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

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.


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.