{"id":23279965,"url":"https://github.com/stdlib-js/stats-base-dvariancepn","last_synced_at":"2025-08-21T12:31:25.946Z","repository":{"id":41467252,"uuid":"376893797","full_name":"stdlib-js/stats-base-dvariancepn","owner":"stdlib-js","description":"Calculate the variance of a double-precision floating-point strided array using a two-pass algorithm.","archived":false,"fork":false,"pushed_at":"2024-12-01T09:22:57.000Z","size":982,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2024-12-09T00:05:54.012Z","etag":null,"topics":["array","deviation","dispersion","javascript","math","mathematics","node","node-js","nodejs","sample-variance","standard-deviation","statistics","stats","stdlib","strided","strided-array","typed","unbiased","var","variance"],"latest_commit_sha":null,"homepage":"https://github.com/stdlib-js/stdlib","language":"JavaScript","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/stdlib-js.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE_OF_CONDUCT.md","threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null},"funding":{"github":["stdlib-js"],"open_collective":"stdlib","tidelift":"npm/@stdlib/stdlib"}},"created_at":"2021-06-14T16:48:00.000Z","updated_at":"2024-12-01T04:10:55.000Z","dependencies_parsed_at":"2023-09-24T01:31:49.242Z","dependency_job_id":"e6a4d836-db4d-46a7-b125-6ee14720999b","html_url":"https://github.com/stdlib-js/stats-base-dvariancepn","commit_stats":{"total_commits":67,"total_committers":1,"mean_commits":67.0,"dds":0.0,"last_synced_commit":"48988d33310db1ee193cad994e434ee0dd8fe97b"},"previous_names":[],"tags_count":26,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dvariancepn","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dvariancepn/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dvariancepn/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dvariancepn/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/stats-base-dvariancepn/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":230494916,"owners_count":18235046,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["array","deviation","dispersion","javascript","math","mathematics","node","node-js","nodejs","sample-variance","standard-deviation","statistics","stats","stdlib","strided","strided-array","typed","unbiased","var","variance"],"created_at":"2024-12-19T23:19:55.162Z","updated_at":"2025-08-21T12:31:25.936Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2020 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.\u003c/p\u003e\n  \u003cp\u003eThe library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.\u003c/p\u003e\n  \u003cp\u003eWhen you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# dvariancepn\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Calculate the [variance][variance] of a double-precision floating-point strided array using a two-pass algorithm.\n\n\u003csection class=\"intro\"\u003e\n\nThe population [variance][variance] of a finite size population of size `N` is given by\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:population_variance\" align=\"center\" raw=\"\\sigma^2 = \\frac{1}{N} \\sum_{i=0}^{N-1} (x_i - \\mu)^2\" alt=\"Equation for the population variance.\"\u003e --\u003e\n\n```math\n\\sigma^2 = \\frac{1}{N} \\sum_{i=0}^{N-1} (x_i - \\mu)^2\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\sigma^2 = \\frac{1}{N} \\sum_{i=0}^{N-1} (x_i - \\mu)^2\" data-equation=\"eq:population_variance\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@63c490687f6e665dd9827abc99bfbd09353d175c/lib/node_modules/@stdlib/stats/base/dvariancepn/docs/img/equation_population_variance.svg\" alt=\"Equation for the population variance.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere the population mean is given by\n\n\u003c!-- \u003cequation 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.\"\u003e --\u003e\n\n```math\n\\mu = \\frac{1}{N} \\sum_{i=0}^{N-1} x_i\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\mu = \\frac{1}{N} \\sum_{i=0}^{N-1} x_i\" data-equation=\"eq:population_mean\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@63c490687f6e665dd9827abc99bfbd09353d175c/lib/node_modules/@stdlib/stats/base/dvariancepn/docs/img/equation_population_mean.svg\" alt=\"Equation for the population mean.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nOften 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`,\n\n\u003c!-- \u003cequation 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 computing an unbiased sample variance.\"\u003e --\u003e\n\n```math\ns^2 = \\frac{1}{n-1} \\sum_{i=0}^{n-1} (x_i - \\bar{x})^2\n```\n\n\u003c!-- \u003cdiv 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\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@63c490687f6e665dd9827abc99bfbd09353d175c/lib/node_modules/@stdlib/stats/base/dvariancepn/docs/img/equation_unbiased_sample_variance.svg\" alt=\"Equation for computing an unbiased sample variance.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere the sample mean is given by\n\n\u003c!-- \u003cequation 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.\"\u003e --\u003e\n\n```math\n\\bar{x} = \\frac{1}{n} \\sum_{i=0}^{n-1} x_i\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\bar{x} = \\frac{1}{n} \\sum_{i=0}^{n-1} x_i\" data-equation=\"eq:sample_mean\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@63c490687f6e665dd9827abc99bfbd09353d175c/lib/node_modules/@stdlib/stats/base/dvariancepn/docs/img/equation_sample_mean.svg\" alt=\"Equation for the sample mean.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nThe 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.\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-base-dvariancepn\n```\n\nAlternatively,\n\n-   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]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   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]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo 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.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar dvariancepn = require( '@stdlib/stats-base-dvariancepn' );\n```\n\n#### dvariancepn( N, correction, x, strideX )\n\nComputes the [variance][variance] of a double-precision floating-point strided array `x` using a two-pass algorithm.\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x = new Float64Array( [ 1.0, -2.0, 2.0 ] );\n\nvar v = dvariancepn( x.length, 1, x, 1 );\n// returns ~4.3333\n```\n\nThe function has the following parameters:\n\n-   **N**: number of indexed elements.\n-   **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 `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).\n-   **x**: input [`Float64Array`][@stdlib/array/float64].\n-   **strideX**: stride length for `x`.\n\nThe `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`,\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );\n\nvar v = dvariancepn( 4, 1, x, 2 );\n// returns 6.25\n```\n\nNote that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.\n\n\u003c!-- eslint-disable stdlib/capitalized-comments --\u003e\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );\nvar x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element\n\nvar v = dvariancepn( 4, 1, x1, 2 );\n// returns 6.25\n```\n\n#### dvariancepn.ndarray( N, correction, x, strideX, offsetX )\n\nComputes the [variance][variance] of a double-precision floating-point strided array using a two-pass algorithm and alternative indexing semantics.\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x = new Float64Array( [ 1.0, -2.0, 2.0 ] );\n\nvar v = dvariancepn.ndarray( x.length, 1, x, 1, 0 );\n// returns ~4.33333\n```\n\nThe function has the following additional parameters:\n\n-   **offsetX**: starting index for `x`.\n\nWhile [`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 [variance][variance] for every other element in `x` starting from the second element\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );\n\nvar v = dvariancepn.ndarray( 4, 1, x, 2, 1 );\n// returns 6.25\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n## Notes\n\n-   If `N \u003c= 0`, both functions return `NaN`.\n-   If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar discreteUniform = require( '@stdlib/random-array-discrete-uniform' );\nvar dvariancepn = require( '@stdlib/stats-base-dvariancepn' );\n\nvar x = discreteUniform( 10, -50, 50, {\n    'dtype': 'float64'\n});\nconsole.log( x );\n\nvar v = dvariancepn( x.length, 1, x, 1 );\nconsole.log( v );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- C interface documentation. --\u003e\n\n* * *\n\n\u003csection class=\"c\"\u003e\n\n## C APIs\n\n\u003c!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"intro\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003c!-- C usage documentation. --\u003e\n\n\u003csection class=\"usage\"\u003e\n\n### Usage\n\n```c\n#include \"stdlib/stats/base/dvariancepn.h\"\n```\n\n#### stdlib_strided_dvariancepn( N, correction, \\*X, strideX )\n\nComputes the [variance][variance] of a double-precision floating-point strided array using a two-pass algorithm.\n\n```c\nconst double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 }\n\ndouble v = stdlib_strided_dvariancepn( 8, 1.0, x, 1 );\n// returns 6.0\n```\n\nThe function accepts the following arguments:\n\n-   **N**: `[in] CBLAS_INT` number of indexed elements.\n-   **correction**: `[in] double` 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 `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).\n-   **X**: `[in] double*` input array.\n-   **strideX**: `[in] CBLAS_INT` stride length for `X`.\n\n```c\ndouble stdlib_strided_dvariancepn( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX );\n```\n\n#### stdlib_strided_dvariancepn_ndarray( N, correction, \\*X, strideX, offsetX )\n\nComputes the [variance][variance] of a double-precision floating-point strided array using a two-pass algorithm and alternative indexing semantics.\n\n```c\nconst double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 }\n\ndouble v = stdlib_strided_dvariancepn_ndarray( 4, 1.0, x, 2, 0 );\n// returns ~6.666667\n```\n\nThe function accepts the following arguments:\n\n-   **N**: `[in] CBLAS_INT` number of indexed elements.\n-   **correction**: `[in] double` 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 `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).\n-   **X**: `[in] double*` input array.\n-   **strideX**: `[in] CBLAS_INT` stride length for `X`.\n-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.\n\n```c\ndouble stdlib_strided_dvariancepn_ndarray( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003c!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003c!-- C API usage examples. --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n### Examples\n\n```c\n#include \"stdlib/stats/base/dvariancepn.h\"\n#include \u003cstdio.h\u003e\n\nint main( void ) {\n    // Create a strided array:\n    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };\n\n    // Specify the number of elements:\n    const int N = 4;\n\n    // Specify the stride length:\n    const int strideX = 2;\n\n    // Compute the variance:\n    double v = stdlib_strided_dvariancepn( N, 1.0, x, strideX );\n\n    // Print the result:\n    printf( \"sample variance: %lf\\n\", v );\n}\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.c --\u003e\n\n* * *\n\n\u003csection class=\"references\"\u003e\n\n## References\n\n-   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].\n-   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].\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n* * *\n\n## See Also\n\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-strided/dnanvariancepn`][@stdlib/stats/strided/dnanvariancepn]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecalculate the variance of a double-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-strided/dstdevpn`][@stdlib/stats/strided/dstdevpn]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecalculate the standard deviation of a double-precision floating-point strided array using a two-pass algorithm.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-strided/dvariance`][@stdlib/stats/strided/dvariance]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecalculate the variance of a double-precision floating-point strided array.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-base/svariancepn`][@stdlib/stats/base/svariancepn]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecalculate the variance of a single-precision floating-point strided array using a two-pass algorithm.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-base/variancepn`][@stdlib/stats/base/variancepn]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecalculate the variance of a strided array using a two-pass algorithm.\u003c/span\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\n\n* * *\n\n## Notice\n\nThis 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.\n\nFor 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].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright \u0026copy; 2016-2025. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dvariancepn.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dvariancepn\n\n[test-image]: https://github.com/stdlib-js/stats-base-dvariancepn/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-base-dvariancepn/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dvariancepn/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dvariancepn?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dvariancepn.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dvariancepn/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg\n[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/stats-base-dvariancepn/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dvariancepn/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dvariancepn/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dvariancepn/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dvariancepn/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dvariancepn/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dvariancepn/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dvariancepn/main/LICENSE\n\n[variance]: https://en.wikipedia.org/wiki/Variance\n\n[@stdlib/array/float64]: https://github.com/stdlib-js/array-float64\n\n[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray\n\n[@neely:1966a]: https://doi.org/10.1145/365719.365958\n\n[@schubert:2018a]: https://doi.org/10.1145/3221269.3223036\n\n\u003c!-- \u003crelated-links\u003e --\u003e\n\n[@stdlib/stats/strided/dnanvariancepn]: https://github.com/stdlib-js/stats-strided-dnanvariancepn\n\n[@stdlib/stats/strided/dstdevpn]: https://github.com/stdlib-js/stats-strided-dstdevpn\n\n[@stdlib/stats/strided/dvariance]: https://github.com/stdlib-js/stats-strided-dvariance\n\n[@stdlib/stats/base/svariancepn]: https://github.com/stdlib-js/stats-base-svariancepn\n\n[@stdlib/stats/base/variancepn]: https://github.com/stdlib-js/stats-base-variancepn\n\n\u003c!-- \u003c/related-links\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dvariancepn","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-base-dvariancepn","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dvariancepn/lists"}