mad {stats} | R Documentation |

## Median Absolute Deviation

### Description

Compute the median absolute deviation, i.e., the (lo-/hi-) median of the absolute deviations from the median, and (by default) adjust by a factor for asymptotically normal consistency.

### Usage

```
mad(x, center = median(x), constant = 1.4826, na.rm = FALSE,
low = FALSE, high = FALSE)
```

### Arguments

`x` |
a numeric vector. |

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

`constant` |
scale factor. |

`na.rm` |
if |

`low` |
if |

`high` |
if |

### Details

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

with the default value of `center`

being `median(x)`

, and
`cMedian`

being the usual, the ‘low’ or ‘high’ median, see
the arguments description for `low`

and `high`

above.

In the case of `n = 1`

non-missing values and default `center`

, the
result is `0`

, consistent with “no deviation from the center”.

The default `constant = 1.4826`

(approximately
`1/\Phi^{-1}(\frac 3 4)`

= `1/qnorm(3/4)`

)
ensures consistency, i.e.,

`E[mad(X_1,\dots,X_n)] = \sigma`

for `X_i`

distributed as `N(\mu, \sigma^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
x <- c(1,2,3,5,7,8)
sort(abs(x - median(x)))
c(mad(x, constant = 1),
mad(x, constant = 1, low = TRUE),
mad(x, constant = 1, high = TRUE))
```

*stats*version 4.4.1 Index]