skatinginbc said:
Joubert interpretation: 8.25 8.00 8.50 8.50 8.50 8.50 8.50 9.50 8.00 (median = 8.50)
The median is a more subtle statistic than it is given credit for. If we assume that these data represent measurement along a continuum, then rounded to the nearest .25 point, we probably should handle it a little differently in the case where the median class has more than one datum. The most convincing way to see this is to draw a histogram. We want 50% of the data to be above the median and 50% below.
8.00 8.00 8.25 8.50
8.50 8.50 8.50 8.50 9.50
The median is the 8.50 that is bolded, not the 8.50 that is a little less than that one or the three that are a little bigger. The class boundaries for the five 8.50s are 8.375 to 8.625. Since three numbers are below 8.375 we need 1.5 data points to make 4.5 (half). 1.5/5 = .3. So we need to split the 8.5 class, not down the middle, but in the ratio of .3 to .7.
Median = 8.375+.3x,25 = 8.45
Check: 8.625-.7x.25 = 8.45
So Joubert's median for Interpretation is 8.45.
Hanyu's median for Interpretation , by this method, is 8.125+.25x(2.5/3) = 8.33.
This takes into account the fact that Hanyu had three data points in his median class of 8.25.
skatinginbc said:
Adding medians is slippery sands. Better, if the are many categories, to say, One skater got a higher median than the other in four out of five components, or whatever. The old problem again, are we counting or measuring, Cop or ordinals.
Even the trimmed mean suffers a little in this regard (what exactly do we get when to add them?) compared to the mean over all judges. Speaking of the trimmed mean, that 9.50 that Joubert got for interpretation stands out like a sore thumb. It is 2.34 standard deviations above the mean. Was there a French Judge on the panel?

I think Skatefiguring had a point when he observed that Hanyu was the beneficiary of trimming.
Anyway, all of these numbers are so close together I don't think any conclusion can be drawn. Mrs. T. liked Joubert. OK. So did I in 2008, but what do I know?
