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
```

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