# When the Median Absolute Deviation (MAD) is zero

Suppose my data look like the following:

(10, 10, 10, 10, 10, 0)

Would it be possible to remove an outlier in this distribution using the median absolute deviation?

Of course, you wouldn't need to worry about outliers in a dataset like that, but how would you use the MAD to detect outliers in a similar dataset, when the MAD value equals 0?

• What would it mean to have an outlier in a dataset where the MAD was 0? If there were an outlier, what difference would it make? Commented Dec 9, 2015 at 12:24
• If you want to detect outliers then it's probably best not to use a measure that ignores them. Commented Dec 9, 2015 at 14:11
• @dsaxton: actually it is the opposite. If you want to detect the outliers, you have to use a measure that is not liable to being swayed by them. The reference are too numerous to cite here but you could start with C. Becker and U. Gather (1999). The Masking Breakdown Point of Multivariate Outlier Identification Rules.. Commented Dec 21, 2015 at 1:54
• I'm familiar with the point you're making, and my comment may have been misleading. The poster seemed to be suggesting he could use median absolute deviation alone to detect outliers (that is, see if removing a point caused it to go down). This wouldn't work because the median absolute deviation wouldn't change as a result of removing an outlier. Commented Dec 21, 2015 at 6:00
• Take a look at: this post There is a section about the MAD=0 problem. Commented Sep 30, 2016 at 8:24