Draw a population, repeatedly sample from it, and watch the sampling distribution form. Compare sampling distributions for means, variances, standard deviations, proportions, and other statistics.
Create a population
Drag across the graph to draw relative frequencies on a 0–100 scale.
Population mean μ
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Population variance σ²
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Population SD σ
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1. Specify the population proportion
Each observation is a success (1) with probability p and a failure (0) with probability 1 − p.
0 (failure):
1 (success):
Sample repeatedly
Each sample produces one sample mean.
Runs of 250 samples or fewer can fall into the graph one at a time.
Sampling distribution of x̄
The original population stays faintly visible behind the sampling distribution.
PopulationSimulated statisticsPopulation value
Population mean
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Mean of simulated x̄
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SD of simulated x̄
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The reference line marks the corresponding population quantity.