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)

Average of 5

In cubing competitions, an "average of 5" (Ao5/Avg5) refers to the calculation of an average time for a competitor's five attempts at solving a cube. The best and worst times are discarded, and the average is calculated using the remaining three times.

To calculate the average of 5 take away the best and worst times of your solves and add the remaining 3 solves together, then divide them by 3

For demo: (11.05), 12.93, 12.64, 11.30, (14.58) In this case 11.05 is the best solve and 14.58 is the worst. So add the remaining 3 solves; 12.93 + 12.64 + 11.30 equals 36.87. Now divide the 36.87 by 3 (36.87/3 or 36.87 ÷ 3) equals "12.29".

"12.29" is the average of 5.

Average of 12

Average of 12 (ao12) is used to determine how good a speedcuber is, since average of 5 only needs 5 solves, sometimes cubers get lucky during average of 5. Average of 12 is longer and requirs more solves and skills.

To calculate the average of 12 it's the same concept as average of 5. First do 12 solves and then take away the best and worst solves, next add the 10 remaining solves and divide them by 10.

Average of 50

Sometimes speedcubers do more than 5, 12 or even 20-30 solves, this is when average of 50 comes in. Doing 50 solves

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

Average of 100

Average of 100 (ao100) needs 100 solves and obviously depending on your ability, one can take up to 2-4 hours doing average of 100. But online timers such as cstimer can show your average of 100 after doing 100 solves.

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

Average of 1000

Apparently some people are crazy enough to do average of 1000. Professional cubers like Max Park has ao1000 of 5.2X seconds.

Mean (MoX)

Mean of 3

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".