Central Limit Theorem (CLT) — build the sampling distribution of x̄

Choose a population mean μ and standard deviation σ, then repeatedly sample n observations. Each sample produces a sample mean x̄, which gets added to the dot plot (the sampling distribution of x̄).

Population mean (μ)

Population standard deviation (σ)

Sample size (n)

Actions

Population distribution

(Normal with mean μ and SD σ)

Population parameters

μ = 0, σ = 1

Horizontal scale

[−4, 4]

The sample plot below uses the same x-axis scale. After you take your first sample, μ and σ are locked until you press Reset.

Most recent sample

(Histogram of n observations)

Sample statistics

x̄ = —, s = —

Sample size

n = 10

Sampling distribution of x̄ (dot plot)

Each dot = one sample mean

Counts + center

Samples = 0
Mean(x̄) = —

Spread

SE = —
σ/√n = —

As n increases, the sampling distribution of x̄ becomes tighter, and its shape approaches Normal.