Another way to robustly estimate the standard deviation in the presence
of outliers is to use the median absolute deviation (MAD). To compute
the MAD, we first compute the median, and then for each value we compute
the distance between that value and the median. The MAD is defined as
the median of these distances. For technical reasons not discussed here,
this quantity needs to be multiplied by 1.4826 to assure it approximates
the actual standard deviation. The mad
function already incorporates
this correction. For the height data, we get a MAD of:
mad(outlier_example)
#> [1] 0.237
which is about 3 inches.