Why this is lesson one. A model doesn't see units, only numbers. Put a house's size (500–5,000 sq ft) next to its bedroom count (1–5) and the model treats size as roughly a thousand times more important — purely because its numbers are bigger, not because it matters more. Scaling puts every feature on equal footing before any learning starts. It is the first thing you do to real data, so it is the first thing here.
Stuck on a label? Any label followed by a small mark explains itself — try this one and the explanation opens underneath it. Click again to close. For the formulas, open 📝 Notes at the top of the page.
The boxes below start empty on purpose. Press Calculate to see the same numbers rewritten two different ways.
Everything here is yours to choose. Everything below the Calculate button is worked out from it.
Identical shapes — only the ruler changed. Hover a dot to trace one value through both transformations.
Normalized squeezed them into 0–1 using only the min and the max — the lowest value became 0, the highest became 1. Standardized re-centred them on the mean, so 0 is average and ±1 is one standard deviation. Neither changed the data. Both removed the units.
Try this: your largest value is —, which standardized sits at —. Change it to — and press Calculate again. The normalized row pins it to exactly 1.00 — the same value any maximum gets, so the outlier becomes invisible. Watch the standardized row instead: it climbs, pulling that one value away from the pack. That is how you choose between them.