 # Central Limit Theorem

Updated on September 27, 2023 , 4063 views

## What is Central Limit Theorem?

The Central Limit Theorem shows the distribution of samples that means a normal distribution (a bell-shaped curve). It is a sample size that becomes larger and the size of the sample is over 30. If the sample size increases then, the sample mean and Standard Deviation will be closer in value to the population mean and standard deviation This concept was developed by Abraham de Moivre in 1733, but it was not named till 1930. Later when Hungarian mathematician George Polya noted and officially named it as Central Limit Theorem.

## Why is the Central Limit Theorem is important?

The Central Limit Theorem says that whatever the distribution of the population may be, the shape of the Sampling Distribution will approach as normal on sample size. It is useful because the sampling distribution is the same as the population mean, but by selecting a random sample from the population sample means will cluster together. This makes the research easy in order to make a good estimate of the population mean.

If the sample size increases, then the sampling error will decrease. The small size equal or greater to 30 is required for the Central Limit Theorem, which is precisely perfect. A large number can predict the parameters of the population like mean and standard deviation. And, if the sample size increases the distribution of the frequencies come closer to the normal distribution.