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 Question from michelle, a student: the average of x and y is 20. If z = 5, what is the average of x, y, and z.

Hi Michelle.

When we say the "average" of a number, we usually mean the "mean" of a number, which is a more precise word than average, because there are three commonly used definitions of the word "average": the mean, the mode and the median. Anyway, I am pretty sure you mean the "mean" average.

To calculate the mean, you add up all the values and divide by the number of values. So if I have the three values 10, 26 and 30, then I start by adding 10+26+30 = 66 and then divide by 3 to get 66 / 3 = 22. That's the mean.

What would happen if I add a fourth to this? Say the fourth number is another 26. Then I add 10+26+30+26 = 92, divide by 4 and get 23.

What if I didn't have the original three numbers, but I knew there were 3 and the mean was 22? Then I could multiply the original mean (22) by the original number of values (3) to get the original total: 22x3 = 66. Now I add 26 to get 92 and then divide by 4 to get the right answer.