# Median Absolute Deviation vs Standard Deviation

To measure spread we use Variance or Standard Deviation. Variance and hence Standard deviation uses mean to find out the spread.

Recently came across the MAD (median absolute deviation). http://en.wikipedia.org/wiki/Median_absolute_deviation

Why is Median absolute deviation not as popular as Standard Deviation, although it looks more robust (immune to outlier)? In other words why are artifacts which measure the SD from the median are not as popular as the artifacts which measure it from Mean?

• – Tim May 4 '15 at 22:20
• @Tim: In case the square form have better closed properties, Why is the squared deviation (variance) from median not popular? It will make the math consistent and make the moment immune to outlier also! – David May 4 '15 at 22:31
• Many of the comments in posts about using variance rather than mean absolute deviation from the mean (e.g. here) apply also to median absolute deviation from the median. Then on top of that, generally speaking properties of medians are not as nice as those of means. For example in general $\text{med}(X+Y)\neq$ $\text{med}(X)+\text{med}(Y)$; things like this makes it much less convenient to work with. – Glen_b May 4 '15 at 23:11