Sample from any distribution and watch sample means converge to normal. Adjust sample size and see the magic of CLT unfold.
Choose a source distribution, set the number of observations in each sample, and run repeated draws. The demo computes one mean per sample and plots those means so you can compare their shape with the original population. Increasing sample size usually makes the sampling distribution more nearly normal when the central limit theorem's conditions hold. The common surprise is that the theorem concerns sample means, not the raw observations, and it does not promise an exactly normal result for every finite sample size.
Each simulation repetition draws n observations from the selected source distribution and reduces them to one arithmetic mean. Repeating that process produces a collection of means, which forms the displayed sampling distribution. The sample-size control changes how many observations contribute to each mean; it is distinct from how many repetitions are used to fill the display.
For independent observations from one distribution with finite mean and variance, the means remain centered at the population mean. Their standard deviation is the population standard deviation divided by the square root of n. As n grows, the standardized distribution of means approaches a normal distribution under the usual central limit theorem conditions, though the visible histogram still contains simulation noise.
That is the central limit effect the demo is designed to expose. Averaging combines independent contributions, so the distribution of properly standardized means approaches normality under the theorem's conditions. The source distribution itself does not change. With small n, strong skewness or discreteness can remain visible, and the approximation may still be poor.
No. A larger n changes each calculated mean and its sampling distribution. It neither transforms the underlying population nor makes each observation normal. It usually tightens the means around the population mean, with standard error proportional to 1 divided by the square root of n, provided the observations are independent and the population variance is finite.
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