On This Page:TogglePurpose of Sampling DistributionsHow to Find Sampling DistributionThe Central Limit Theorem
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In statistics, a sampling distribution is the probability distribution of a statistic (such as the mean) derived from all possible samples of a given size from a population.
The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
In statistics, a sampling distribution shows how a sample statistic, like the mean, varies across many random samples from a population. It helps make predictions about the whole population. For large samples, the central limit theorem ensures it often looks like a normal distribution.
Purpose of Sampling Distributions
Sample statistics only estimate population parameters, such as the mean or standard deviation. This is because, in real-world research, only a sample of cases is selected from the population.Due to time restraints and practical issues, a researcher cannot test the total population.Therefore, it is likely that the sample mean will be different from the (unknown) population mean.
Sample statistics only estimate population parameters, such as the mean or standard deviation. This is because, in real-world research, only a sample of cases is selected from the population.
Due to time restraints and practical issues, a researcher cannot test the total population.Therefore, it is likely that the sample mean will be different from the (unknown) population mean.
Three different distributions are involved in building the sampling distribution.
How to Find Sampling Distribution
It is important to note that sampling distributions are theoretical, and the researcher does not select an infinite number of samples.
To create a sampling distribution, research must:
The Central Limit Theorem
In practical applications, it’s not feasible to draw infinite samples to create a sampling distribution. However, the concept of drawing “all possible samples” is a theoretical foundation underlying the idea of a sampling distribution.
Thecentral limit theoremtells us that no matter the population distribution, the sampling distribution’s shape will approachnormalityas the sample size (N) increases.
Figure 1.Distributions of the sampling mean (Publisher: Saylor Academy).
Thus, the sampling error will decrease as the sample size (n) increases.
Further InformationSampling Distribution of the Sample Mean (Kahn Academy)Statistics for Psychology Book Download
Further Information
Sampling Distribution of the Sample Mean (Kahn Academy)Statistics for Psychology Book Download
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.
