# Median Absolute Deviation

`D00-F05-A04` · 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/median-absolute-deviation/
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 { medianAbsoluteDeviation } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation";
```

## Signature

```ts
medianAbsoluteDeviation(input)
```

Takes the median of the absolute distances from the series median, and rescales it by 1.4826 so it lines up with a standard deviation under normality.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[] }` | yes | The observations to measure, under the key `values`. Both the centre and the spread are medians, so a handful of extreme observations cannot drag the result. |

## Returns

`{ medianAbsoluteDeviation: number; median: number; scaledMad: number }`

`medianAbsoluteDeviation` is the raw median of the absolute deviations, `median` is the centre they were taken from, and `scaledMad` is that raw figure multiplied by 1.4826.

## 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
medianAbsoluteDeviation(input)
```

### Returns

object with 2 fields: medianAbsoluteDeviation, median

```json
{
  "medianAbsoluteDeviation": 1,
  "median": 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/median-absolute-deviation/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt