# Trimmed and Winsorized Means

`D00-F04-A05` · 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/trimmed-and-winsorized-means/
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 { trimmedAndWinsorizedMeans } from "fintech-algorithms/foundations/location-ranking-and-exploratory-summaries/trimmed-and-winsorized-means";
```

## Signature

```ts
trimmedAndWinsorizedMeans(input)
```

Cuts the same number of observations off each tail of the sorted series and averages what is left, then averages again with those tails replaced by the surviving boundary values instead of discarded.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[]; trimProportion: number }` | yes | `values` holds the observations and `trimProportion` the share to remove from each tail. The cut size is `floor(values.length * trimProportion)`, so small samples may round the trim down to zero. · trimProportion: 0 <= trimProportion < 0.5, and the two cuts together must leave at least one observation |

## Returns

`{ trimmedMean: number; winsorizedMean: number; trimmedCount: number }`

`trimmedMean` averages only the surviving middle, `winsorizedMean` averages the full-length series with each tail replaced by the nearest kept value, and `trimmedCount` is how many observations the trimmed mean was computed 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
- When `trimProportion` is negative, is 0.5 or more, or is not a number — throws RangeError
- When the two cuts together would remove every observation — 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
trimmedAndWinsorizedMeans(input)
```

### Returns

object with 2 fields: trimmedMean, winsorizedMean

```json
{
  "trimmedMean": 2.6666666666666665,
  "winsorizedMean": 2.8
}
```

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