Statistics Interactive

Five core concepts, one page — explore them with sliders and animations.

1. Normal Distribution

The bell curve is the most important distribution in statistics. The μ (mean) controls the center, and σ (standard deviation) controls the spread. The 68–95–99.7 rule: ~68% of data falls within 1σ, ~95% within 2σ, ~99.7% within 3σ.

2. Central Limit Theorem

No matter what the original population looks like, the distribution of sample means approaches a normal distribution as sample size n grows. Drag the slider to increase n and watch the sampling distribution narrow and become bell-shaped.

3. Correlation

The Pearson correlation coefficient r measures linear association between two variables, ranging from −1 (perfect negative) to +1 (perfect positive). Drag the points on the scatter plot to see how r changes in real time.

4. Law of Large Numbers

As you repeat a random experiment, the average of results converges to the expected value. Click Roll to simulate rolling a fair die and watch the running average converge toward 3.5.

5. Bayes' Theorem

Bayes' theorem updates our belief about a hypothesis given new evidence. This is crucial in medical testing, spam filtering, and scientific inference.