given a sufficiently large sample size.

Jupyter Lab code from the video – https://github.com/Vitosh/Python_personal/tree/master/YouTube/014_Python-Central-Limit-Theorem

Enjoy it 🙂

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