Sampling distribution
Sampling distribution is the probability distribution of an estimator, such as a sample mean, across all possible samples of size n from a population. It shows how much the estimate varies from sample to sample.
See it move
A bell-shaped distribution chart plots sample mean (x̄) on the horizontal axis against frequency on the vertical axis. Each draw of n observations from the population produces one x̄; collected across all possible samples they form this bell curve — the sampling distribution of the mean. With a population standard deviation σ = 30, the standard error is 30/√100 = 3 at n = 100; increasing to n = 400 narrows the bell to a standard error of 1.5, demonstrating that larger samples produce less variable and more precise estimates of the population mean.
The formula
Variables
- Standard deviation of the sampling distribution of the mean
- Population standard deviation
- Sample size
Larger n compresses the sampling distribution, making the sample mean a more precise estimator.