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Central Limit Theorem Calculator

The central limit theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size increases. This is the case no matter the shape of the population distribution. Sample sizes >= 30 are considered sufficient for the central limit theorem to hold.

The sampling distribution has the following properties

The mean of the sample means is equal to the mean of the population distribution:

$$\bar{x}= \mu $$

The standard deviation of the sampling distribution is equal to the standard deviation of the population distribution divided by the sample size:

$$\text{s}= \frac{\sigma}{\sqrt{n}} $$

You can find the sample mean and sample standard deviation of a given sample and entering the required values and clicking the Calculate button

Sample mean =

Population standard deviation =