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Sampling Lab

Pick a population (any shape, as skewed as you like), then draw samples from it. Panel 2 shows each sample; panel 3 collects the sample means. Two of the most important theorems in statistics appear before your eyes: the running mean settles onto μ (Law of Large Numbers) and the histogram of sample means turns into a bell curve centered at μ with spread σ/√n (Central Limit Theorem).

How to use
  1. Choose a population and set its parameters. Try something skewed, like the Exponential.
  2. Set the sample size n, then click "Draw 100" a few times.
  3. In the CLT lens, compare the histogram of sample means to the overlaid normal curve, then increase n and reset.
  4. Switch to the LLN lens to watch the running mean converge to μ as observations accumulate.
  5. Check the readouts: the SD of the sample means should sit right next to σ/√n.
1 · Population
2 · Latest sample
3 · Sampling distribution
μ
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σ
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σ/√n
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Samples
0
Mean of x̄
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SD of x̄
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