2
The mean as a fair share
Discover Mathematics P6: Term 1, Unit 7, Lessons 1–2
GoalUse levelling out and sum ÷ count to find the mean and explain what it tells us.
New words
fair share · the equal amount each one would get if everything were shared evenlysum · all the values added togetherlevel out · to move amounts from the larger to the smaller until all are equal
Explanation
The mean is also a fair share. Suppose some friends have different amounts. If they put everything together and share it out equally, each one gets the mean. This is called levelling out: the ones who have more give to those who have less until all have the same. There is a quick way. Add all the values to get the total, then divide the total by the number of friends. The answer does not have to be one of the values, and it can be a decimal.
★Remember
Fair share = total ÷ number of people. Levelling out and dividing the total give the same answer.
Worked examples
Amal has 7 stickers, Mina 3, Hana 5 and Karim 9. Together they have 24. Shared equally, each gets 24 ÷ 4 = 6. Levelling out: Amal gives 1, Karim gives 3; Mina gets 3 and Hana gets 1. Now all four have 6.
| Step | What we do | Result |
|---|---|---|
| 1 | add all the values | 40 |
| 2 | divide by the number of values (5) | 8 |
The mean need not be a data value. Five pupils have 4, 6, 5, 3 and 4 pencils. The total is 22 and 22 ÷ 5 = 4.4. No pupil has 4.4 pencils, but it still describes the fair share: if the pencils could be cut, each would get 4.4.
Class activity
Fair share at home. Ask four family members how many glasses of water they drank today. Add the answers and divide by four. Is the mean one of their answers? Who drank more than the mean and who drank less?
Practice
1
Find the mean of 4, 8, 6, 10.
(4 + 8 + 6 + 10) ÷ 4 = 28 ÷ 4 = 7.
2
Find the mean of 12, 15, 9, 14, 20, 2.
The total is 72 and 72 ÷ 6 = 12.
3
Four pupils have 5, 9, 4 and 6 stickers. They share them fairly. How many does each get?
5 + 9 + 4 + 6 = 24 and 24 ÷ 4 = 6 stickers each.
4
Three baskets of tomatoes weigh 2.5 kg, 3.5 kg and 4.5 kg. Find the mean mass.
2.5 + 3.5 + 4.5 = 10.5 and 10.5 ÷ 3 = 3.5 kg.
5
Can a mean be a number that is not in the data? Give an example.
Yes. The mean of 1 and 2 is 1.5, which is not in the data.