Central Limit Theorem Demonstration

Central Limit Theorem demonstration based on simulation: a pure frontend Shiny app using Shinylive.

The Central Limit Theorem is a key concept in probability theory that is often introduced to first and second year undergraduate students as it implies that probabilistic and statistical methods such as parametric tests that work for normal distributions can be applied to many problems involving other types of distributions.

This Shiny app is built using Shinylive, which allows it to run entirely on the frontend without the need for a server. However, this also means that it may take some time to load in the web browser. The app displays the histogram of the sample distribution, as well as the histogram and normal quantile plot of the sampling distribution of the sample mean for simulated samples drawn from various distributions, such as normal, uniform, chi-squared, and others. The app demonstrates that the sampling distribution of the mean will always be approximately normal, as long as the sample size is large enough.

To access the web app, please click on this link.