# Central Limit Theorem Example

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**Formula:**`Mean = populationMean, Standard Error = populationSD / sqrt(sampleSize)`

## Introduction to Central Limit Theorem

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that describes the characteristics of the distribution of sample means. It states that when an infinite number of successive random samples are taken from a population, the sample means will approximate a normal distribution (a bell-shaped curve), regardless of the shape of the population distribution, provided the sample size is sufficiently large (usually n > 30).

## Parameter usage:

`sampleSize`

= number of observations in each sample`populationMean`

= mean of the population`populationSD`

= standard deviation of the population`numberOfSamples`

= number of samples taken from the population

## Example valid values:

`sampleSize`

= 36`populationMean`

= 100`populationSD`

= 20`numberOfSamples`

= 100

## Output:

`mean`

= mean of the sampling distribution of the sample mean`standardError`

= standard error of the sample means

## Data validation

Sample size must be greater than 30 for the theorem to hold true.

## Summary

This calculator approximates the mean and standard error of the sampling distribution of the sample mean, based on the Central Limit Theorem.

Tags: Statistics, Central Limit Theorem, Normal Distribution, Sampling