The central limit theorem formula provides a relationship between the sample means and the population mean. For this it is assumed that the samples have been collected from a larger population with replacement. For a sufficient larger set of samples, the sample means are normally distributed. The central limit theorem formula helps to make inferences about the sample mean and the population mean values. Further, central limit theorem formula helps us to identify if the sample belongs to the referred population.
What is Central Limit Theorem Formula?
The formula is based on the central limit theorem, which states that the average of the sample means taken from a large population is equal to the population mean. Here \(\bar x_1 \), \( \bar x_2 \), \( \bar x_3\), ......\(\bar x_n\) are the individual means of the samples picked from larger population, and \(\mu \) is the population mean. Then, the central limit theorem formula is given as: