Calculating Averages?

[byu]

I have trouble with calculating averages for Rubik's Cubing. I don't understand the different types of averages and how they work. I tried using Google, but different websites have different explanations. For example, do you just add up all the times and divide by the number of times? If so, what happens if you get a DNF? Any information is appreciated.

 

[Sa967St]

For averages of 5 , you would not count the worst and best time, and you just average the remaining 3 times. For means of 3 (events like clock, megaminx etc.) you would average all 3 times. If you get a DNF in an average of 5, it would count as your worst solve. If you get 2 DNFs in an average of 5, you would get a DNF average (it is very bad to do this in a competition! I would know). If you get a DNF in a mean of 3 if would also be a DNF average.

 

[cmhardw]

http://www.worldcubeassociation.org/regulations/#speedsolving
See Article 9f)

9f) The results of a round are measured as follows:

9f1) All timed results under 10 minutes, and corresponding averages/means are measured in hundredths of a second, with averages/means rounded to the nearest hundredth of a second (x.004 becomes x.00, x.005 becomes x.01).

9f2) All timed results over 10 minutes, and corresponding averages/means are measured in seconds, with averages/means rounded to the nearest second (x.4 becomes x, x.5 becomes x+1).

9f3) All counted results and averages/means are measured in natural numbers, with averages/means rounded to the nearest tenth (x.04 becomes x.0, x.05 becomes x.1).

9f4) DNF (Did Not Finish) is the result if the solve was disqualified or unfinished.

9f5) DNS (Did Not Start) is the result if a competitor skipped an attempt in a round.

9f6) In 'Best of x' rounds competitors get x (<= 3) attempts, with the best attempt counting. There may be a combined time limit, example: 30 minutes for 'Best of 1' or 'Best of 2'.

9f7) In 'Best of x' rounds a DNF or DNS is the worst result of a competitor, if all results are DNF and/or DNS the best result of the competitor is DNF.

9f8) In 'Average of 5' rounds competitors get 5 attempts. Of these 5 attempts, the best and worst attempt are removed, with the mean of the remaining 3 attempts counting.

9f9) In 'Average of 5' rounds one DNF or DNS is counted as the worst result, with more than one DNF and/or DNS the average is DNF.

9f10) In 'Mean of 3' rounds competitors get 3 attempts, with the mean of the 3 attempts counting.

9f11) In 'Mean of 3' rounds if the competitor has at least one DNF or DNS the mean is DNF.

9f12) In 'Best of x' rounds the order in the results is based on the best result per competitor, with lower meaning better.

9f13) In 'Mean of' and 'Average of' rounds the order in the results is based on the best average/mean per competitor, with lower meaning better.

9f14) If in 'Mean of' and 'Average of' rounds competitors have the same average/mean result, then the order in the results for these competitors is based on the best result per competitor, with lower meaning better.

9f15) Competitors with the same result in a round finish at the same position.

9f16) For the Rubik's Cube: Multiple Blindfolded event the order in the results is based on number of puzzles solved minus the number of puzzles not solved (higher is better). If the result is lower than 0, the solve is disqualified.
If competitors have the same result, then the order is based on total time (lower is better).

 

[brunson]

WCA abuses the definitions of "mean" and "average", but at least they do it consistently.