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# Definite Integrals

# Averages with Numbers

To find the average of a bunch of numbers, you add all the numbers and divide by how many there are.

### Sample Problem

Five students took a test. Their scores were 60, 70, 80, 85, and 87. The average of their scores is

In that example, if we add all the students' scores, we get 382. Now suppose we added up the students' scores and got 382, but that all the students got the same score on the test. In order for that to happen, each student would have had to score

You can think of averaging as redistributing points so that everyone gets an equal share.