Definition of Central Limit Theorem:

The Central Limit Theorem is a fundamental concept in statistics that states that, given a sufficiently large sample size, the sampling distribution of the mean of a random variable will be approximately normally distributed, regardless of the shape of the population distribution.

Key Points:

• The Central Limit Theorem applies to a wide range of random variables, as long as certain conditions are met.
• It is not necessary for the population distribution to be normally distributed in order for the sample mean to follow a normal distribution.
• As the sample size increases, the sampling distribution of the mean tends to approach a normal distribution.
• The mean of the sampling distribution will be equal to the population mean.
• The standard deviation of the sampling distribution, also known as the standard error, decreases as the sample size increases.
• The Central Limit Theorem is particularly useful in inferential statistics, as it allows for the use of normal distribution-based techniques, such as confidence intervals and hypothesis tests.