# Range and Interquartile Range

`D00-F05-A02` · Financial Mathematics, Statistics, and Data Foundations → Dispersion, Shape, and Robust Statistics · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/dispersion-shape-and-robust-statistics/range-and-interquartile-range/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { rangeAndInterquartileRange } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/range-and-interquartile-range";
```

## Signature

```ts
rangeAndInterquartileRange(input)
```

Measures spread two ways on the same series: the full distance from smallest to largest, and the distance covering the middle half between the first and third quartiles.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[] }` | yes | The observations whose spread is being measured, under the key `values`. Quartiles use linear interpolation between neighbouring order statistics. |

## Returns

`{ range: number; iqr: number; q1: number; q3: number }`

`range` is `maximum - minimum`, `iqr` is `q3 - q1`, and `q1` and `q3` are returned alongside so the interquartile range can be traced back to the cut points it came from.

## Errors

- When `input` is null, an array, or not an object — throws TypeError
- When `values` is missing, is not an array, or is empty — throws RangeError
- When any entry of `values` does not coerce to a finite number — throws RangeError

## Complexity

Time `O(n log n)`, space `O(n)`.

## Worked example

This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

### Input

`input`:

```json
{
  "values": [1, 2, 2, 4, 9]
}
```

### Call

```ts
rangeAndInterquartileRange(input)
```

### Returns

object with 2 fields: range, iqr

```json
{
  "range": 8,
  "iqr": 2
}
```

## Verification and provenance

Tier: **verified** (via input-expected).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/foundations/dispersion-shape-and-robust-statistics/range-and-interquartile-range/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/dispersion-shape-and-robust-statistics/range-and-interquartile-range/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt