P6 Maths: Median, Mode And Mean (Paper 3 (challenge))

P6 Maths: Median, Mode and Mean (Paper 3 (challenge))

2026-11-15

Tutor Prep Guide · Ordering for the median, averaging the middle two for an even count, modes and multiple modes, the mean and rebuilding totals, and how the three measures differ under extreme values

P6 Maths: Median, Mode and Mean (Paper 3 (challenge))

Paper 3 (challenge): ten questions on median, mode and mean, covering ordering for the median, identifying modes and computing means, with answers and one-line notes.

Direct answers　Level: P6 maths; format: median and ordering, mode and multiple modes, mean and rebuilding totals, comparing the three measures and the effect of extreme values.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P6 Maths: Median, Mode and Mean
Level	P6

02　Questions (10 items)

FoundationFind the median of 12, 15, 18, 20, 22, 25, 28, 30, 35 and 40.
FoundationSeven numbers have a mean of 15 and six of them add to 88; find the remaining number.
FoundationFind the median of 2, 4, 6, 8, 9, 11 and 13.
IntermediateFour numbers 4, 7, 13 and x have a median of 10; find x.
IntermediateTwenty-one numbers are arranged in order; which position holds the median?
IntermediateFive numbers average 12; after two more numbers are added the seven average 14; find the total of the two new numbers.
ChallengeFor the data 1, 2, 3, 4 and 100, by how much does the mean exceed the median?
ChallengeThe data 6, 6, 9 and 9 gain one more 6; find the new mode.
ChallengeSix numbers 3, 6, 8, x, 15 and 18 have a median of 9.5; find x.
Error redoError clinic: the data 2, 3, 3, 4, 8 and 9 have a mode of 3, and a student answered 3 as the median too. Find the correct median.

03　Answers and one-line notes

#	Answer	One-line note
1	23.5	For ten values the fifth and sixth, 22 and 25, average to 23.5.
2	17	The total 105 minus 88 leaves 17.
3	8	There are seven values, so the fourth, 8, is the median.
4	13	The median averages the middle two, so 7 and x average to 10, giving x equal to 13.
5	11th	For an odd count the median sits at position 21 plus 1 over 2, which is 11.
6	38	The old total is 60 and the new total 98, so the two new numbers add to 38.
7	19	The mean is 110 over 5, which is 22, while the median is 3, a difference of 19.
8	6	After the addition 6 appears three times while 9 appears twice.
9	11	The middle two are 8 and x, and 8 plus 11 is 19, which averages to 9.5.
10	3.5	The median averages the middle two values 3 and 4, giving 3.5.

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.

Check the answers, and for any wrong item confirm the data were ordered before the median was taken.Tutor Registration →

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.