# Numeric, Categorical, Ordinal, and Binary Variables

`D00-F03-A02` · 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/numeric-categorical-ordinal-and-binary-variables/
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 { numericCategoricalOrdinalAndBinaryVariables } from "fintech-algorithms/foundations/data-variables-samples-and-measurement/numeric-categorical-ordinal-and-binary-variables";
```

## Signature

```ts
numericCategoricalOrdinalAndBinaryVariables(input)
```

Classifies every column of a table as binary, numeric, ordinal or categorical by inspecting the values actually present in it.

## 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. This topic then reads `ordinalColumns`, an optional array of column names that should be treated as ordered rather than merely categorical; it defaults to empty. |

## Returns

`{ types: Record<string, string> }`

`types` maps each column name to one of `binary`, `numeric`, `ordinal` or `categorical`. Null and undefined entries are ignored when judging a column. A column whose remaining values are all booleans is `binary`; all numbers with two or fewer distinct values is also `binary`, otherwise `numeric`; anything else is `ordinal` when the column is listed in `ordinalColumns` and `categorical` when it is not.

## Errors

- When input is not a plain object — throws TypeError
- When rows is missing, empty, or not an array — throws RangeError

## Complexity

Time `O(r * c)`, space `O(r * c)`.

## 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
numericCategoricalOrdinalAndBinaryVariables(input)
```

### Returns

object with 1 field: types

```json
{
  "types": {
    "censored": "binary",
    "entity": "categorical",
    "rating": "ordinal",
    "timestamp": "categorical",
    "value": "numeric"
  }
}
```

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