Week 4: A range says more than a number

What a point estimate hides, why a national agency publishes its uncertainty on purpose, and how to choose a width honestly

15 March 2027

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A point estimate can be wrong. So can a range. That is not the difference between them, and it is worth being exact about what is.

What a point estimate withholds

When you publish a single number, you have made a claim about the world and said nothing about how firmly you hold it. The figure looks identical whether you spent a week on it or thirty seconds, whether you would bet your salary on it or would not be surprised to be out by half.

The cost lands later. When the number turns out to be off, nobody — including you — can tell which of two very different things happened.

You might have been well calibrated and unlucky: your figure was the right centre and the world landed in the tail. Or you might have been overconfident: you had no business being that specific. Those call for opposite responses, and a point estimate destroys the evidence needed to tell them apart.

A range with a stated confidence keeps that evidence. It says what you thought and how firmly, in a form that can be set against an observed value afterwards. It does not make you right more often. It makes you legible, to others and eventually to yourself.

An institution that does this on purpose

The Bureau of Meteorology publishes rainfall as a range with confidences attached, and explains why in public: rainfall forecasts, it says, are probabilistic, giving a range of amounts and the chance of receiving at least that amount — “different to a maximum or minimum temperature forecast, which is represented by one single number.”

Two things are worth taking from that.

The first is that a serious organisation, whose output is scrutinised daily, decided that for some quantities a single number would be a worse answer. Not a simpler one that everybody prefers — a worse one. Publishing the shape was the more useful, and the more defensible, choice.

The second is that BOM then reports how well its stated confidences held. When it says fifty per cent, it publishes how often that came true. An institution that says how sure it is has made itself checkable, and this one submits to the check in public. Very little of professional life works this way. Nothing stops you doing it anyway.

Choosing a width

Ranges have a failure mode of their own, and it is the reason this is a skill rather than a formatting rule.

A range wide enough that nothing could land outside it is not caution. It is a refusal to answer, wearing the costume of care — and it is worse than the point estimate it replaced, because it looks responsible while carrying less information. If your range cannot be wrong, it is not telling anyone anything.

A range narrowed to look authoritative is the same error week 1 was about: the appearance of knowledge you do not have.

The width is not a rhetorical dial. It is a report on the state of your knowledge, and the honest width is sometimes embarrassingly wide. Saying so is the professional move. “Somewhere between two and twenty, and I’d want a day with the data before I said tighter” is a real answer, and a decision-maker can act on it — if only by deciding to buy you the day.

Plain language is enough

None of this needs notation. “I’d be surprised if it were under X, and quite surprised if it were over Y” carries a range and a confidence, and any reader can act on it. You will do this in words all semester and never need a formula for it.

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