All simulators
Central Limit Theorem Simulator
Draw thousands of sample means from skewed or bimodal parents and watch the normal shape appear.
Day 7: The Law of Large Numbers & Central Limit Theorem4,000 simulated sample meansCLT: N(μ, σ²/n)
Parent distribution
mean of x̄
1.003
μ = 1.000
sd of x̄
0.182
σ/√n = 0.183
skewness of x̄
0.32
normal = 0
4,000 samples of size n. Even when the parent is skewed or lumpy, the sample mean's distribution approaches N(μ, σ²/n). Skewness shrinks like 1/√n.