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Central Limit Theorem Lab

Sampling Distributions & The Magic of Averaging

Parent Distribution

Each value equally likely — like rolling a fair die.

Sample Size N5

130100

Draw Samples

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Ready to Explore

You're working with a Dice Rolls (Uniform) distribution. Press "Draw 1" to collect your first sample mean and start building the distribution below.

Population DistributionSource of all samples

Sampling ActionN = 5 values per sample

Distribution of Sample Means0 means collected

x̄ → μ

Mean of means → pop. mean

σ_x̄ = σ/√N

Std. error shrinks with N

x̄ ~ N(μ, σ²/N)

Means become normal as N↑