The central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases. This fact holds especially true for sample sizes over 30.
Therefore, as a sample size increases, the sample mean and standard deviation will be closer in value to the population mean μ and standard deviation σ.
Why is the central limit theorem important?
The central limit theorem tells us that no matter what the distribution of the population is, the shape of the sampling distribution will approachnormalityas the sample size (N) increases.
Thus, the sampling error will decrease as the sample size (N) increases.
Summary
Olivia Guy-Evans, MSc
BSc (Hons) Psychology, MSc Psychology of Education
Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.
Saul McLeod, PhD
BSc (Hons) Psychology, MRes, PhD, University of Manchester
Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.
