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)

John DoyleOne limitation of the geometric mean is that it needs strictly positive data, whereas mean, median, and meandian do not. So if the “wise crowd” were asked to guess percentage economic growth, say, for the coming year, we would have a problem if any single person were to guess zero or negative growth – and why would they not in today’s climate!

janloPost authorIndeed, that’s a problem of the geomean. By the way, the case of negative growth rates could be solved by changing e.g. from -4% to 0.96 and +10% to 1.1. Now, only people which predict a decline by more than 100% are a problem…

Another weakness of geomean is, that it is as vulnerable to malicious extreme outliers as the mean.