# Stable Summation and Mean Calculation

`D00-F12-A02` · Financial Mathematics, Statistics, and Data Foundations → Statistical Computing and Reproducibility · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/statistical-computing-and-reproducibility/stable-summation-and-mean-calculation/
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 { stableSummationAndMeanCalculation } from "fintech-algorithms/foundations/statistical-computing-and-reproducibility/stable-summation-and-mean-calculation";
```

## Signature

```ts
stableSummationAndMeanCalculation(input)
```

Adds a list twice, once straight left to right and once carrying a running compensation term, so the two totals can be put side by side.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | Reads `values`, a non-empty list of finite numbers to be summed. |

## Returns

`D00Output`

`naiveSum` is the plain running total, `stableSum` the compensated one, `stableMean` that compensated total divided by the observation count, and `difference` the compensated total minus the naive one.

## Errors

- When `values` is absent, empty, or holds a non-finite number — throws RangeError

## Complexity

Time `O(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": [10000000000000000, 1, -10000000000000000, 3],
  "floatingValue": 0.1,
  "maxSafeMagnitude": 1.7976931348623157e+308,
  "window": 3,
  "rawValues": [1, null, 2, "bad", 3],
  "invalidPolicy": "drop-and-report",
  "seed": 42,
  "sampleCount": 5,
  "leftVector": [
    {
      "index": "A",
      "value": 1
    },
    {
      "index": "B",
      "value": 2
    }
  ],
  "rightVector": [
    {
      "index": "B",
      "value": 20
    },
    {
      "index": "C",
      "value": 30
    }
  ],
  "train": [10, 12, 14, 16],
  "test": [18, 20],
  "actual": [1, 2.0000001, 3],
  "expected": [1, 2, 3]
}
```

Showing 14 of 18 fields.

### Call

```ts
stableSummationAndMeanCalculation(input)
```

### Returns

object with 2 fields: naiveSum, stableSum

```json
{
  "naiveSum": 3,
  "stableSum": 4
}
```

## 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/statistical-computing-and-reproducibility/stable-summation-and-mean-calculation/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/statistical-computing-and-reproducibility/stable-summation-and-mean-calculation/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt