Week 1 Session: The Right Number of Digits

The first session — a published population figure resolved to the last person, and the four different questions its digits invite you to confuse

22 February 2027

Bring something to write on that you are willing to be wrong on in public.

Nothing to read beforehand. The session works because you commit before you know, and reading ahead spoils the only chance this semester you get to do that cold.

The four questions in one number#

The Australian Bureau of Statistics publishes a population clock: a figure for Australia’s population, resolved to the individual person, advancing while you watch it. The same page says, of the figures it is built from, “These projections are not predictions or forecasts.” The clock takes the estimated resident population at a base date and assumes rates of change since then for births, deaths, arrivals, departures and interstate movement.

Both of those things are true at once, and the gap between them is where this course starts. A number can be:

• precise — written to many digits;
• accurate — close to the thing it describes;
• uncertain — known only within some spread, whether or not that spread is shown;
• sufficient — good enough for the particular decision in front of you.

Those are four separate questions. Only the last one has an answer that depends on you, and it is the one to settle first.

What happens in the room#

1 — Commit, before you know anything. The clock goes up on the screen. Write down the figure to the last digit. Then, privately and on paper, commit to a range: how far from the truth could this be? You will not be asked to share it, and you will not be able to revise it.

2 — Read the page, not the number. Find the sentence about projections yourself. Sit with the fact that a national statistical agency is doing exactly what it should — publishing a figure and disclosing what it rests on — and that the display still invites a reading the disclosure does not support. The misreading is ours, not theirs.

3 — A different kind of evidence. The clock is a projection from a base. Separately, the ABS measures how well a count covers the population it is counting. After the 2021 Census, its Post Enumeration Survey put net undercount at 0.7%, or 190,044 persons: a Census count of 25,417,978 residents present on Census night against a PES estimate of 25,608,022. That is the lowest net undercount recorded for an Australian census; the 2016 figure was 1.0%.

This is not the clock’s error bar — the two are different measurements of different things, and the ABS cautions that undercount adjustment factors “should not be used alone to derive an alternative measure of the Estimated Resident Population”. It is evidence about something more general: counting a population has coverage uncertainty, even when it is done extremely well.

Now look back at the range you committed in move 1, without adjusting it, and say out loud what you were reasoning from when you wrote it. Compare its width with the scale of the coverage effects above — not as a score, because these figures cannot tell you how wide a range around the clock should have been. The question is only what your width says about what you assumed. The reflex that official numbers must be badly wrong is as lazy as the reflex that they are exact.

4 — The same evidence, looked at again. In that same survey, net undercount for Aboriginal and Torres Strait Islander people was 17.4% — a PES estimate of 983,257 against a Census count of 812,505, a shortfall of 170,752 persons. The 2016 figure was 17.5%.

One census night, one methodology, two very different coverage uncertainties depending on which population you are asking about. Take a minute with this one before discussing it. Undercounting a population is not a curiosity about statistics; it is a group of people being less visible to every process that uses the count.

5 — Two decisions. In groups, take the two scenarios below. They are teaching exercises, not descriptions of any actual funding formula or allocation process — neither is a claim about how any real decision is made.

Scenario A. A national planning task needs to know roughly how many people the country will need to house over a decade. Does a difference of a few tenths of a percent change what you decide?

Scenario B. A service is being sized for a small community. The relevant population is a few thousand people, and it belongs to a group whose count carries substantially higher coverage uncertainty. Does the same relative error change what you decide?

For each: is the available figure sufficient? If not, say what would have to be true of a number for it to be sufficient — not “more accurate”, but how much better, and known how.

6 — One sentence out. Before you leave, write and hand in:

This number is precise enough to decide ______, and not precise enough to decide ______, because ______.

What to make visible#

Whatever you write today, the assumptions have to be on the page rather than in your head. For the clock, that means at least: the rates it assumes have held since its base date, and the coverage uncertainty in the base itself. For the scenarios, the assumption people miss is the one about which population the decision is actually about.

There is no house style for this. A list, a sentence, a margin note — what matters is that a reader can find your assumptions without asking you.

Afterwards#

The sentences are read, not marked. A handful get quoted back at the start of week 2, anonymously.

Nothing is due. The habit from move 1 — commit to a range before you look it up — is worth keeping now, because from week 4 you will be keeping it on the record.