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Mistake Master · AP Statistics · Unit 1 · Step-Through Animation

A Column Full of Digits Is Not Yet a Quantity

You'll learnthe test that decides a variable's type — whether arithmetic on its values means anything — and what goes wrong downstream when the digits are allowed to decide instead.

Ten students, one row each. Two of those columns hold nothing but digits — jersey number and height in centimeters — and a spreadsheet will happily average either one. This animation averages both, then applies the test that tells them apart: change the labels and see which summary survives. The same ten players are renumbered 1 to 10 and the mean jersey number falls from 16.5 to 5.5 with nothing about the team altered. The same ten heights are converted to inches and the mean transforms by exactly the rule every value did. Then five real zip codes are averaged, and the answer is a place none of the five students is anywhere near. One of those columns was measuring something; the other was wearing a costume. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · OBSERVATIONAL UNIT · THE ARITHMETIC TEST · DISCRETE vs CONTINUOUS · WHICH DISPLAY · v2

Renumber the same ten players and the mean jersey falls 16.5 to 5.5.
Before you start
What you're looking at
Ten students, one row each. Every row is one person; every column is one thing recorded about them.
The question
Jersey number and height are both digits and both average fine. So what makes only one of them a quantity?
Step 1 / 12