Central Limit Theorem Visualizer

Regardless of the parent distribution, the distribution of sample means tends to a Normal distribution.

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Population Shape (X)

Sampling Distribution of $\bar{X}$

Central Limit Theorem Even if the population is not Normal, the distribution of sample means approaches Normal when n is large:
$$ \bar{X} \approx N\left(\mu, \frac{\sigma^2}{n}\right) $$