Why can a total be recovered from an average?

Because average = total ÷ count, so total = average × count — knowing both gives the total back.

Must every value be added again after one is corrected?

No. Subtract the old value and add the new one to the old total, then divide by the count.

Primary 6 Maths: Averages and Line Graphs — Practice Paper 3 (10 Questions)

2026-10-29

Paper 3 works backwards and forwards: a total from an average, a missing number from a total, a new average after adding a value or correcting a wrong one, and comparing two stretches of a line graph.

Quick answer　Ten questions, about 20 minutes. Items 01 to 04 find an average, a total and a difference read off a graph; items 05 to 07 recover a missing number, a new average after adding a value and the difference between two averages; items 08 and 09 correct a wrong value and find the score needed; item 10 redoes adding without dividing.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	20 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: Primary 6 Maths: Averages and Line Graphs — Tutor Lesson Plan
Level	Primary 6

02　Questions (10 items)

FoundationFour numbers are 12, 15, 18 and 15. What is their average?
FoundationKen reads 8, 12, 10, 14 and 6 pages in five days. What is the daily average?
FoundationSix numbers have an average of 24. What is their total?
FoundationOn a line graph January reads 30 books and March reads 45 books. How many more books in March?
IntermediateFive numbers have an average of 18. Four of them are 15, 20, 16 and 19. Find the fifth.
IntermediateThree numbers average 20. After adding 40, what is the new average?
IntermediateA line graph shows sales of 20, 30 and 40 in the first three months, then 40, 50 and 60. What is the difference between the two averages?
ChallengeEight numbers average 15. One of them, 20, was wrongly recorded as 4. What is the corrected average?
ChallengeFour tests average 72 marks. What must the fifth test score be so that the average becomes 75?
Error redoA student averages 10, 20 and 30 and writes “10 + 20 + 30 = 60, so the average is 60”. What is the correct answer?

03　Answers and one-line notes

#	Answer	One-line note
1	The total is 60, so the average is 15	Average = total ÷ count = 60 ÷ 4 = 15.
2	The total is 50 pages, so the average is 10 pages	Five days give 50 pages in all, and 50 ÷ 5 = 10 pages a day.
3	144	Total = average × count = 24 × 6 = 144.
4	15 more books	Increase = 45 − 30 = 15 books.
5	The total is 90; minus 70 the fifth number is 20	Total = 18 × 5 = 90, so the fifth number is 90 − 70 = 20.
6	The new total is 100, so the new average is 25	The old total is 60; add 40 to get 100 and divide by 4.
7	The first average is 30 and the second 50, a difference of 20 items	First (20 + 30 + 40) ÷ 3 = 30 and second (40 + 50 + 60) ÷ 3 = 50, a difference of 20.
8	The corrected total is 104, so the average is 13	The total was 120; subtract 20 and add 4 to get 104, then divide by 8.
9	87 marks	Four tests total 288; five tests need 375, so the fifth must be 375 − 288 = 87.
10	The average is 20; the adding was done but never divided by the count	60 is the total; divide by 3 to get 20. Always add first, then divide.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.