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# incrmeanstdev

> Compute an [arithmetic mean][arithmetic-mean] and a [corrected sample standard deviation][sample-stdev] incrementally.

<section class="intro">

The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/5ca648efa8739942a21b07ad7df1947cdd01b662/lib/node_modules/@stdlib/stats/incr/meanstdev/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div>

<!-- </equation> -->

and the [corrected sample standard deviation][sample-stdev] is defined as

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}" alt="Equation for the corrected sample standard deviation."> -->

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/5ca648efa8739942a21b07ad7df1947cdd01b662/lib/node_modules/@stdlib/stats/incr/meanstdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for the corrected sample standard deviation.">
    <br>
</div>

<!-- </equation> -->

<section class="usage">

## Usage

```javascript
var incrmeanstdev = require( '@stdlib/stats/incr/meanstdev' );
```

#### incrmeanstdev( \[out] )

Returns an accumulator `function` which incrementally computes an [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][sample-stdev].

```javascript
var accumulator = incrmeanstdev();
```

By default, the returned accumulator `function` returns the accumulated values as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var accumulator = incrmeanstdev( new Float64Array( 2 ) );
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns updated accumulated values. If not provided an input value `x`, the accumulator function returns the current accumulated values.

```javascript
var accumulator = incrmeanstdev();

var ms = accumulator();
// returns null

ms = accumulator( 2.0 );
// returns [ 2.0, 0.0 ]

ms = accumulator( 1.0 );
// returns [ 1.5, ~0.71 ]

ms = accumulator( 3.0 );
// returns [ 2.0, 1.0 ]

ms = accumulator( -7.0 );
// returns [ -0.25, ~4.57 ]

ms = accumulator( -5.0 );
// returns [ -1.2, ~4.49 ]

ms = accumulator();
// returns [ -1.2, ~4.49 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN`, the accumulated values are equal to `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var Float64Array = require( '@stdlib/array/float64' );
var ArrayBuffer = require( '@stdlib/array/buffer' );
var incrmeanstdev = require( '@stdlib/stats/incr/meanstdev' );

var offset;
var acc;
var buf;
var out;
var ms;
var N;
var v;
var i;
var j;

// Define the number of accumulators:
N = 5;

// Create an array buffer for storing accumulator output:
buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element

// Initialize accumulators:
acc = [];
for ( i = 0; i < N; i++ ) {
    // Compute the byte offset:
    offset = i * 2 * 8; // stride=2, bytes_per_element=8

    // Create a new view for storing accumulated values:
    out = new Float64Array( buf, offset, 2 );

    // Initialize an accumulator which will write results to the view:
    acc.push( incrmeanstdev( out ) );
}

// Simulate data and update the sample means and standard deviations...
for ( i = 0; i < 100; i++ ) {
    for ( j = 0; j < N; j++ ) {
        v = randu() * 100.0 * (j+1);
        acc[ j ]( v );
    }
}

// Print the final results:
console.log( 'Mean\tStDev' );
for ( i = 0; i < N; i++ ) {
    ms = acc[ i ]();
    console.log( '%d\t%d', ms[ 0 ].toFixed( 3 ), ms[ 1 ].toFixed( 3 ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean

[sample-stdev]: https://en.wikipedia.org/wiki/Standard_deviation

</section>

<!-- /.links -->
