# Central Limit Theorem (CLT) ### Written byTrue Tamplin, BSc, CEPF® | Reviewed by Editorial Team

Updated on December 19, 2022

## Central Limit Theorem (CLT) Definition

The Central Limit Theorem (CLT) is a statistical theory that posits that the mean and standard deviation derived from a sample, will accurately approximate the mean and standard deviation of the population the sample was taken from as the size of the sample increases.

The minimum number of members of a population needed in order for a sample to adequately represent the population it was pulled from, is 30 according to the central limit theorem.

## Defining CLT in Simple Terms

To define CLT in another way, let's imagine that a sample of 30 stock analysts were gathered together and asked how much they thought a certain stock was going to rise in the next quarter.

If the average answer from the sampled analysts was 5%, then according to the CLT, this answer would reasonably approximate the answer of every person working as a stock analyst.

## Purpose of the Central Limit Theorem

In finance, the central limit theorem can be used to expedite analysis. Since indices often have hundreds, sometimes thousands of stocks contained within them an analyst doesn't have enough time in a month, much less a day to go through them all.

By putting the CLT to work, an analyst can take just 30 stocks out of an index and be able to approximate the quality of the index as a whole and thereby make a confident assessment.

## Central Limit Theorem (CLT) FAQs

### What does CLT stand for?

CLT stands for Central Limit Theorem.

### What is the CLT?

The CLT is a theory saying that the mean and standard deviation derived from a sample, will accurately approximate the mean and standard deviation of the population the sample was taken from as the size of the sample increases.

### What is the purpose of the CLT?

In finance, the central limit theorem can be used to expedite analysis.

### What sample is neccessary to make the CLT adequate?

The minimum number of members of a population needed in order for a sample to adequately represent the population it was pulled from is 30 according to the central limit theorem.

### What is an example of the CLT in action?

Let’s imagine that a sample of 30 stock analysts were gathered and asked how much they thought a certain stock would rise in the next quarter. If the average answer was 5%, then according to the CLT, this answer would reasonably approximate the answer of every person working as a stock analyst. 