# Central Limit Theorem

In this lesson, concepts of the central limit theorem are explored.

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In inferential statistics, operations are performed on a sample of data, and then predictions are made about an entire population. The central limit theorem is considered an important concept in inferential statistics due to its widely used applications.

## What is it?

The central limit theorem or CLT states that:

The mean of a random sample will closely resemble the mean of the whole population as the sample size increases, regardless of the shape of the data distribution.

The above statement means that whatever the data distribution is, whether it be uniform, binomial, normal, etc., if the sample size or the size of the subset of the data keeps increasing, the average value of the entire population of data can be inferred by taking the average of that sample data. Let’s test this theorem with an example to verify its credibility.

### Example

The following steps will be performed in this example:

• An array with one-thousand random values will be created.

• Then, the average of this dataset is computed, which is our original mean value. Later it will be compared with the inferred one.

• Then, thirty random samples are gathered with each sample containing twenty-five data points.

• The average value of each random sample is computed and stored in a list.

• The inferred mean value is calculated by taking an average of the values in the list.

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