MKmisc (version 1.6)

# IQrange: The Interquartile Range

## Description

Computes (standardized) interquartile range of the `x` values.

## Usage

```IQrange(x, na.rm = FALSE, type = 7)
sIQR(x, na.rm = FALSE, type = 7, constant = 2*qnorm(0.75))```

## Arguments

x

a numeric vector.

na.rm

logical. Should missing values be removed?

type

an integer between 1 and 9 selecting one of nine quantile algorithms; for more details see `quantile`.

constant

standardizing contant; see details below.

## Details

This function `IQrange` computes quartiles as `IQR(x) = quantile(x,3/4) - quantile(x,1/4)`. The function is identical to function `IQR`. It was added before the `type` argument was introduced to function `IQR` in 2010 (r53643, r53644).

For normally \(N(m,1)\) distributed \(X\), the expected value of `IQR(X)` is `2*qnorm(3/4) = 1.3490`, i.e., for a normal-consistent estimate of the standard deviation, use `IQR(x) / 1.349`. This is implemented in function `sIQR` (standardized IQR).

## References

Tukey, J. W. (1977). Exploratory Data Analysis. Reading: Addison-Wesley.

## See Also

`quantile`, `IQR`.

## Examples

```# NOT RUN {
IQrange(rivers)

## identical to
IQR(rivers)

## other quantile algorithms
IQrange(rivers, type = 4)
IQrange(rivers, type = 5)

## standardized IQR
sIQR(rivers)

## right-skewed data distribution
sd(rivers)
mad(rivers)

## for normal data
x <- rnorm(100)
sd(x)
sIQR(x)
mad(x)
# }
```