Research Topics:

Data Analysis

Content Type:

Glossary

Central Limit Theorem (CLT) Definition

A distribution of a large number of sample means or sample proportions will approximate a normal distribution regardless of the actual distribution of the population from which they were drawn.

The central limit theorem, or CLT, is a statistical principle that says that regardless of the underlying distribution of a population, the distribution of sample means will tend to follow a normal distribution. That is the case regardless of the actual distribution of the population from which they were drawn. What this means is that even if the population data is not normally distributed, the means of different samples drawn from that population will be about the same. What’s important about this theorem is that it allows marketing researchers to make accurate inferences about a population based on a sample. It helps mitigate the impact of irregular population distributions, thus making it possible to apply parametric statistical methods. Parametric statistics are based on assumptions about the distribution of population from which the sample was taken. CLT is the foundation for hypothesis testing, confidence intervals and other key statistical methods used in marketing research.

Who relies on the central limit theorem?

Researchers, analysts and marketing research professionals who conduct surveys, experiments or any form of data collection rely on CLT, especially when dealing with large and diverse populations. The theorem helps ensure that the collected data accurately represents the population's characteristics.

Why should I care about the central limit theorem?

The theorem safeguards the reliability of marketing research conclusions because without a sufficiently large sample size, data might not reflect the true population characteristics. Understanding and applying the CLT will ensure that data findings are generalizable and representative, thus adding validity to marketing strategies and decisions.