Median Absolute Deviation Measure

A Median Absolute Deviation Measure is a statistical dispersion measure of univariate quantitative data based on absolute deviation to a median value.

• Example(s):
  • for the data set {2, 2, 3, 4, 14}: [math]\displaystyle{ \frac{|2 - 3| + |2 - 3| + |3 - 3| + |4 - 3| + |14 - 3|}{5} = 2.8 }[/math].
  • …
• Counter-Example(s):
  • Average Absolute Deviation.
  • Mode Absolute Deviation.
  • Median Absolute Error.
• See: Absolute Deviation, Median Statistic, Mean Squared Error, Population Statistic, Robust Statistics, Statistical Dispersion.

---

---

References

2020

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Median_absolute_deviation Retrieved:2020-7-24.
  • In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample.

    For a univariate data set X₁, X₂, ..., X_n, the MAD is defined as the median of the absolute deviations from the data's median [math]\displaystyle{ \tilde{X}=\operatorname{median}(X) }[/math] : : [math]\displaystyle{ \operatorname{MAD} = \operatorname{median}( |X_i - \tilde{X}|) }[/math] that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values.

---