> For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4

> For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma. Could you sketch out why similar statements couldn't be made about MAD? My (possibly flawed) intuition is that the expected proportion of observations within n\*MAD should be similarly independent of the parameters of the normal distribution.