Central Limit Theorem Visualizer
Overview
The Central Limit Theorem Visualizer demonstrates one of the most fundamental concepts in statistics: no matter what the population distribution looks like, the sampling distribution of means becomes approximately normal as sample size increases. Watch as skewed, uniform, or bimodal populations transform into beautifully normal sampling distributions through the magic of the Central Limit Theorem.
Tips
- Start with a highly skewed distribution (like Exponential) to see the CLT’s power - even extreme distributions become normal
- Increase sample size gradually (5, 10, 30, 50) to watch the sampling distribution transform from the population shape to normal
- With sample size of 1, the sampling distribution matches the population distribution exactly - this is your baseline
- The “magic number” of 30 is a rule of thumb, but you’ll see that even n=10 shows substantial normalization for most distributions
- Compare the standard deviation of the sampling distribution to the population SD divided by sqrt(n) - they should match!
- Use the uniform distribution to understand that CLT applies even when the population has no resemblance to normal
- Generate multiple samples to see the stability of the phenomenon - the CLT is not a fluke, it’s mathematical law
- Pay attention to how quickly the distribution normalizes - some population shapes (like bimodal) take longer than others