https://github.com/stdlib-js/stats-array-variancepn
Calculate the variance of an array using a two-pass algorithm.
https://github.com/stdlib-js/stats-array-variancepn
array deviation dispersion javascript math mathematics node node-js nodejs sample-variance standard-deviation statistics stats stdlib unbiased var variance
Last synced: 5 months ago
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Calculate the variance of an array using a two-pass algorithm.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-array-variancepn
- Owner: stdlib-js
- License: apache-2.0
- Created: 2025-06-30T11:27:41.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2025-07-01T15:00:34.000Z (6 months ago)
- Last Synced: 2025-07-01T16:23:55.498Z (6 months ago)
- Topics: array, deviation, dispersion, javascript, math, mathematics, node, node-js, nodejs, sample-variance, standard-deviation, statistics, stats, stdlib, unbiased, var, variance
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 442 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# variancepn
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Calculate the [variance][variance] of an array using a two-pass algorithm.
The population [variance][variance] of a finite size population of size `N` is given by
```math
\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2
```
where the population mean is given by
```math
\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i
```
Often in the analysis of data, the true population [variance][variance] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [variance][variance], the result is biased and yields a **biased sample variance**. To compute an **unbiased sample variance** for a sample of size `n`,
```math
s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2
```
where the sample mean is given by
```math
\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```
The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample variance and population variance. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
## Installation
```bash
npm install @stdlib/stats-array-variancepn
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var variancepn = require( '@stdlib/stats-array-variancepn' );
```
#### variancepn( x\[, correction] )
Computes the variance of an array.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var v = variancepn( x );
// returns ~4.3333
```
The function has the following parameters:
- **x**: input array.
- **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `N` corresponds to the number of array elements and `c` corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction). Default: `1.0`.
By default, the function computes the sample [variance][variance]. To adjust the degrees of freedom when computing the [variance][variance], provide a `correction` argument.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var v = variancepn( x, 0.0 );
// returns ~2.8889
```
## Notes
- If provided an empty array, the function returns `NaN`.
- If provided a `correction` argument which is greater than or equal to the number of elements in a provided input array, the function returns `NaN`.
- The function supports array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array-base/accessor`][@stdlib/array/base/accessor]).
## Examples
```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var variancepn = require( '@stdlib/stats-array-variancepn' );
var x = discreteUniform( 10, -50, 50, {
'dtype': 'float64'
});
console.log( x );
var v = variancepn( x );
console.log( v );
```
* * *
## References
- Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958][@neely:1966a].
- Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036][@schubert:2018a].
* * *
## Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-array-variancepn.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-array-variancepn
[test-image]: https://github.com/stdlib-js/stats-array-variancepn/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-array-variancepn/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-array-variancepn/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-array-variancepn?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-array-variancepn/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-array-variancepn/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-array-variancepn/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-array-variancepn/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-array-variancepn/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-array-variancepn/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-array-variancepn/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-array-variancepn/main/LICENSE
[variance]: https://en.wikipedia.org/wiki/Variance
[@neely:1966a]: https://doi.org/10.1145/365719.365958
[@schubert:2018a]: https://doi.org/10.1145/3221269.3223036
[@stdlib/array/base/accessor]: https://github.com/stdlib-js/array-base-accessor