How do you calculate an average of a set of numbers by only counting?

Answer 1

The average of two numbers is the number directly between the two. For example, the average of 85 and 89 is 87, because 87 is directly between 85 and 89.

The number directly between two numbers is half of the count from one number to the other, added to the lesser number. Starting from 85 and going to 89, you count four numbers (86, 87, 88, 89). Half of four is two, and two added to 85 is 87.

To find the average of more than two numbers, I often subtract a certain amount from a greater number and add the same amount to a lesser number until I can see the average. For example, to find the average of 100, 90, 85 and 89, I would start by changing the 100 to 95 and the 85 to 90. So then we have 95, 90, 90 and 89. Since there's a difference of six from 89 to 95, I would take three from 95 and add it to 89, making 92, 92, 90 and 90. Now I see that each pair of 92 and 90 could be changed to a pair of 91's. Since the average of 91, 91, 91 and 91 is 91, the average of 100, 90, 85 and 89 is 91. No calculator needed.