Average

An average is a single time calculated from a set of consecutive solves. Traditionally these averages are calculated as a truncated mean, in which 5% of the best and 5% of the worst times are removed. (If 5% of the total is not an integer, it is rounded up. For example, in an Ao5 only the best solve and the worst solve are removed because 5 * 5% rounded up gives one). The remaining 90% of the times are then averaged together by taking their mean. This approach has the benefit of preventing extreme outliers from skewing the data and misleading the reader.

In an average, the removed times are placed in brackets. The times that are not removed by this process are called "counting times". If any counting time is a DNF or DNS, the average is a DNF.

As an example, here are five times we want to determine the Ao5 of: (5.43) 4.32 3.21 2.10 (1.00). 5.43 and 1.00 are the outlier times so they are discarded. 4.32 + 3.21 + 2.10 sum to 9.63, divide by 3 to get the mean of 3.21.

Most WCA events use averages of 5. There are a few exceptions however -- longer events such as 7x7 take the mean of 3 solves as competition time is limited. Most speedcubers use averages of 100 to gauge their ability at home, owing to the common sentiment that averages of 5 can be easily skewed by a lucky streak.

Types of Averages

The most common averages tracked by solvers are Mo3, Ao5, Ao12, Ao50 and Ao100. Ao25, Ao1000 and more may be used occasionally depending on context.

Average of X (AoX)

To calculate averages of 5 or 12, or for any average of 20 or fewer elements, it is only necessary to remove the single fastest and slowest times before taking the mean.

To calculate an average of 50, remove the three fastest and slowest times before taking the mean.

To calculate an average of 100, remove the five fastest and slowest times before taking the mean.

Mean (MoX)

A mean is very similar to an average, except the best and worst times are not removed. Means of 3 (Mo3) are usually used when a puzzle takes a long time, such as 6x6 and 7x7. The usage of mean for a number greater than 3 is rare.

Rolling Averages

A rolling average is when you do an average, then continue to do solves. The first solves are then removed from the average and replaced with the newer ones. For example, if you did an average of 5 with (15.32) 14.64 13.17 (11.22) 12.88, you can do another two solves to remove your two highest times and attempt to get faster times. The times that are removed are considered "rolled".