# Ranks, Ties, and Percentile Rank

`D00-F04-A07` · Financial Mathematics, Statistics, and Data Foundations → Location, Ranking, and Exploratory Summaries · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
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 { ranksTiesAndPercentileRank } from "fintech-algorithms/foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank";
```

## Signature

```ts
ranksTiesAndPercentileRank(input)
```

Assigns each observation its position in the sorted series, giving tied observations the average of the positions they span, and rescales those ranks onto a 0-to-100 percentile scale.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[] }` | yes | The observations to rank, under the key `values`. Ranks are returned in the caller's original order, not in sorted order. |

## Returns

`{ ranks: number[]; percentileRanks: number[]; tieCount: number }`

`ranks` holds one-based average ranks aligned to the input order, `percentileRanks` maps each rank onto 0 to 100 as `(rank - 1) / (n - 1) * 100`, and `tieCount` is how many observations are duplicates of a value already seen.

## 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, which would make the percentile scale divide by zero — 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],
  "weights": [1, 1, 2, 1, 1],
  "trimProportion": 0.2,
  "bins": 4
}
```

### Call

```ts
ranksTiesAndPercentileRank(input)
```

### Returns

object with 2 fields: ranks, percentileRanks

```json
{
  "ranks": [1, 2.5, 2.5, 4, 5],
  "percentileRanks": [0, 37.5, 37.5, 75, 100]
}
```

## 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/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt