mad {base} | R Documentation |

## Median Absolute Deviation

### Description

Compute a scale estimate based on the median absolute deviation.

### Usage

mad(x, center, constant = 1.4826, na.rm = FALSE)

### Arguments

`x` |
a numeric vector. |

`center` |
Optionally, the centre: defauls to the median. |

`constant` |
scale factor. |

`na.rm` |
if `TRUE` then `NA` values are stripped
from `x` before computation takes place. |

### Details

The actual value calculated is
`constant * (median(abs(x - center)))`

with the default value of
`center`

being `median(x)`

.

The default `constant = 1.4826`

(approximately
*1/ Phi^(-1)(3/4)* = `1/qnorm(3/4)`

)
ensures consistency, i.e.,

*E[mad(X_1,...,X_n)] = σ*

for *X_i* distributed as *N(μ,σ^2)* and large *n*.
If `na.rm`

is `TRUE`

then `NA`

values are stripped from `x`

before computation takes place.
If this is not done then an `NA`

value in
`x`

will cause `mad`

to return `NA`

.

### See Also

`IQR`

which is simpler but less robust,
`median`

, `var`

.

### Examples

mad(c(1:9))
print(mad(c(1:9), constant=1)) ==
mad(c(1:8,100), constant=1) # = 2 ; TRUE