math1

← 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

Your results

Is a test score good? Only if you know the average and how spread out everyone else was. One number alone tells you nothing.

Who's lying with "average"

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.

Sports, pay, weather

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.

Practice

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.

Next in this unit: comparing two data sets and reading box plots & histograms. Pairs with linear functions when you fit a line to data.