Central Limit Theorem

The central limit theorem (CLT) is the foundation of statistics. Just by collecting a subset of data from a population and using statistics, we can draw conclusions about that population.

CLT says that mean of the sampling distribution of the sample means is equal to the population mean irrespective of the distribution of the population and when the sample size is greater than 30.

In general central limit theorem states that when an infinite number of successive random samples are taken from a population, the sampling distribution of the means of those samples will become approximately normally distributed with mean μ and variance σ²/n as the sample size (n)becomes larger, irrespective of the shape of the population distribution

The CLT essentially simplifies the job of a data analyst! When we want to compare two different populations through statistical significance tests/hypothesis testing, CLT is very useful. If we can claim normal distribution, there are a number of things we can say about the data set.

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