Central Limit Theorem Demo

This project demonstrates the principles of the Central Limit Theorem by sampling a given input distribution 1000 times with a user specified sample size.

Requirements

If plotting is enabled, Matplotlib and Seaborn are required.

Usage

The central_limit_theorem_demo.py file contains a CentralLimitTheorem class. It can be instantiated with a distribution in the form of a list.

import central_limit_theorem_demo as clt

some_distribution = create_distribution(...)
cltDemo = clt.CentralLimitTheorem(some_distribution)

The demo can be run via the run_sample_demo method on CentralLimitTheoremDemo. This method takes a sample size N, a plotting flag plot, and an optional num_bins parameter describing the number of bins to use when plotting the demo output.

Example

A full example might look something like this.

import central_limit_theorem_demo as clt

def create_uniform_sample_distribution():
    return range(100)

def run():
    sampleDistribution = create_uniform_sample_distribution()
        
    # Plot the original population distribution
    clt.plot_distribution(sampleDistribution, "Population Distribution", 0, 100, 20)
        
    # Plot a sampling distribution for values of N = 2, 3, 10, and 30
    cltDemo = clt.CentralLimitTheoremDemo(sampleDistribution)
    n_vals = [2, 3, 10, 30]
    for N in n_vals:
        cltDemo.run_sample_demo(N = N, plot = True, num_bins = 40)

This produces the following output images.