# Frequency Tables and Relative Frequency

`D00-F04-A08` · 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/frequency-tables-and-relative-frequency/
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 { frequencyTablesAndRelativeFrequency } from "fintech-algorithms/foundations/location-ranking-and-exploratory-summaries/frequency-tables-and-relative-frequency";
```

## Signature

```ts
frequencyTablesAndRelativeFrequency(input)
```

Counts how often each distinct value occurs in a numeric series and expresses those counts as shares of the total.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[] }` | yes | The observations to tabulate, under the key `values`. Distinctness is exact numeric equality after `Number` coercion, so this suits repeated discrete levels rather than continuous measurements. |

## Returns

`{ frequency: Record<string, number>; relativeFrequency: Record<string, number> }`

Both maps are keyed by the distinct values rendered as strings, in ascending numeric order. `frequency` holds raw counts and `relativeFrequency` holds each count divided by the number of observations.

## 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],
  "weights": [1, 1, 2, 1, 1],
  "trimProportion": 0.2,
  "bins": 4
}
```

### Call

```ts
frequencyTablesAndRelativeFrequency(input)
```

### Returns

object with 2 fields: frequency, relativeFrequency

```json
{
  "frequency": {
    "1": 1,
    "2": 2,
    "4": 1,
    "9": 1
  },
  "relativeFrequency": {
    "1": 0.2,
    "2": 0.4,
    "4": 0.2,
    "9": 0.2
  }
}
```

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