MAD {DescTools} | 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. This function wraps the specific base R function `mad`

and extends it for the use of weights.

### Usage

```
MAD(x, weights = NULL, center = Median, constant = 1.4826,
na.rm = FALSE, low = FALSE, high = FALSE)
```

### Arguments

`x` |
a numeric vector. |

`weights` |
a numerical vector of weights the same length as |

`center` |
the centre given either as numeric value or as a function to be applied to |

`constant` |
scale factor (default is |

`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.

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, `IQRw`

for weights,
`mad`

, `median`

, `var`

, `MADCI`

(confidence intervals).

### 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))
# use weights
x <- sample(20, 30, replace = TRUE)
z <- as.numeric(names(w <- table(x)))
(m1 <- MAD(z, weights=w))
(m2 <- MAD(x))
stopifnot(identical(m1, m2))
```

*DescTools*version 0.99.55 Index]