npm package: @stdlib/stats-incr-variance
Description: Compute an unbiased sample variance incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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</details>

# incrvariance

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute an [unbiased sample variance][sample-variance] incrementally.

<section class="intro">

The [unbiased sample variance][sample-variance] is defined as

<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->

<div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/variance/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-variance
```

</section>

<section class="usage">

## Usage

```javascript
var incrvariance = require( '@stdlib/stats-incr-variance' );
```

#### incrvariance( \[mean] )

Returns an accumulator `function` which incrementally computes an [unbiased sample variance][sample-variance].

```javascript
var accumulator = incrvariance();
```

If the mean is already known, provide a `mean` argument.

```javascript
var accumulator = incrvariance( 3.0 );
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated [unbiased sample variance][sample-variance]. If not provided an input value `x`, the accumulator function returns the current [unbiased sample variance][sample-variance].

```javascript
var accumulator = incrvariance();

var s2 = accumulator( 2.0 );
// returns 0.0

s2 = accumulator( 1.0 ); // => ((2-1.5)^2+(1-1.5)^2) / (2-1)
// returns 0.5

s2 = accumulator( 3.0 ); // => ((2-2)^2+(1-2)^2+(3-2)^2) / (3-1)
// returns 1.0

s2 = accumulator();
// returns 1.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random-base-randu' );
var incrvariance = require( '@stdlib/stats-incr-variance' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrvariance();

// For each simulated datum, update the unbiased sample variance...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-incr/kurtosis`][@stdlib/stats/incr/kurtosis]</span><span class="delimiter">: </span><span class="description">compute a corrected sample excess kurtosis incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mean`][@stdlib/stats/incr/mean]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mstdev`][@stdlib/stats/incr/mstdev]</span><span class="delimiter">: </span><span class="description">compute a moving corrected sample standard deviation incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/skewness`][@stdlib/stats/incr/skewness]</span><span class="delimiter">: </span><span class="description">compute a corrected sample skewness incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/stdev`][@stdlib/stats/incr/stdev]</span><span class="delimiter">: </span><span class="description">compute a corrected sample standard deviation incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/summary`][@stdlib/stats/incr/summary]</span><span class="delimiter">: </span><span class="description">compute a statistical summary incrementally.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[stdlib]: https://github.com/stdlib-js/stdlib

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[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-incr-variance/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-incr-variance/blob/deno/README.md
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[branches-url]: https://github.com/stdlib-js/stats-incr-variance/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-variance/main/LICENSE

[sample-variance]: https://en.wikipedia.org/wiki/Variance

<!-- <related-links> -->

[@stdlib/stats/incr/kurtosis]: https://www.npmjs.com/package/@stdlib/stats-incr-kurtosis

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