“Facts are stubborn things, but statistics are pliable.” — Mark Twain
An interactive demonstration of the Central Limit Theorem: the sampling distribution of the mean converges to normal as sample size grows.
Central Limit Theorem
The distribution of sample means approximates a normal distribution as sample size increases.
\( \frac{\bar{X} - \mu}{\sigma / \sqrt{n}} \approx N(0,1) \)
Key: \(\bar{X}\) = sample mean, \(\mu\) = population mean, \(\sigma\) = std dev, \(n\) = sample size.