Central Limit Theorem Visualization - Binomial Distribution

This project demonstrates the Central Limit Theorem (CLT) using a Binomial distribution and animated histograms.
It shows how the distribution of sample means approaches a normal distribution as the sample size increases.

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📌 Features

• Interactive Matplotlib animation showing the CLT in action.
• Multiple sample sizes compared in real-time.
• Overlay of the theoretical normal distribution for comparison.
• Clean and modular code using NumPy, SciPy, and Matplotlib.

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🖼 Preview

(Generated using the script — save as GIF with ani.save("clt_binomial.gif", writer='imagemagick').)

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📚 Theory: Central Limit Theorem The Central Limit Theorem states that, for a large enough sample size, the distribution of sample means will approximate a normal distribution — regardless of the population's original distribution — as long as samples are independent and identically distributed.

In this project: Population: Binomial distribution (n_trials = 10, p = 0.5) Sample sizes tested: 5, 10, 30, 100, 500 Comparison: Theoretical normal curve is plotted alongside histograms.