Enter the population mean, population standard deviation, and sample size into the central limit theorem calculator. The calculator will return the sample standard deviation. This calculator can also evaluate the population standard deviation and the samples size, given the other two values.

## 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

To calculate the central limit theorem, divide the population standard deviation by the square root of the sample size.

To calculate the population standard deviation, multiply the sample standard deviation by the square root of the sample size.

To calculate the sample size divide the population standard deviation by the sample standard deviation, then square the result.

## Central Limit Theorem Definition

A central limit theorem is a theorem that states the standard deviation of a sample is equal to the standard deviation of the population divided by the square root of the sample size.

## How to calculate central limit theorem?

How to calculate standard deviation using the central limit theorem

1. First, determine the standard deviation of the population

Using the formula for standard deviation, calculate this value for the entire population.

2. Next, determine the same size

This is the total size of the sample, denoted as n in the calculator above.

3. 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 calculating the sample standard deviation to the equation mentioned above.