Central Limit Theorem Calculator

This function calculates the variance of a sample according to the central limit theorem. The central limit theorem states that the sample means form their own normal distribution, called the sampling distribution of the mean.

To calculate, enter the deviation of the total amount and the size of the sample (min. 30). Then click on the 'Calculate' button.

Formula for the central limit theorem

This distribution has the same mean as the original distribution and a variance equal to the original variance divided by the sample size.

Given a known population mean and a sufficiently large sample, the central limit theorem says that the sample mean is equal to the population mean. This applies to sample sizes greater than 30

Sample Mean   \(\displaystyle μ_\overline{x} = μ \)

Standard deviation for a sample

\(\displaystyle σ_\overline{x}=\frac{σ}{\sqrt{n}}\)