1
The arithmetic mean of a list and finding a missing value
Mathematics Prep 1 Term 1, Unit 3, Lesson 2
GoalFind the mean of a list as a fair share and find a missing value when the mean is known.
New words
arithmetic mean · the sum of the values divided by how many there arefair share · what each would get if the total were shared equallysum · all the values added togethermissing value · the unknown value when the mean is given
Explanation
The arithmetic mean tells what each value would be if the total were shared out equally. Mean = sum of the values ÷ number of values. Four children have 6, 2, 9 and 3 stickers: the total is 20, and 20 ÷ 4 = 5, so a fair share is 5 stickers each. The mean does not have to be one of the values, and it can be a decimal. If the mean is known, the total is mean × number of values. This lets you find a missing value: total needed minus the sum of the known values. Do not forget to divide by the number of values.
ƒFormula
mean = sum of values ÷ number of values
Total = mean × number of values.
Worked examples
Stickers. Amal, Bassem, Chadi and Dalia have 6, 2, 9 and 3 stickers. Sum = 6 + 2 + 9 + 3 = 20. Mean = 20 ÷ 4 = 5. If they share equally, each has 5.
Marks. Four marks are 12, 15, 9 and 14. Sum = 50. Mean = 50 ÷ 4 = 12.5. The mean is not one of the marks, and that is fine.
A missing value. The mean of five numbers is 8, and four of them are 6, 7, 9 and 10. Total needed = 5 × 8 = 40. Known sum = 6 + 7 + 9 + 10 = 32. The fifth number is 40 − 32 = 8. Check: 40 ÷ 5 = 8.
Class activity
Share it out. With a grown-up, take 20 small objects and divide them unequally into four cups. Count each cup. Now move objects between cups until every cup holds the same number. That number is the mean.
Practice
1
Find the mean of 4, 7, 9 and 12.
Sum = 32, and 32 ÷ 4 = 8.
2
Find the mean of 2.5, 3.5 and 4.5.
Sum = 10.5, and 10.5 ÷ 3 = 3.5.
3
The mean of five marks is 14. Four of them are 12, 15, 16 and 13. Find the fifth.
Total = 5 × 14 = 70. Known sum = 56. The fifth mark is 70 − 56 = 14.
4
Hana’s three test marks have the mean 16. What mark must she get in a fourth test to have the mean 17?
Total for 4 tests = 4 × 17 = 68. She has 3 × 16 = 48. She needs 68 − 48 = 20.
5
Youssef says the mean of 6, 8 and 10 is 6 + 8 + 10 = 24. What is wrong?
He forgot to divide by the number of values: 24 ÷ 3 = 8.