# `stats`::`stdev`

Standard deviation of a data sample

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## Syntax

```stats::stdev(`x1, x2, …`, <`Sample | Population`>)
stats::stdev(`[x1, x2, …]`, <`Sample | Population`>)
stats::stdev(`s`, <`c`>, <`Sample | Population`>)
```

## Description

```stats::stdev( x1, x2, ..., xn)``` returns the standard deviation

,

where is the arithmetic mean of the data xi.

```stats::stdev( x1, x2, ..., xn, Population)``` returns

.

The standard deviation is the square root of the variance.

The column index `c` is optional, if the data are given by a `stats::sample` object containing only one non-string column. Cf. Example 3.

External statistical data stored in an ASCII file can be imported into a MuPAD® session via `import::readdata`. In particular, see Example 1 of the corresponding help page.

## Examples

### Example 1

We calculate the standard deviation of three values:

`stats::stdev(2, 3, 5)`

Alternatively, the data may be passed as a list:

`stats::stdev([2, 3, 5])`

### Example 2

We create a sample:

`stats::sample([[a1, b1, c1], [a2, b2, c2]])`
```a1 b1 c1 a2 b2 c2 ```

The standard deviation of the second column is:

`expand(stats::stdev(%, 2))`

### Example 3

We create a sample consisting of one string column and one non-string column:

`stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])`
```"1996" 1242 "1997" 1353 "1998" 1142 ```

We compute the standard deviation of the second column. In this case this column does not have to be specified, since it is the only non-string column:

`float(stats::stdev(%))`

We repeat the computation with the option `Population`:

`float(stats::stdev(%2, Population))`

## Parameters

 `x1, x2, …` The statistical data: arithmetical expressions `s` A sample of domain type `stats::sample` `c` An integer representing a column index of the sample `s`. This column provides the data x1, x2 etc.

## Options

 `Population`, `Sample` With `Sample`, the data are regarded as a “sample”, not as a full population. The default is `Sample`.

## Return Values

Arithmetical expression.

#### Mathematical Modeling with Symbolic Math Toolbox

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