What an average means

A class ran a book drive for 4 days. The numbers of books collected on the 4 days were 11, 5, 0 and 8. Find the average number of books collected in a day. An average is what each day would be, if the same number came in every day. So we even the bars out. The purple is what moves across. Even the day with 0 books fills up. They all settle at the same height, and that height is the average. We didn't add any books, and we didn't throw any away, so the total hasn't changed. 11 plus 5 plus 0 plus 8 is 24 books. Now we share that total across the days. Monday, Tuesday, Wednesday, Thursday. 4 days, so 4 pieces of data. On Wednesday they collected 0 books. That is still a piece of data, and it is not left out. So we divide by 4, not by 3. 24 divided by 4 is 6 books. That 6 is where the bars levelled off. An average doesn't have to be one of the given numbers.

Your turn. Sometimes a question comes with no story at all. Find the average of 9, 0, 14, 6 and 11. Try it first. Pause if you like. 5 numbers, so 5 bars. 9, 0, 14, 6 and 11. We even them out. 9 plus 0 plus 14 plus 6 plus 11 is 40. The 0 is one of the 5 pieces of data, so we divide by 5. 40 divided by 5 is 8. Levelling doesn't change the total. We only share it out equally, and the height the bars settle at is the average. Every number in the set is one bar, and a 0 is one of them.