Primary 6 Maths: Average
Average moved from P5 to P6 under the 2021 MOE syllabus. Mean of a set, total = average × number, missing values, and how the average shifts when items join or leave — worked PSLE examples.
Most schools typically cover this topic in Term 3, around weeks 2–4 — though every school sets its own sequence.
Average is a newcomer to Primary 6: under the pre-2021 syllabus it was taught at P5, but the 2021 MOE syllabus moved it to P6, so today's P6 cohort meets it for the first time in the PSLE year itself. That means less runway between first meeting the idea and sitting the exam — worth knowing if an older sibling's notes suggest it should already be familiar.
The idea itself is simple: an average (or mean) is what every item in a set would be worth if the total were shared out equally. The engine behind every question is one formula, used in both directions: total = average × number of items. Most P6 average questions are really "find the total, then find what changed it" — a value is added, removed, or one value is unknown, and the total is the bridge to the answer.
The mistakes to watch for
- Writing the total when the question asks for the average, or vice versa. They're related by the same formula but they are not the same number — always check which one the question wants in the final line.
- Assuming a missing value equals the average. It doesn't, unless the numbers happen to work out that way. The missing value is found from the total, not guessed from the average.
- Forgetting that adding or removing one item changes the total by more than "the difference from the old average." Recompute the total for the new group size each time, rather than trying to shortcut the arithmetic.
- Averaging two averages directly when the group sizes differ. If Group A and Group B don't have the same number of items, the combined average is a weighted average — found from the combined total, not from (average A + average B) ÷ 2.
Levelling out a set of values
Easy: mean of a set and finding totals
Easy: find the average
Find the average of 12, 18 and 15.
Show the worked solution
Total = 12 + 18 + 15 = 45.
Average = 45 ÷ 3 = 15.
Easy: total from the average
The average of 6 numbers is 9. Find their total.
Show the worked solution
Total = average × number of items = 9 × 6 = 54.
Easy: a missing number
The average of four numbers is 10. Three of the numbers are 8, 11 and 9. Find the fourth number.
Show the worked solution
Total of all four = 10 × 4 = 40. Sum of the three known numbers = 8 + 11 + 9 = 28.
Fourth number = 40 − 28 = 12.
Easy: average weight
Three parcels weigh 4 kg, 5 kg and 6 kg respectively. Find their average weight.
Show the worked solution
Total = 4 + 5 + 6 = 15 kg. Average = 15 ÷ 3 = 5 kg.
Exam: when the average changes
Exam: a number is added
The average of 5 numbers is 20. A sixth number is added and the new average becomes 21. Find the sixth number.
Show the worked solution
Total of the first 5 numbers = 20 × 5 = 100. Total of all 6 numbers = 21 × 6 = 126.
Sixth number = 126 − 100 = 26.
Exam: a box is removed
The average mass of 8 boxes is 12 kg. One box is removed, and the average mass of the remaining boxes becomes 11 kg. Find the mass of the box that was removed.
Show the worked solution
Total of 8 boxes = 12 × 8 = 96 kg. Total of the remaining 7 boxes = 11 × 7 = 77 kg.
Mass removed = 96 − 77 = 19 kg.
Exam: the score needed for a target average
Mei scored 72 and 85 in her first two Mathematics tests. What must she score in her third test for her average across all three tests to be 80?
Show the worked solution
Total needed for 3 tests averaging 80 = 80 × 3 = 240.
Total of her first two tests = 72 + 85 = 157.
Third-test score = 240 − 157 = 83.
Exam: combining two groups of different sizes
Class A has 20 pupils with an average height of 140 cm. Class B has 30 pupils with an average height of 145 cm. Find the average height of all 50 pupils together.
Show the worked solution
Total height of Class A = 140 × 20 = 2800 cm. Total height of Class B = 145 × 30 = 4350 cm.
Combined total = 2800 + 4350 = 7150 cm, over 50 pupils.
Combined average = 7150 ÷ 50 = 143 cm.
Note this is not (140 + 145) ÷ 2 = 142.5 — the groups are different sizes, so the average leans towards the bigger group.
Exam: an average that stays the same
The average of 3 numbers is 15. A fourth number is included, and the average remains 15. What is the fourth number?
Show the worked solution
Total of 3 numbers = 15 × 3 = 45. Total of 4 numbers, still averaging 15, = 15 × 4 = 60.
Fourth number = 60 − 45 = 15.
Makes sense: adding a number equal to the current average never changes the average.
PSLE challenge: multi-step average problems
PSLE challenge: one number is replaced
The average of 8 numbers is 15. One of the numbers, 10, is replaced by another number, and the new average becomes 16. Find the value of the new number.
Show the worked solution
Total of the original 8 numbers = 15 × 8 = 120. Total of the 8 numbers after the swap = 16 × 8 = 128.
The total rose by 128 − 120 = 8, and that rise is entirely due to the swap.
New number = 10 + 8 = 18.
Check: replace 10 with 18 in a total of 120 → 120 − 10 + 18 = 128; 128 ÷ 8 = 16. ✓
PSLE challenge: combining averages across a ratio
In a class, the ratio of boys to girls is 3 : 2. The boys' average score in a test is 70, and the girls' average score is 80. There are 12 boys in the class. Find the average score of the whole class.
Show the worked solution
3 units = 12 boys, so 1 unit = 4. Girls = 2 units = 8.
Total of boys' scores = 70 × 12 = 840. Total of girls' scores = 80 × 8 = 640.
Combined total = 840 + 640 = 1480, over 12 + 8 = 20 pupils.
Class average = 1480 ÷ 20 = 74.
Check: 74 sits between 70 and 80, closer to 70 — correct, since there are more boys than girls. ✓
PSLE challenge: finding how many numbers there were
The average of a set of numbers is 18. When a new number, 30, is added to the set, the average becomes 20. How many numbers were in the set originally?
Show the worked solution
Let the original count be n. Original total = 18n. After adding 30, the total is 18n + 30, shared among (n + 1) numbers, averaging 20.
18n + 30 = 20 × (n + 1) = 20n + 20.
30 − 20 = 20n − 18n, so 10 = 2n, and n = 5.
Check: 5 numbers averaging 18 have a total of 90. Adding 30 gives 120 over 6 numbers: 120 ÷ 6 = 20. ✓
How to practise this topic
Because average is now learned in the PSLE year, there's no year of exposure to fall back on — treat "total = average × number of items" as the one formula worth over-learning, since every variant of this topic is a different route back to it. The "before-after" structure here (a value added, removed, or a target average to reach) is the same reasoning skill tested more broadly under PSLE problem-solving, so strength in one supports the other. When arithmetic with the totals gets messy, check the working against P6 Fractions division skills — most average questions end in a division step.
Source: MOE 2021 Primary Mathematics Syllabus (P1 to P6).
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 6 Average includes the concepts below. (P6-M-13 is Test Paper's own topic code, not an MOE reference.)
- Concept of average (mean)
- Finding the average of a set of data
- Finding total from average
- Finding a missing value given the average
- Average word problems
Where to go next
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