Math CentralQuandaries & Queries


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.

So to answer your question, use the same technique, Michelle.

Hope this helps,
Stephen La Rocque.

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS