Accelerating the pace of engineering and science

# Documentation Center

• Trial Software

# stats::median

Median value of a data sample

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::median(x1, x2, …, <Averaged>)
stats::median([x1, x2, …], <Averaged>)
stats::median(s, <c>, <Averaged>)
```

## Description

stats::median(x1, x2, …) returns the median of the data xi.

The median of n sorted values x1 ≤ … ≤ xn is .

The averaged median of n sorted values x1 ≤ … ≤ xn is .

For odd n, both the median and the averaged median coincide with the element of the sorted data list. For even n, the median is , whilst the averaged median is .

The median coincides with the -quantile of the data: the calls stats::median(data <Averaged>) and stats::empiricalQuantile(data)(1/2 <Averaged>) are equivalent. See the help page of stats::empiricalQuantile for details on the parameters specifying the data.

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 median of a sequence of five values:

`stats::median(3, 8, 5, 9/2, 11)`

Alternatively, data may be passed as a list:

```stats::median([2, 7, 3, 9/2, 11, 12]),
stats::median([2, 7, 3, 9/2, 11, 12], Averaged)```

### Example 2

We create a sample:

`stats::sample([[4, 7, 5], [3, 6, 17], [8, 2, 2]])`
```4  7   5
3  6  17
8  2   2
```

The median of the second column is 6:

`stats::median(%, 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
```

The median of the second column is calculated. In this case, there is no need to specify the index of the column, since it is the only non-string data column in the sample:

`stats::median(%)`

## Parameters

 x1, x2, … The statistical data: real numerical values. 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 etc.

## Options

 Averaged Return the averaged median value

## Return Values

arithmetical expression. FAIL is returned if the data sample is empty.