Sampling Simulator
Draw repeated samples and observe sample-to-sample variation, standard error and the sampling distribution of the mean.
Sampling variation is expected—even when the population does not change.
This simulator generates deterministic repeated samples from normal, right-skewed or bimodal population models. Learners can change sample size, population variability, the selected sample and the number of repeated samples, then compare empirical and theoretical standard error.
Sampling Simulator — Step by Step
Eight locked stages move from one sample to repeated sampling, sample-size effects, population shape, a small-sample shock and management interpretation.
Population, Current Sample and Sampling Distribution
Reveal the population context to begin.
Interpret sampling variation and precision.
Build Your Own Sampling Scenario
Experiment Mode is isolated from the guided demonstration. Change population shape, sample size, variability, repeated samples and the selected draw without changing guided progress.
Test sampling-distribution interpretation.
Sampling-distribution cues
Sampling Variation
Statistics vary across random samples even when the population is stable. Variation alone is not evidence of bias or data error.
Sampling Distribution
The distribution of a statistic across repeated samples of the same size from the same population.
Standard Error
The standard deviation of a sampling distribution. For the mean, theoretical SE is approximately σ/√n.
Sample Size
Larger n reduces the spread of sample means. Precision improves with the square root of n.
Population Shape
Population skewness or multiple modes can affect small-sample behaviour. The mean's sampling distribution often becomes more regular as n grows.
Simulation Repeats
More simulated samples stabilize the displayed sampling distribution but do not change the precision of each individual sample mean.
Use sample size, population variability and sampling-distribution behaviour to judge how much uncertainty should accompany the estimate.