mathjs/docs/reference/functions/std.md

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# Function std

Compute the standard deviation of a matrix or a  list with values.
The standard deviations is defined as the square root of the variance:
`std(A) = sqrt(variance(A))`.
In case of a (multi dimensional) array or matrix, the standard deviation
over all elements will be calculated by default, unless an axis is specified
in which case the standard deviation will be computed along that axis.

Additionally, it is possible to compute the standard deviation along the rows
or columns of a matrix by specifying the dimension as the second argument.

Optionally, the type of normalization can be specified as the final
parameter. The parameter `normalization` can be one of the following values:

- 'unbiased' (default) The sum of squared errors is divided by (n - 1)
- 'uncorrected'        The sum of squared errors is divided by n
- 'biased'             The sum of squared errors is divided by (n + 1)


## Syntax

```js
math.std(a, b, c, ...)
math.std(A)
math.std(A, normalization)
math.std(A, dimension)
math.std(A, dimension, normalization)
```

### Parameters

Parameter | Type | Description
--------- | ---- | -----------
`array` | Array &#124; Matrix |  A single matrix or or multiple scalar values
`normalization` | string |  Determines how to normalize the variance. Choose 'unbiased' (default), 'uncorrected', or 'biased'. Default value: 'unbiased'.

### Returns

Type | Description
---- | -----------
* | The standard deviation


## Examples

```js
math.std(2, 4, 6)                     // returns 2
math.std([2, 4, 6, 8])                // returns 2.581988897471611
math.std([2, 4, 6, 8], 'uncorrected') // returns 2.23606797749979
math.std([2, 4, 6, 8], 'biased')      // returns 2

math.std([[1, 2, 3], [4, 5, 6]])      // returns 1.8708286933869707
math.std([[1, 2, 3], [4, 6, 8]], 0)    // returns [2.1213203435596424, 2.8284271247461903, 3.5355339059327378]
math.std([[1, 2, 3], [4, 6, 8]], 1)    // returns [1, 2]
math.std([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.7071067811865476, 1.4142135623730951]
```


## See also

[mean](mean.md),
[median](median.md),
[max](max.md),
[min](min.md),
[prod](prod.md),
[sum](sum.md),
[variance](variance.md)