# Central Limit Theorem

### Introduction: What is the Central Limit Theorem?

The Central Limit Theorem is a very important theorem in statistics. It says that if you take a sample of size "n" from a population, then the distribution of your sample's mean will be approximately normal, regardless of the underlying population distribution.

This theorem has many implications in different fields. One implication is that it provides statistical justification for using averages as an estimate of the central tendency in populations.

### Why Use the Central Limit Theorem?

The Central Limit Theorem is an important theorem that you should know. It states that as the sample size increases, the distribution of the sample means approaches a normal distribution. This is because of the law of large numbers.

Section topic: What are some uses for the Central Limit Theorem?

Section keywords:

Introduction:

The Central Limit Theorem is used in statistics for many different things. It can be used to estimate population parameters, test hypotheses about population parameters and make decisions on whether or not to use parametric or non-parametric tests. It can also be used to calculate confidence intervals and construct graphs.

### Working Through an Example of the Central Limit Theorem

The Central Limit Theorem is a theorem in probability theory that describes the distribution of the sum of many independent random variables.

The Central Limit Theorem states that if we have a population of size N, and we take samples of size n from this population, then the distribution of the sum of all these samples will be approximately normal (bell-shaped) with mean μ and standard deviation σ/√N.

This means that if you take a sample from a population, then the average value in your sample will be close to the population mean. It also means that as you get more samples, their average values will be closer together.