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.

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

x

a numeric vector.

center

Optionally, the centre: defaults to the median.

constant

scale factor.

na.rm

if `TRUE`

then `NA`

values are stripped
from `x`

before computation takes place.

low

if `TRUE`

, compute the ‘lo-median’, i.e., for even
sample size, do not average the two middle values, but take the
smaller one.

high

if `TRUE`

, compute the ‘hi-median’, i.e., take the
larger of the two middle values for even sample size.

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`

.

# NOT RUN { 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)) # }