Illustrations for the Central Limit Theorem

Final project for Developing Data Products course from Johns Hopkins University on Coursera

This is the presentation for the app that you can check out here

Have you ever wanted to see the Central Limit Theorem in action? It is an asymptotic result that tells us about the distribution of the mean of a sequence of n independent and identically distributed (i.i.d.) random variables drawn from a distribution with given expected value μ and finite variance σ²: for large n (or as n → ∞), we have X̄_n ∼ N(μ, σ² / n)

It is a powerful and general result that we can use to build confidence intervals, for example. But the theorem does not answer an important question for us to use this result, that is

How large should n be?

That is the question we are investigating in this application, mainly due to a rule of thumb present in statistics, where it is said that n = 30 is good enough. Now you have a simple app to test that for some distributions:

• Firstly, you select a distribution to draw samples from;

• Then, according to the distribution chosen, you can select its parameters;

• Now it is time select n under “Sample Size - Chosen Distribution”;

• The last input, “Mean Distribution Samples”, is the real trick for our investigation: we are having this number of samples from the mean distribution in order to plot our graphs.