> ## Documentation Index
> Fetch the complete documentation index at: https://docs.citino.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# How bands are computed

> How the ± range beside a number is worked out, why it is built across questions, and why a number sometimes has none.

*Version 1 · 7 November 2026*

> How far the true number could reasonably be from the one shown. It is wide when there are few answers or few questions behind it, and narrows as more come in.

## Why answers alone are not enough

Ask the same question day after day and you get many answers, but not many independent ones. Answers to one question tend to name much the same brands. Treating them as independent draws would make the range look several points narrower than it really is, and a range that is too narrow turns noise into news.

So the range is built across **questions**, not single answers.

## The method, in plain words

1. Take the questions behind the number, each with its answers in the period: how many answers there were and how many named the brand.
2. Draw a new set of questions at random from that list, the same size as the original, where any question can be drawn more than once.
3. Work the number out again from the drawn set.
4. Repeat 600 times.
5. The range is half the width of the middle 95% of those 600 results.

Statisticians call this a cluster bootstrap over prompts. The random draws start from a fixed seed, so the same answers always give the same range. A range changes only when the answers behind it do.

Two things follow from building it this way:

* **Few questions mean a wide range**, however many days have passed. A project with a small set of questions keeps a wider range than one with many.
* **More days narrow it slowly.** Each day adds answers, but answers to the same questions add less certainty than new questions would.

## Within noise

A change smaller than its range is not a move:

> How much this moved since the previous period of the same length, in percentage points. “Within noise” means the move is smaller than the ± range, so it could be chance.

A change within noise is shown muted, with no arrow colour. It never raises an alert, never appears as a movement in a digest and never sorts as one. Alerts use a slightly stricter test than the charts: they combine the ranges of both periods, which is wider.

## When there is no range

| What you see | Why |
| - | - |
| `—` with "needs one full run" | There are no answers yet, so there is no number and no range. |
| A single question's figures with no ± | The range is drawn across questions, and one question cannot be drawn across. |
| A figure for one engine with no ± | Ranges are not worked out per engine. |

Where a range is missing, a change is treated as within noise. Not knowing how wide the noise is never counts as evidence that something moved.

## A low sample never hides a number

> This number rests on only a few answers, so read it as an early signal rather than a settled result. It firms up as we collect more each day.

From the first answer, a number is shown with its range and its `n`. The low-sample badge sits beside it as a cue, not in its place.

## Related

> [card] [The ± band and n](https://docs.citino.ai/guides/bands-and-sample-size.md)
>
> Reading the two marks beside every number.

> [card] [Within noise](https://docs.citino.ai/guides/within-noise.md)
>
> What a muted change means for you.

> [card] [Cadence](https://docs.citino.ai/guides/methodology/cadence.md)
>
> How many answers each day adds.

> [card] [Metric objects](https://docs.citino.ai/api/metric-objects.md)
>
> How the API returns a value, its band and n.


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