Probability and statistics

Means, charts and chance

Four courses cover the statistics that turn up in school and in the news, mostly with real data. Salaries, house prices and class scores come from the OpenStax statistics textbook, births and the fertility rate from Korea's national statistics office, regional populations from the 2020 US census. Every unit of Averages and Probability carries a short teacher's note on where a class usually gets stuck. A fifth course, on sampling and surveys, is still being written.

Averages first, chance last

Begin with Averages. Its five units go from the mean as a balance point to the 1.5 × IQR rule for outliers.

Reading charts comes next. Six units use Korean births, Korea's total fertility rate and the US census to cover bar charts, pie charts, line graphs, axes that mislead, and histograms whose shape changes with the class width.

Distributions builds frequency tables and histograms, then fits a normal curve to Quetelet's chest sizes of 5,738 Scottish soldiers and works through z-scores and the 68-95-99.7 rule.

Finish with Probability. Its seven units run from a single coin flip to the central limit theorem, by way of two dice, conditional probability and the Galton board.

Questions you can settle afterwards

Say why one salary of $120,000 lifts the mean of 11 salaries well above their median of $54,000. Combine a class of 20 averaging 70 with a class of 30 averaging 80 and get 76, not 75. Catch a bar chart whose axis starts at 220 thousand drawing a 10.6% rise in births as a bar 3.43 times as tall. Explain why 7 is the most common sum of two dice, with 6 of the 36 outcomes. And see why 10 fair flips give exactly 5 heads with probability 252/1024, about 0.246.

Dots, dice and a Galton board

Most units put a lab next to the reading. In Averages the data sit as dots on a line. Drag the $120,000 salary along it and the mean follows while the median stays at 54. Switch on Outlier fences and the red fences move with every drag. The chart lab lets you tap a bar to read its value, slide the point where the axis starts, and change a histogram's class width and starting point. In Probability you flip a coin 10,000 times, roll up to four dice, drop 1,000 balls through a Galton board and change the sample size, and each readout is set against the exact probability. Each unit ends with a quiz that explains every answer.

Misreadings of a mean or a chance

Most slips here are about what a number means. Averaging two class means as if the classes were the same size. Taking the middle of a list before sorting it. Building outlier fences from the median instead of the quartiles. Believing heads is due after seven tails. Treating the 11 sums of two dice as equally likely. Adding 1/6 + 1/6 for at least one six on two dice, which counts the double six twice. Each of these sits in a mistakes box in its unit, with the calculation that shows where it fails.