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Calculate the standard deviation of a strided array using a twopass algorithm.
The population standard deviation 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 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, the result is biased and yields an uncorrected sample standard deviation. To compute a corrected sample standard deviation for a sample of size n
,
where the sample mean is given by
The use of the term n1
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., n1.5
, n+1
, etc) can yield better estimators.
npm install @stdlib/statsbasestdevpn
var stdevpn = require( '@stdlib/statsbasestdevpn' );
Computes the standard deviation of a strided array x
using a twopass algorithm.
var x = [ 1.0, 2.0, 2.0 ];
var v = stdevpn( x.length, 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 according toNc
wherec
corresponds to the provided degrees of freedom adjustment. When computing the standard deviation of a population, setting this parameter to0
is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample standard deviation, setting this parameter to1
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
Array
ortyped array
. 
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 of every other element in x
,
var floor = require( '@stdlib/mathbasespecialfloor' );
var x = [ 1.0, 2.0, 2.0, 7.0, 2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );
var v = stdevpn( N, 1, x, 2 );
// returns 2.5
Note that indexing is relative to the first index. To introduce an offset, use typed array
views.
var Float64Array = require( '@stdlib/arrayfloat64' );
var floor = require( '@stdlib/mathbasespecialfloor' );
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length / 2 );
var v = stdevpn( N, 1, x1, 2 );
// returns 2.5
Computes the standard deviation of a strided array using a twopass algorithm and alternative indexing semantics.
var x = [ 1.0, 2.0, 2.0 ];
var v = stdevpn.ndarray( x.length, 1, x, 1, 0 );
// returns ~2.0817
The function has the following additional parameters:

offset: starting index for
x
.
While 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 for every other value in x
starting from the second value
var floor = require( '@stdlib/mathbasespecialfloor' );
var x = [ 2.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );
var v = stdevpn.ndarray( N, 1, x, 2, 1 );
// returns 2.5
var randu = require( '@stdlib/randombaserandu' );
var round = require( '@stdlib/mathbasespecialround' );
var Float64Array = require( '@stdlib/arrayfloat64' );
var stdevpn = require( '@stdlib/statsbasestdevpn' );
var x;
var i;
x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0)  50.0 );
}
console.log( x );
var v = stdevpn( x.length, 1, x, 1 );
console.log( v );
 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.
 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.

@stdlib/statsbase/dstdevpn
: calculate the standard deviation of a doubleprecision floatingpoint strided array using a twopass algorithm. 
@stdlib/statsbase/nanstdevpn
: calculate the standard deviation of a strided array ignoring NaN values and using a twopass algorithm. 
@stdlib/statsbase/sstdevpn
: calculate the standard deviation of a singleprecision floatingpoint strided array using a twopass algorithm. 
@stdlib/statsbase/stdev
: calculate the standard deviation of a strided array. 
@stdlib/statsbase/variancepn
: calculate the variance of a strided array using a twopass algorithm.
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.
See LICENSE.
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