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Statistics and Probability
Learn to read the world in numbers: how to sum up data, measure chance, and tell a real pattern from a lucky streak.
Lessons for high school students in grades 9–12, with worked examples, simulations you can run yourself, a practice game with hints, and a short quiz. We start with a nurse who used a chart to change how hospitals were run.
Units
The course is growing one unit at a time. The first unit is ready now; the others are being written.
- Unit 1 · Ready
Averages: Mean, Median and Mode
What “average” really means: the mean, median and mode, weighted means, how outliers and skew can mislead, and a first look at spread. Opens with Florence Nightingale's rose diagram.
Rose diagram · Dot plot explorer · Practice game · Quiz - Coming soon
Probability
Sample spaces, the rules of chance, the law of large numbers, counting, conditional probability and Bayes' theorem.
- Coming soon
Distributions
Random variables, the binomial and normal distributions, sampling and the central limit theorem.
- Coming soon
Inference
Confidence intervals, hypothesis tests and p-values.
- Coming soon
Correlation and Regression
Scatterplots, correlation and least-squares lines.
Why we start with Florence Nightingale
Florence Nightingale was born in Florence, Italy, on 12 May 1820, and was named after the city. She is famous as a nurse, but she was also a serious statistician. In November 1854 she arrived with 38 nurses at the British army hospital at Scutari, during the Crimean War.
She and her colleagues kept careful counts of how soldiers died. The counts showed something shocking: far more men died of diseases they caught in camp and in hospital than of wounds from battle. In her figures for April 1854 to March 1856, 14,476 of 17,982 deaths, about 4 in 5, were from disease.
To make officials and politicians see this, she drew wedge-shaped charts she called “coxcombs”, now often called rose diagrams. She did not invent the polar-area chart, which others had used before, but her use of it is one of the most famous in history.
A statistician's honors
- In 1858 she became the first woman member of the Statistical Society of London, now the Royal Statistical Society.
- In 1874 she was made an honorary member of the American Statistical Association.
- In 1907 she became the first woman appointed to the Order of Merit, one of Britain’s highest honors.
Simulations you can run
Statistics makes more sense when you can change the data yourself. The averages unit includes:
| Tool | What you do |
|---|---|
| Nightingale rose | Step through 24 months of her data and compare a fair area chart with a misleading radius chart |
| Dot plot and box plot explorer | Add scores or an outlier and watch the mean, median, IQR and standard deviation react |
| Practice game | Endless mean, median, mode and weighted-mean problems with hints and a saved best streak |
About this course
When finished, this course will cover the statistics and probability usually taught in high school (grades 9–12), from describing a data set to building a confidence interval. You'll need arithmetic, fractions and percents, and a little algebra: reading a formula, and the slope and intercept of a line. If lines feel rusty, the Jugami Algebra lessons will help.
Your quiz scores and best streaks are saved only in your own browser on this device. Nothing is sent anywhere.
Every example data set is labeled as real (with its source) or made up for practice. The only real historical data set used here is Nightingale's, as transcribed by the HistData project.
Sources
- MacTutor History of Mathematics, Florence Nightingale biography (birth, Scutari, coxcombs, honors).
- Wikipedia, Florence Nightingale (earlier polar-area charts by Guerry and Lalanne).
- HistData / Rdatasets, Florence Nightingale's data on deaths from various causes in the Crimean War (the monthly counts).
- Royal Statistical Society, Nightingale 2020: the bicentenary of our first female fellow (joined the Statistical Society of London in 1858).
- Britannica, Order of Merit (first woman to receive the honor, 1907).
- The London Gazette, issue 28084, 29 November 1907, page 8331 (PDF: her appointment to the Order of Merit).
Credits: all drawings and charts on this site are original SVG made for Jugami.