## 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

 ```1 2``` ```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 `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.

## 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/ Φ^(-1)(3/4) = `1/qnorm(3/4)`) ensures consistency, i.e.,

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`.
`IQR` which is simpler but less robust, `median`, `var`.
 ```1 2 3 4 5 6 7 8``` ```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)) ```