mathjs/docs/reference/functions/std.md

# 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(var(A))`.
In case of a (multi dimensional) array or matrix, the standard deviation
over all elements will be calculated.

Optionally, the type of normalization can be specified as second
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)
```

### Parameters

Parameter | Type | Description
--------- | ---- | -----------
`array` | Array | 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
```


## See also

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


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