# meankbn
> Calculate the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm.
The [arithmetic mean][arithmetic-mean] is defined as
## Usage
```javascript
var meankbn = require( '@stdlib/stats/base/meankbn' );
```
#### meankbn( N, x, stride )
Computes the [arithmetic mean][arithmetic-mean] of a strided array `x` using an improved Kahan–Babuška algorithm.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;
var v = meankbn( N, x, 1 );
// returns ~0.3333
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-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 [arithmetic mean][arithmetic-mean] of every other element in `x`,
```javascript
var floor = require( '@stdlib/math/base/special/floor' );
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 = meankbn( N, x, 2 );
// returns 1.25
```
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
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 = meankbn( N, x1, 2 );
// returns 1.25
```
#### meankbn.ndarray( N, x, stride, offset )
Computes the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;
var v = meankbn.ndarray( N, x, 1, 0 );
// returns ~0.33333
```
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 [arithmetic mean][arithmetic-mean] for every other value in `x` starting from the second value
```javascript
var floor = require( '@stdlib/math/base/special/floor' );
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 = meankbn.ndarray( N, x, 2, 1 );
// returns 1.25
```
## Notes
- If `N <= 0`, both functions return `NaN`.
- Depending on the environment, the typed versions ([`dmeankbn`][@stdlib/stats/base/dmeankbn], [`smeankbn`][@stdlib/stats/base/smeankbn], etc.) are likely to be significantly more performant.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var meankbn = require( '@stdlib/stats/base/meankbn' );
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 = meankbn( x.length, x, 1 );
console.log( v );
```
* * *
## References
- Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].
[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[@stdlib/stats/base/dmeankbn]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dmeankbn
[@stdlib/stats/base/smeankbn]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/smeankbn
[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
