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 the columns are filled with nothing but digits — jersey number and height in centimetres — 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. Renumber the same ten players 1 to 10 and the mean jersey number falls from 16.5 to 5.5 with nothing about the team altered. Convert the same ten heights to inches and the mean transforms by exactly the rule every value did. One of those columns was measuring something. The other was wearing a costume.

8 STEPS · 6 QUICK CHECKS · OBSERVATIONAL UNIT · THE ARITHMETIC TEST · DISCRETE vs CONTINUOUS · WHICH DISPLAY · v1

mean jersey 16.5 → 5.5 after renumbering · mean height 169.1 cm → 66.57 in

Before you start

What you're looking at

Ten students, one row each. Each row is an observational unit; each column is a variable recorded about it.

The question

Jersey number and height are both written in digits and both can be averaged. So what actually makes one of them a quantity?

Watch for

The mean jersey number moving when the team is renumbered, the mean height moving by exactly 1/2.54 when the unit changes, and the zip code that loses its leading zero.

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