Central limit theorem simulator
Paste population values and set sample size and repetitions.
Histogram of sample means
| From | To | Samples | Share |
|---|---|---|---|
| Fill in the fields above — the result is computed on this page. | |||
How do I use this page?
- Paste a finite population or empirical distribution.
- Set n, repetitions and seed.
- Compare the histogram with theoretical and simulated standard errors.
What this page does not do: Simulation does not prove normality for a particular small sample. Dependence, infinite-variance heavy tails and unrepresentative data violate the model.
Further reading
Theory — what is the central limit theorem?
The central limit theorem states that the distribution of sample means approaches a normal distribution as sample size grows, even when the population itself is not normal. The mean of that distribution tends toward μ, while its standard deviation tends toward σ divided by the square root of sample size n. The simulator lets you paste population values and set sample size and the number of repetitions to see this effect on a chart. A fixed seed reproduces the same experiment, making it easy to compare settings.
Frequently asked questions
Why use a random seed?
Is n = 30 always enough?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.