# Coefficient of Variation and Scale Comparability

`D00-F05-A07` · 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/coefficient-of-variation-and-scale-comparability/
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 { coefficientOfVariationAndScaleComparability } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/coefficient-of-variation-and-scale-comparability";
```

## Signature

```ts
coefficientOfVariationAndScaleComparability(input)
```

Divides the sample standard deviation by the absolute value of the mean, turning spread into a unit-free figure that can be compared across series measured on different scales.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[] }` | yes | The observations to measure, under the key `values`. The ratio is only meaningful for series on a ratio scale with a mean away from zero. · values: at least two observations, and a non-zero mean |

## Returns

`{ coefficientOfVariation: number; scaleFree: boolean }`

`coefficientOfVariation` is the sample standard deviation over the absolute mean, and `scaleFree` is always `true`, marking the figure as carrying no units.

## 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
- When `values` holds fewer than two observations, so the sample divisor `n - 1` would be zero — throws RangeError
- When the arithmetic mean of `values` is exactly zero, leaving the ratio undefined — 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
coefficientOfVariationAndScaleComparability(input)
```

### Returns

object with 2 fields: coefficientOfVariation, scaleFree

```json
{
  "coefficientOfVariation": 0.8914892519934007,
  "scaleFree": true
}
```

## 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/coefficient-of-variation-and-scale-comparability/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/dispersion-shape-and-robust-statistics/coefficient-of-variation-and-scale-comparability/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt