Enter the population mean, population standard deviation, and sample size into the central limit theorem calculator. The calculator will return the sample mean and sample standard deviation.

## Central Limit Theorem Calculator

The following formula is used to calculate the standard deviation of a sample using the central limit theorem.

s = σ / √n

- Where s is the sample standard deviation
- σ is the population standard deviation
- n is the sample size

How to calculate standard deviation using the central limit theorem

**First, determine the standard deviation of the population**Using the formula for standard deviation, calculate this value for the entire population.

**Next, determine the same size**This is the total size of the sample, denoted as n in the calculator above.

**Calculate the standard deviation**Determine the standard deviation of the sample using the formula above and the values from steps 1 and 2.

## FAQ

**What is the central limit theorem?**

The central limit theorem states that the population and sample mean of a data set are so close that they can be considered equal. That is the X = u. This simplifies the equation for calculate the sample standard deviation to the equation mentioned above.

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