npm package: @stdlib/stats-base-ndarray-dmeanstdev
Description: Compute the mean and standard deviation of a one-dimensional double-precision floating-point ndarray.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dmeanstdev

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

> Compute the [arithmetic mean][arithmetic-mean] and [standard deviation][standard-deviation] of a one-dimensional double-precision floating-point ndarray.

<section class="intro">

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by

<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/strided/dmeanstdev/docs/img/equation_population_standard_deviation.svg" alt="Equation for the population standard deviation.">
    <br>
</div> -->

<!-- </equation> -->

where the population mean is given by

<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/strided/dmeanstdev/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
    <br>
</div> -->

<!-- </equation> -->

Often in the analysis of data, the true population [standard deviation][standard-deviation] 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 [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->

<!-- <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/strided/dmeanstdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for computing a corrected sample standard deviation.">
    <br>
</div> -->

<!-- </equation> -->

where the sample mean is given by

<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->

<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/strided/dmeanstdev/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
    <br>
</div>

<!-- </equation> -->

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 standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-ndarray-dmeanstdev
```

</section>

<section class="usage">

## Usage

```javascript
var dmeanstdev = require( '@stdlib/stats-base-ndarray-dmeanstdev' );
```

#### dmeanstdev( arrays )

Computes the [arithmetic mean][arithmetic-mean] and [standard deviation][standard-deviation] of a one-dimensional double-precision floating-point ndarray.

```javascript
var Float64Array = require( '@stdlib/array-float64' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray = require( '@stdlib/ndarray-base-ctor' );

var opts = {
    'dtype': 'float64'
};

var xbuf = new Float64Array( [ 1.0, 3.0, 4.0, 2.0 ] );
var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var out = new ndarray( opts.dtype, new Float64Array( 2 ), [ 2 ], [ 1 ], 0, 'row-major' );

var correction = scalar2ndarray( 1.0, opts );

var v = dmeanstdev( [ x, out, correction ] );
// returns <ndarray>[ 2.5, ~1.2910 ]
```

The function has the following parameters:

-   **arrays**: array-like object containing the following ndarrays in order:

    1.  a one-dimensional input ndarray.
    2.  a one-dimensional output ndarray to store the [mean][arithmetic-mean] and [standard deviation][standard-deviation].
    3.  a zero-dimensional ndarray specifying the degrees of freedom adjustment. Setting this to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this 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).

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If provided an empty one-dimensional ndarray, the computed [arithmetic mean][arithmetic-mean] and [standard deviation][standard-deviation] are equal to `NaN`.
-   If `N - c` is less than or equal to `0` (where `N` corresponds to the number of elements in the input ndarray and `c` corresponds to the provided degrees of freedom adjustment), the computed [arithmetic mean][arithmetic-mean] and [standard deviation][standard-deviation] are equal to `NaN`.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray = require( '@stdlib/ndarray-base-ctor' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var dmeanstdev = require( '@stdlib/stats-base-ndarray-dmeanstdev' );

var opts = {
    'dtype': 'float64'
};

var xbuf = discreteUniform( 10, -50, 50, opts );
var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

var out = new ndarray( opts.dtype, new Float64Array( 2 ), [ 2 ], [ 1 ], 0, 'row-major' );

var correction = scalar2ndarray( 1.0, opts );

var v = dmeanstdev( [ x, out, correction ] );
console.log( ndarray2array( v ) );
```

</section>

<!-- /.examples -->

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<section class="related">

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## License

See [LICENSE][stdlib-license].


## Copyright

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

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[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

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