Interactive Tools

See statistics happen.

Change a number and watch the diagram, curve, or simulation respond. 23 free tools, no login required, each linked to the article that explains the idea behind it.

Probability

Venn Diagram Maker

Two or three sets, with counts and probabilities

Enter set sizes and overlaps for two or three sets and see the Venn diagram with the count in every region, plus the union, the intersection, and each probability, worked out with inclusion–exclusion.

Probability

Coin Flip Simulator

Watch the law of large numbers happen

Flip a fair or biased coin up to 10,000 times and watch the running proportion of heads settle toward the true probability, with streak counts and a full tally.

Sampling & Inference

Random Number Generator

Integers or decimals, with or without repeats

Generate random whole numbers or decimals in any range, choose how many, allow or forbid repeats, sort the results, and copy them in one click.

Distributions

Bell Curve Explorer

Drag the mean and spread, shade any area

Adjust the mean and standard deviation of a normal distribution, shade the area between any two values, and read off the probability, z-scores, and the 68-95-99.7 bands.

Descriptive Statistics

Box Plot Generator

Paste data, get the box plot and five-number summary

Enter a data set and see its box plot with quartiles, whiskers, and outliers marked using the 1.5 × IQR rule, alongside the full five-number summary.

Regression & Correlation

Scatter Plot & Correlation Visualizer

Click to add points and watch r change

Type or click points onto a scatter plot and watch the correlation coefficient, regression line, slope, and intercept update instantly, with outlier and curved-relationship examples.

Descriptive Statistics

Histogram Maker

Paste data, choose a class width, get the table

Turn a data set into a histogram and a frequency, relative frequency, and cumulative table, with Sturges and Freedman–Diaconis class-width suggestions.

Probability

Probability Tree Builder

Branches, joint probabilities, and Bayes

Build a two-stage probability tree and see every branch multiply out to a joint probability, then reverse the conditioning with Bayes' theorem, with a natural-frequency summary.

Hypothesis Testing

Rejection Region Diagram

Critical values and the decision, drawn

Choose a z or t test, one- or two-tailed, set the significance level, and see the critical values, the shaded rejection region, the p-value, and the decision for your observed statistic.

Sampling & Inference

Central Limit Theorem Simulator

Watch sample means become normal

Draw repeated samples from a skewed, uniform, or bimodal population and watch the distribution of sample means become bell-shaped as the sample size grows.

Sampling & Inference

Confidence Interval Simulator

See what 95% confidence really means

Draw many samples from a population with a known true mean and watch how often the resulting confidence intervals actually capture it.

Distributions

Binomial Distribution Explorer

Drag n and p, watch the shape change

Drag the number of trials and the success probability and watch the binomial probability chart update in real time.

Distributions

Poisson Distribution Explorer

Drag λ, watch the shape change

Drag the average rate and watch the Poisson probability bar chart update, with an optional normal-approximation overlay.

Distributions

T-Distribution Explorer

Watch the tails shrink as df grows

Drag the degrees of freedom and watch the t-distribution converge toward the normal curve, with shaded-area probabilities.

Regression & Correlation

Regression Diagnostics Explorer

Residuals, leverage, and Cook's distance

Paste (x, y) data and see the fitted line, a residuals-vs-fitted plot, and every point's leverage and Cook's distance, with influential points flagged.

Sampling & Inference

Confidence Interval for a Proportion Simulator

Wilson vs. Wald, side by side

Draw repeated samples and compare Wilson and Wald confidence interval coverage for a proportion, including the Wald interval's collapse when a sample has zero successes.

Hypothesis Testing

ANOVA Visualizer

Drag means and spread, watch F respond

Drag each group's mean and a shared spread slider and watch the F statistic and p-value update, showing between-group versus within-group variance directly.

Regression & Correlation

Spearman Rank Correlation Visualizer

Watch rho and r diverge, live

Paste paired data and see the rank scatter, Spearman's rho, Pearson's r, and approximate significance update together.

Data Science & Applications

Time Series Decomposition Tool

Split a series into trend, season, noise

Paste a time series and see it split live into trend, a repeating seasonal pattern, and residual noise, additive or multiplicative.

Distributions

Daily Distribution Challenge

A new mystery histogram every day — build a streak

Look at a histogram with no axis labels and guess whether it's normal, uniform, skewed, or bimodal. Same puzzle for everyone each day, with a streak counter and a shareable result.

Probability

Monty Hall Simulator

Should you switch doors? Play it and find out

Play the classic three-door problem yourself, then run thousands of trials at once to see why switching wins about twice as often as staying.

Regression & Correlation

Regression Line Challenge

Fit a line by eye, then see how close you got

Drag the slope and intercept to fit a scatter plot by eye, lock in your guess, and see your score against the true least-squares regression line.

Probability

Birthday Paradox Simulator

Guess the odds, then see how far off you were

Guess the probability that two people in a room share a birthday before revealing the real answer, verified by simulation, then explore the full probability curve from 2 to 100 people.

Need an exact answer rather than a picture? Try the statistics calculators, or browse the glossary for definitions.