# Documentation

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# `stats`::`moment`

The K-th moment of a data sample

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

```stats::moment(`k`, `X`, `x1, x2, …`)
stats::moment(`k`, `X`, `[x1, x2, …]`)
stats::moment(`k`, `X`, `s`, <`c`>)
```

## Description

`stats::moment`(k, X, [x1, x2, …, xn]) returns the k-th moment

of the data xi centered around `X`.

If k is an integer, rational or float, and all data `X`, x1, x2, … are floating-point numbers, then the moment is returned as a floating-point number. For symbolic data, a symbolic expression is returned.

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

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.

## Environment Interactions

The function is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

We calculate the third moment of some data centered around `0`:

`stats::moment(3, 0, 2, 33/7, 21/9, PI)`

Alternatively, the data may be passed as a list:

`data := [2, 33/7, 21/9, PI]: stats::moment(3, 0, data)`

If all data are floating-point numbers, the result is a float:

`data := float(data): stats::moment(3, 0, data)`

We use `stats::moment` to compute the variance of the data:

```m := stats::mean(data): stats::moment(2, m, data) = stats::variance(data, Population)```

`delete data, m:`

### Example 2

We create a sample of type `stats::sample`:

`s := stats::sample([[22, 4, 1], [9, 8/3, 1], [0.1, 2, 3]])`
``` 22 4 1 9 8/3 1 0.1 2 3 ```

The fourth moment around a symbolic center `X` is computed for all columns in the sample:

`stats::moment(4, X, s, i) \$ i = 1..3`

`delete s:`

### Example 3

For symbolic arguments, the moment is returned as a symbolic expression:

`stats::moment(k, X, [x1, x2, x3, x4])`

## Parameters

 `k` `X` The center: an arithmetical expression `x1, x2, …` The statistical data: arithmetical expressions `s` A sample of domain type stats::sample `c` A column index of the sample `s`: a positive integer. This column provides the data x1, x2, ….