# Measurement Error, Resolution, Accuracy, and Precision

`D00-F03-A08` · Financial Mathematics, Statistics, and Data Foundations → Data, Variables, Samples, and Measurement · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
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 { measurementErrorResolutionAccuracyAndPrecision } from "fintech-algorithms/foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision";
```

## Signature

```ts
measurementErrorResolutionAccuracyAndPrecision(input)
```

Compares repeated measurements against a known reference to separate accuracy from precision, and reads the instrument's resolution off the spacing of the values it reports.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | A plain object. Every F03 topic first reads `rows`, which must be a non-empty array of row objects, and derives the sorted union of every key seen across them before any per-topic branch runs, even though this topic does not use them. The calculation itself reads `measurements`, a non-empty array of finite numbers, and `referenceValue`, the true value they are aimed at. |

## Returns

`{ bias: number; mae: number; resolution: number; precisionStd: number }`

`bias` is the mean signed error against `referenceValue` and `mae` is the mean absolute error. `resolution` is the smallest gap between consecutive distinct measurements. `precisionStd` is the population standard deviation of the measurements, dividing by n rather than n-1.

## Errors

- When input is not a plain object — throws TypeError
- When rows is missing, empty, or not an array — throws RangeError
- When measurements is missing, empty, not an array, or contains a non-finite number — throws RangeError

## Complexity

Time `O(r * c + m log m)`, space `O(r * c + m)`.

## 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
{
  "rows": [
    {
      "entity": "A",
      "timestamp": "2025-01-01T00:00:00Z",
      "value": 10,
      "rating": "low"
    },
    {
      "entity": "A",
      "timestamp": "2025-01-02T00:00:00Z",
      "value": null,
      "rating": "medium",
      "censored": true
    },
    {
      "entity": "B",
      "timestamp": "2025-01-01T00:00:00Z",
      "value": 12,
      "rating": "high"
    }
  ],
  "ordinalColumns": ["rating"],
  "populationSize": 100,
  "frameSize": 80,
  "keyColumns": ["entity", "timestamp"],
  "truncationRule": "values below 5 excluded",
  "measurements": [9.9, 10, 10.1, 10],
  "referenceValue": 10,
  "vintages": [
    {
      "availableAt": "2025-02-01T00:00:00Z",
      "value": 100
    },
    {
      "availableAt": "2025-03-01T00:00:00Z",
      "value": 102
    },
    {
      "availableAt": "2025-04-01T00:00:00Z",
      "value": 101
    }
  ],
  "asOf": "2025-03-15T00:00:00Z",
  "provenance": {
    "source": "teaching.csv",
    "owner": "Fintech Builder",
    "license": "CC-BY-4.0",
    "retrievedAt": "2026-08-10",
    "transformations": ["parse", "validate"]
  }
}
```

### Call

```ts
measurementErrorResolutionAccuracyAndPrecision(input)
```

### Returns

object with 2 fields: bias, mae

```json
{
  "bias": 0,
  "mae": 0.04999999999999982
}
```

## 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/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt