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# Standard Deviation

> [Chi][chi-distribution] distribution [standard deviation][stdev].

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<section class="intro">

The [standard deviation][stdev] for a [chi][chi-distribution] random variable is

<!-- <equation class="equation" label="eq:chi_stdev" align="center" raw="\sigma = \sqrt{ k - \mathbb{E}\left[ X \right]^2 }" alt="Standard deviation for a chi distribution."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{ k - \mathbb{E}\left[ X \right]^2 }" data-equation="eq:chi_stdev">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/chi/stdev/docs/img/equation_chi_stdev.svg" alt="Standard deviation for a chi distribution.">
    <br>
</div>

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where `k >= 0` is the degrees of freedom.

</section>

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<section class="usage">

## Usage

```javascript
var stdev = require( '@stdlib/stats/base/dists/chi/stdev' );
```

#### stdev( k )

Returns the [standard deviation][stdev] of a [chi][chi-distribution] distribution with degrees of freedom `k`.

```javascript
var v = stdev( 9.0 );
// returns ~0.697

v = stdev( 0.5 );
// returns ~0.521
```

If provided `k < 0`, the function returns `NaN`.

```javascript
var v = stdev( -1.0 );
// returns NaN
```

</section>

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</section>

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<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var stdev = require( '@stdlib/stats/base/dists/chi/stdev' );

var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = randu() * 20.0;
    v = stdev( k );
    console.log( 'k: %d, SD(X,k): %d', k.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</section>

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</section>

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[chi-distribution]: https://en.wikipedia.org/wiki/Chi_distribution

[stdev]: https://en.wikipedia.org/wiki/Standard_deviation

</section>

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