In this post (in German) I demonstrated the superiority of the median over the mean in aggregating a good estimate for a guessing question which answers are bounded by zero but have no upper limit. I speculated further that the correct value often lies slightly above the median. John Doyle recently invented the meandian (see Meandian: A Measure of Location Based on Signed Rank of Deviations) as a measure in between the mean and the median. As a consequence the meandian is typically slightly larger than the median. Doyle showed on our PNAS dataset that the meandian indeed delivers as good results as the median and often better ones.
As I really liked the idea of the meandian, I quickly checked the measure on my “Weisheit der Bremer”-dataset and found:
Truth = 10788, Median = 9843, Meandian = 12170.
Deviations: |Median-Truth| = 945, |Meandian-Truth| = 1382.
Conclusion: Meandian is also good, but the Median wins in this case.
By the way: All are beaten by the geometric mean:
Geomean = 10510 (Deviation |Geomean-Truth| = 278)