← all units · Unit 01 · Statistics
Descriptive statistics
Two questions turn a messy pile of numbers into something you can actually judge: where's the middle, and how spread out is it? Get those, and you can spot when a number is lying to you.
Where you'll actually use this
Is a test score good? Only if you know the average and how spread out everyone else was. One number alone tells you nothing.
One billionaire walks into a room and the mean net worth says everyone's rich. The median tells the truth. Knowing which is which is a superpower.
Batting averages, median salaries, temperature ranges — center and spread are how the whole world summarizes anything.
The idea
Center asks where the numbers pile up. Two ways to answer it:
- mean
- add every value, divide by how many — the "balance point"
- median
- line them up in order and take the middle one
- range
- highest − lowest — the simplest measure of spread
The catch: the mean gets dragged toward extreme values; the median barely moves. That's exactly why "average" can mislead.
Worked example Five quiz scores: 7, 8, 8, 9, 18. Mean = 50 ÷ 5 = 10; median = 8. That one 18 drags the mean up to 10, but the median stays at 8 — closer to how most people actually did.
Your turn
Fresh data every time. Miss one and the full worked solution appears — seeing the steps is the point.
Loading a problem…
Tug of Mean
Drag any dot along the line. Watch the mean get pulled toward the extremes while the median holds its ground — the whole reason "average" can deceive.
Drag a dot. Mean chases it; median holds.
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Next in this unit: comparing two data sets and reading box plots & histograms. Pairs with linear functions when you fit a line to data.