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https://github.com/stdlib-js/stats-base-sstdevyc

Calculate the standard deviation of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.
https://github.com/stdlib-js/stats-base-sstdevyc

deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation spread standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

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Calculate the standard deviation of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.

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README 

        



  

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# sstdevyc



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



> Calculate the [standard deviation][standard-deviation] of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.



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



```math

\sigma = \sqrt{\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 [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`,



```math

s = \sqrt{\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 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.



## Installation



```bash

npm install @stdlib/stats-base-sstdevyc

```



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 sstdevyc = require( '@stdlib/stats-base-sstdevyc' );

```



#### sstdevyc( N, correction, x, stride )



Computes the [standard deviation][standard-deviation] of a single-precision floating-point strided array `x` using a one-pass algorithm proposed by Youngs and Cramer.



```javascript

var Float32Array = require( '@stdlib/array-float32' );



var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var N = x.length;



var v = sstdevyc( N, 1, x, 1 );

// returns ~2.0817

```



The function has the following parameters:



-   **N**: number of indexed elements.

-   **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 [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 parameter 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 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).

-   **x**: input [`Float32Array`][@stdlib/array/float32].

-   **stride**: index increment for `x`.



The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [standard deviation][standard-deviation] of every other element in `x`,



```javascript

var Float32Array = require( '@stdlib/array-float32' );

var floor = require( '@stdlib/math-base-special-floor' );



var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var N = floor( x.length / 2 );



var v = sstdevyc( N, 1, x, 2 );

// returns 2.5

```



Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.



```javascript

var Float32Array = require( '@stdlib/array-float32' );

var floor = require( '@stdlib/math-base-special-floor' );



var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element



var N = floor( x0.length / 2 );



var v = sstdevyc( N, 1, x1, 2 );

// returns 2.5

```



#### sstdevyc.ndarray( N, correction, x, stride, offset )



Computes the [standard deviation][standard-deviation] of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer and alternative indexing semantics.



```javascript

var Float32Array = require( '@stdlib/array-float32' );



var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var N = x.length;



var v = sstdevyc.ndarray( N, 1, x, 1, 0 );

// returns ~2.0817

```



The function has the following additional parameters:



-   **offset**: starting index for `x`.



While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [standard deviation][standard-deviation] for every other value in `x` starting from the second value



```javascript

var Float32Array = require( '@stdlib/array-float32' );

var floor = require( '@stdlib/math-base-special-floor' );



var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var N = floor( x.length / 2 );



var v = sstdevyc.ndarray( N, 1, x, 2, 1 );

// returns 2.5

```



## Notes



-   If `N <= 0`, both functions return `NaN`.

-   If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var round = require( '@stdlib/math-base-special-round' );

var Float32Array = require( '@stdlib/array-float32' );

var sstdevyc = require( '@stdlib/stats-base-sstdevyc' );



var x;

var i;



x = new Float32Array( 10 );

for ( i = 0; i < x.length; i++ ) {

    x[ i ] = round( (randu()*100.0) - 50.0 );

}

console.log( x );



var v = sstdevyc( x.length, 1, x, 1 );

console.log( v );

```



* * *



## References



-   Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." _Technometrics_ 13 (3): 657–65. doi:[10.1080/00401706.1971.10488826][@youngs:1971a].



* * *



## See Also



-   [`@stdlib/stats-base/dstdevyc`][@stdlib/stats/base/dstdevyc]: calculate the standard deviation of a double-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.

-   [`@stdlib/stats-base/snanstdevyc`][@stdlib/stats/base/snanstdevyc]: calculate the standard deviation of a single-precision floating-point strided array ignoring NaN values and using a one-pass algorithm proposed by Youngs and Cramer.

-   [`@stdlib/stats-base/sstdev`][@stdlib/stats/base/sstdev]: calculate the standard deviation of a single-precision floating-point strided array.

-   [`@stdlib/stats-base/stdevyc`][@stdlib/stats/base/stdevyc]: calculate the standard deviation of a strided array using a one-pass algorithm proposed by Youngs and Cramer.

-   [`@stdlib/stats-base/svarianceyc`][@stdlib/stats/base/svarianceyc]: calculate the variance of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.



* * *



## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-sstdevyc.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-base-sstdevyc



[test-image]: https://github.com/stdlib-js/stats-base-sstdevyc/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/stats-base-sstdevyc/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-sstdevyc/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-sstdevyc?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-base-sstdevyc/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-base-sstdevyc/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-base-sstdevyc/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-base-sstdevyc/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-base-sstdevyc/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-base-sstdevyc/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-base-sstdevyc/blob/main/branches.md



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



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



[@stdlib/array/float32]: https://github.com/stdlib-js/array-float32



[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray



[@youngs:1971a]: https://doi.org/10.1080/00401706.1971.10488826



[@stdlib/stats/base/dstdevyc]: https://github.com/stdlib-js/stats-base-dstdevyc



[@stdlib/stats/base/snanstdevyc]: https://github.com/stdlib-js/stats-base-snanstdevyc



[@stdlib/stats/base/sstdev]: https://github.com/stdlib-js/stats-base-sstdev



[@stdlib/stats/base/stdevyc]: https://github.com/stdlib-js/stats-base-stdevyc



[@stdlib/stats/base/svarianceyc]: https://github.com/stdlib-js/stats-base-svarianceyc