Sampling Distribution Explorer

Sample again. Watch the statistic settle into a distribution.

Students can switch population shapes, choose a statistic, and compare one current sample to the long-run sampling distribution that emerges from repeated draws.

Return to Stats & Operations Analysis

Setup

Population, statistic, and run controls

Simulation inputs

Choose what the population looks like, what you measure, and how quickly the animation runs.

Choose Custom drawn to sculpt a strange population directly on the population chart.

Run the experiment

Start with one animated draw, then scale up to see the sampling pattern stabilize.

Live readout

These values update as the simulation runs and the distribution builds.

Population mean -
Population SD -
Sampling dist. mean -
Sampling dist. SD -

Replications: 0. Selected statistic: Mean.

Observed Standard Error

This will update as replications accumulate.

Visualization

Population, sample, and the sampling distribution

Compare the parent population, the current sample, and the chosen statistic's sampling distribution side by side.

Population distribution

Blue marks the mean, purple the median, and orange the sample-space spread around the mean.

Current sample draw

This panel resets on each draw so students can focus on the current sample only.

Sampling distribution of selected statistic

Every sample adds one new statistic box to this growing stack.