Central Limit Theorem

Pick a parent distribution and a sample size (n). We'll draw many random samples of size n, compute the mean of each sample (x̄), and plot the distribution of those means. Watch how it approaches a Gaussian (Normal) shape as n grows — no matter what the parent distribution looks like.

Parent Distribution

Population Draws

Sample Size (n)

Number of Samples

Population (Parent) Distribution

Mean (μ): -

Std Dev (σ): -

Sampling Distribution of x̄

Observed Mean: -

Observed Std Error: -

Predicted SE (σ/√n): -

Population Distribution (5,000 draws)

Individual values

Sampling Distribution of the Mean (x̄)

Sample means (x̄)

Predicted Normal curve

Observed Mean (x̄)

CLT Predicted Mean (μ)