The Central Limit Theorem (CLT) Simulator demonstrates how sample means approximate a normal distribution as sample size increases, regardless of the population’s original distribution. This tool is essential for students, researchers, and analysts who want to visualize and understand this fundamental statistical concept.

Key Features

✅ Simulates Different Population Distributions – Choose from normal, uniform, skewed, or custom distributions.
✅ Adjustable Sample Sizes – Experiment with different sample sizes to see the CLT in action.
✅ Dynamic Visualization – Displays histograms of sample means, illustrating convergence to normality.
✅ Instant Mean & Variance Calculation – Computes the mean and variance of sample distributions.
✅ PDF Report Generation – Export simulation results, including statistical summaries and charts.

Use Cases

📌 Statistics & Probability Education – Learn and teach the CLT with interactive simulations.
📌 Data Analysis & Research – Validate assumptions of normality for statistical testing.
📌 Business & Market Research – Analyze sample trends for decision-making.
📌 Quality Control & Manufacturing – Assess sample consistency in production processes.

How It Works

1️⃣ Select Population Distribution – Choose a predefined distribution or input custom data.
2️⃣ Set Sample Size & Number of Samples – Adjust sample size and the number of iterations.
3️⃣ Run Simulation – The tool draws random samples, calculates sample means, and plots the distribution.
4️⃣ Analyze Results – Observe how sample means tend toward a normal distribution as the sample size increases.
5️⃣ Download PDF Report – Export a statistical summary with detailed calculations and visual insights.

This simulator provides an interactive way to explore the Central Limit Theorem, making statistical concepts clearer and more intuitive. 🚀