variance

Calculate the variance of a one-dimensional ndarray.

The population variance of a finite size population of size N is given by

where the population mean is given by

Often in the analysis of data, the true population 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, the result is biased and yields an uncorrected sample variance. To compute a corrected sample variance for a sample of size n,

where the sample mean is given by

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 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.

Installation

npm install @stdlib/stats-base-ndarray-variance

Usage

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

variance( arrays )

Computes the variance of a one-dimensional ndarray.

var ndarray = require( '@stdlib/ndarray-base-ctor' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );

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

var xbuf = [ 1.0, -2.0, 2.0 ];
var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
var correction = scalar2ndarray( 1.0, opts );

var v = variance( [ x, correction ] );
// returns ~4.3333

The function has the following parameters:

• arrays: array-like object containing two elements: a one-dimensional input ndarray and a zero-dimensional ndarray specifying the degrees of freedom adjustment. Providing a non-zero degrees of freedom adjustment has the effect of adjusting the divisor during the calculation of the variance according to N-c where N is the number of elements in the input ndarray and c corresponds to the provided degrees of freedom adjustment. When computing the 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 corrected sample 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).

Notes

• If provided an empty one-dimensional ndarray, the function returns 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 function returns NaN.

Examples

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

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 correction = scalar2ndarray( 1.0, opts );
var v = variance( [ x, correction ] );
console.log( v );

Notice

This package is part of 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, see the main project repository.

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.