Improve Tuition · GCSE Maths · Grade 2 · 100-question paper
Lesson · Averages · Grade 2 lock

Averages — 100 Questions

Five bands, easy to hardest, all within Grade 2.

100 marks · 5 sections · grade-locked (no Grade 2+ techniques required)

Name:Date:Score: / 100
Grade-locked: every question uses the six averages facts (mean, median, mode, range, even-count medians, mode edge cases). No frequency tables, no grouped data, no quartiles.
Band A
Section — Find the mean
Small sets, whole number answers
Q1.Find the mean of 4, 6, 8, 10, 12.
4681012Sum = 4 + 6 + 8 + 10 + 12 = 40Mean = 40 ÷ 5 = 8
(1 mark)
  1. Read it. Find the mean of 4, 6, 8, 10, 12.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 40. Count = 5.
  4. Do the maths. 40 ÷ 5 = 8.
  5. Answer. 8
Answer: 8
Watch outAdd all values, then divide by the count.
Q2.Find the mean of 2, 5, 7, 6, 5.
25765Sum = 2 + 5 + 7 + 6 + 5 = 25Mean = 25 ÷ 5 = 5
(1 mark)
  1. Read it. Find the mean of 2, 5, 7, 6, 5.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 25. Count = 5.
  4. Do the maths. 25 ÷ 5 = 5.
  5. Answer. 5
Answer: 5
Watch outAdd all values, then divide by the count.
Q3.Find the mean of 10, 20, 30.
102030Sum = 10 + 20 + 30 = 60Mean = 60 ÷ 3 = 20
(1 mark)
  1. Read it. Find the mean of 10, 20, 30.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 60. Count = 3.
  4. Do the maths. 60 ÷ 3 = 20.
  5. Answer. 20
Answer: 20
Watch outAdd all values, then divide by the count.
Q4.Find the mean of 1, 3, 4, 8.
1348Sum = 1 + 3 + 4 + 8 = 16Mean = 16 ÷ 4 = 4
(1 mark)
  1. Read it. Find the mean of 1, 3, 4, 8.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 16. Count = 4.
  4. Do the maths. 16 ÷ 4 = 4.
  5. Answer. 4
Answer: 4
Watch outAdd all values, then divide by the count.
Q5.Find the mean of 7, 9, 11, 13.
791113Sum = 7 + 9 + 11 + 13 = 40Mean = 40 ÷ 4 = 10
(1 mark)
  1. Read it. Find the mean of 7, 9, 11, 13.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 40. Count = 4.
  4. Do the maths. 40 ÷ 4 = 10.
  5. Answer. 10
Answer: 10
Watch outAdd all values, then divide by the count.
Q6.Find the mean of 3, 6, 9.
369Sum = 3 + 6 + 9 = 18Mean = 18 ÷ 3 = 6
(1 mark)
  1. Read it. Find the mean of 3, 6, 9.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 18. Count = 3.
  4. Do the maths. 18 ÷ 3 = 6.
  5. Answer. 6
Answer: 6
Watch outAdd all values, then divide by the count.
Q7.Find the mean of 5, 5, 5, 5.
5555Sum = 5 + 5 + 5 + 5 = 20Mean = 20 ÷ 4 = 5
(1 mark)
  1. Read it. Find the mean of 5, 5, 5, 5.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 20. Count = 4.
  4. Do the maths. 20 ÷ 4 = 5.
  5. Answer. 5
Answer: 5
Watch outAdd all values, then divide by the count.
Q8.Find the mean of 2, 4, 6, 8, 10.
246810Sum = 2 + 4 + 6 + 8 + 10 = 30Mean = 30 ÷ 5 = 6
(1 mark)
  1. Read it. Find the mean of 2, 4, 6, 8, 10.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 30. Count = 5.
  4. Do the maths. 30 ÷ 5 = 6.
  5. Answer. 6
Answer: 6
Watch outAdd all values, then divide by the count.
Q9.Find the mean of 1, 5, 9.
159Sum = 1 + 5 + 9 = 15Mean = 15 ÷ 3 = 5
(1 mark)
  1. Read it. Find the mean of 1, 5, 9.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 15. Count = 3.
  4. Do the maths. 15 ÷ 3 = 5.
  5. Answer. 5
Answer: 5
Watch outAdd all values, then divide by the count.
Q10.Find the mean of 10, 12, 14, 16.
10121416Sum = 10 + 12 + 14 + 16 = 52Mean = 52 ÷ 4 = 13
(1 mark)
  1. Read it. Find the mean of 10, 12, 14, 16.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 52. Count = 4.
  4. Do the maths. 52 ÷ 4 = 13.
  5. Answer. 13
Answer: 13
Watch outAdd all values, then divide by the count.
Q11.Find the mean of 15, 20, 25.
152025Sum = 15 + 20 + 25 = 60Mean = 60 ÷ 3 = 20
(1 mark)
  1. Read it. Find the mean of 15, 20, 25.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 60. Count = 3.
  4. Do the maths. 60 ÷ 3 = 20.
  5. Answer. 20
Answer: 20
Watch outAdd all values, then divide by the count.
Q12.Find the mean of 8, 12, 16.
81216Sum = 8 + 12 + 16 = 36Mean = 36 ÷ 3 = 12
(1 mark)
  1. Read it. Find the mean of 8, 12, 16.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 36. Count = 3.
  4. Do the maths. 36 ÷ 3 = 12.
  5. Answer. 12
Answer: 12
Watch outAdd all values, then divide by the count.
Q13.Find the mean of 3, 5, 7, 9, 11.
357911Sum = 3 + 5 + 7 + 9 + 11 = 35Mean = 35 ÷ 5 = 7
(1 mark)
  1. Read it. Find the mean of 3, 5, 7, 9, 11.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 35. Count = 5.
  4. Do the maths. 35 ÷ 5 = 7.
  5. Answer. 7
Answer: 7
Watch outAdd all values, then divide by the count.
Q14.Find the mean of 6, 10, 14.
61014Sum = 6 + 10 + 14 = 30Mean = 30 ÷ 3 = 10
(1 mark)
  1. Read it. Find the mean of 6, 10, 14.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 30. Count = 3.
  4. Do the maths. 30 ÷ 3 = 10.
  5. Answer. 10
Answer: 10
Watch outAdd all values, then divide by the count.
Q15.Find the mean of 1, 2, 3, 4, 5.
12345Sum = 1 + 2 + 3 + 4 + 5 = 15Mean = 15 ÷ 5 = 3
(1 mark)
  1. Read it. Find the mean of 1, 2, 3, 4, 5.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 15. Count = 5.
  4. Do the maths. 15 ÷ 5 = 3.
  5. Answer. 3
Answer: 3
Watch outAdd all values, then divide by the count.
Q16.Find the mean of 20, 30, 40, 50.
20304050Sum = 20 + 30 + 40 + 50 = 140Mean = 140 ÷ 4 = 35
(1 mark)
  1. Read it. Find the mean of 20, 30, 40, 50.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 140. Count = 4.
  4. Do the maths. 140 ÷ 4 = 35.
  5. Answer. 35
Answer: 35
Watch outAdd all values, then divide by the count.
Q17.Find the mean of 11, 13, 15.
111315Sum = 11 + 13 + 15 = 39Mean = 39 ÷ 3 = 13
(1 mark)
  1. Read it. Find the mean of 11, 13, 15.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 39. Count = 3.
  4. Do the maths. 39 ÷ 3 = 13.
  5. Answer. 13
Answer: 13
Watch outAdd all values, then divide by the count.
Q18.Find the mean of 4, 8, 12, 16.
481216Sum = 4 + 8 + 12 + 16 = 40Mean = 40 ÷ 4 = 10
(1 mark)
  1. Read it. Find the mean of 4, 8, 12, 16.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 40. Count = 4.
  4. Do the maths. 40 ÷ 4 = 10.
  5. Answer. 10
Answer: 10
Watch outAdd all values, then divide by the count.
Q19.Find the mean of 5, 10, 15, 20, 25.
510152025Sum = 5 + 10 + 15 + 20 + 25 = 75Mean = 75 ÷ 5 = 15
(1 mark)
  1. Read it. Find the mean of 5, 10, 15, 20, 25.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 75. Count = 5.
  4. Do the maths. 75 ÷ 5 = 15.
  5. Answer. 15
Answer: 15
Watch outAdd all values, then divide by the count.
Q20.Find the mean of 7, 14, 21.
71421Sum = 7 + 14 + 21 = 42Mean = 42 ÷ 3 = 14
(1 mark)
  1. Read it. Find the mean of 7, 14, 21.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 42. Count = 3.
  4. Do the maths. 42 ÷ 3 = 14.
  5. Answer. 14
Answer: 14
Watch outAdd all values, then divide by the count.
Band B
Section — Find the median
Odd and even counts
Q21.Find the median of 3, 7, 4, 9, 5.
Original:37495sortSorted:34579↑ median
(1 mark)
  1. Read it. Find the median of 3, 7, 4, 9, 5.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 5 values. Odd count.
  4. Do the maths. Sort: 3, 4, 5, 7, 9. Middle value = 5.
  5. Answer. 5
Answer: 5
Watch outALWAYS sort first.
Q22.Find the median of 8, 3, 6, 1, 5.
Original:83615sortSorted:13568↑ median
(1 mark)
  1. Read it. Find the median of 8, 3, 6, 1, 5.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 5 values. Odd count.
  4. Do the maths. Sort: 1, 3, 5, 6, 8. Middle value = 5.
  5. Answer. 5
Answer: 5
Watch outALWAYS sort first.
Q23.Find the median of 4, 9, 2, 7, 5.
Original:49275sortSorted:24579↑ median
(1 mark)
  1. Read it. Find the median of 4, 9, 2, 7, 5.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 5 values. Odd count.
  4. Do the maths. Sort: 2, 4, 5, 7, 9. Middle value = 5.
  5. Answer. 5
Answer: 5
Watch outALWAYS sort first.
Q24.Find the median of 10, 15, 5, 20, 12.
Original:101552012sortSorted:510121520↑ median
(1 mark)
  1. Read it. Find the median of 10, 15, 5, 20, 12.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 5 values. Odd count.
  4. Do the maths. Sort: 5, 10, 12, 15, 20. Middle value = 12.
  5. Answer. 12
Answer: 12
Watch outALWAYS sort first.
Q25.Find the median of 12, 8, 15, 7, 20, 10, 18.
Original:128157201018sortSorted:781012151820↑ median
(1 mark)
  1. Read it. Find the median of 12, 8, 15, 7, 20, 10, 18.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 7 values. Odd count.
  4. Do the maths. Sort: 7, 8, 10, 12, 15, 18, 20. Middle value = 12.
  5. Answer. 12
Answer: 12
Watch outALWAYS sort first.
Q26.Find the median of 2, 6, 4, 8.
Original:2648sortSorted:2468↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 2, 6, 4, 8.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 4 values. Even count.
  4. Do the maths. Sort: 2, 4, 6, 8. Two middles: 4 and 6. Median = (4 + 6) ÷ 2 = 5.
  5. Answer. 5
Answer: 5
Watch outALWAYS sort first.
Q27.Find the median of 1, 3, 5, 7.
Original:1357sortSorted:1357↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 1, 3, 5, 7.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 4 values. Even count.
  4. Do the maths. Sort: 1, 3, 5, 7. Two middles: 3 and 5. Median = (3 + 5) ÷ 2 = 4.
  5. Answer. 4
Answer: 4
Watch outALWAYS sort first.
Q28.Find the median of 10, 20, 30, 40.
Original:10203040sortSorted:10203040↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 10, 20, 30, 40.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 4 values. Even count.
  4. Do the maths. Sort: 10, 20, 30, 40. Two middles: 20 and 30. Median = (20 + 30) ÷ 2 = 25.
  5. Answer. 25
Answer: 25
Watch outALWAYS sort first.
Q29.Find the median of 6, 2, 8, 4.
Original:6284sortSorted:2468↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 6, 2, 8, 4.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 4 values. Even count.
  4. Do the maths. Sort: 2, 4, 6, 8. Two middles: 4 and 6. Median = (4 + 6) ÷ 2 = 5.
  5. Answer. 5
Answer: 5
Watch outALWAYS sort first.
Q30.Find the median of 5, 10, 15, 20, 25, 30.
Original:51015202530sortSorted:51015202530↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 5, 10, 15, 20, 25, 30.
  2. The fact. Median = middle value after sorting.
  3. The numbers. 6 values. Even count.
  4. Do the maths. Sort: 5, 10, 15, 20, 25, 30. Two middles: 15 and 20. Median = (15 + 20) ÷ 2 = 17.5.
  5. Answer. 17.5
Answer: 17.5
Watch outALWAYS sort first.
Band B
Section — Mean without diagrams
Some answers are decimals
Q31.Find the mean of 3, 5, 8, 4.
(1 mark)
  1. Read it. Find the mean of 3, 5, 8, 4.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 20. Count = 4.
  4. Do the maths. 20 ÷ 4 = 5.
  5. Answer. 5
Answer: 5
Watch outThe mean can be a decimal.
Q32.Find the mean of 7, 12, 5, 9, 7.
(1 mark)
  1. Read it. Find the mean of 7, 12, 5, 9, 7.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 40. Count = 5.
  4. Do the maths. 40 ÷ 5 = 8.
  5. Answer. 8
Answer: 8
Watch outThe mean can be a decimal.
Q33.Find the mean of 2, 3, 5, 8, 12.
(1 mark)
  1. Read it. Find the mean of 2, 3, 5, 8, 12.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 30. Count = 5.
  4. Do the maths. 30 ÷ 5 = 6.
  5. Answer. 6
Answer: 6
Watch outThe mean can be a decimal.
Q34.Find the mean of 11, 15, 13, 9.
(1 mark)
  1. Read it. Find the mean of 11, 15, 13, 9.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 48. Count = 4.
  4. Do the maths. 48 ÷ 4 = 12.
  5. Answer. 12
Answer: 12
Watch outThe mean can be a decimal.
Q35.Find the mean of 4, 6, 8, 10.
(1 mark)
  1. Read it. Find the mean of 4, 6, 8, 10.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 28. Count = 4.
  4. Do the maths. 28 ÷ 4 = 7.
  5. Answer. 7
Answer: 7
Watch outThe mean can be a decimal.
Q36.Find the mean of 1, 4, 5, 6.
(1 mark)
  1. Read it. Find the mean of 1, 4, 5, 6.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 16. Count = 4.
  4. Do the maths. 16 ÷ 4 = 4.
  5. Answer. 4
Answer: 4
Watch outThe mean can be a decimal.
Q37.Find the mean of 5, 8, 12.
(1 mark)
  1. Read it. Find the mean of 5, 8, 12.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 25. Count = 3.
  4. Do the maths. 25 ÷ 3 = 8.333.
  5. Answer. 8.333
Answer: 8.333
Watch outThe mean can be a decimal.
Q38.Find the mean of 6, 9, 12, 15.
(1 mark)
  1. Read it. Find the mean of 6, 9, 12, 15.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 42. Count = 4.
  4. Do the maths. 42 ÷ 4 = 10.5.
  5. Answer. 10.5
Answer: 10.5
Watch outThe mean can be a decimal.
Q39.Find the mean of 3, 7, 5, 8, 2.
(1 mark)
  1. Read it. Find the mean of 3, 7, 5, 8, 2.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 25. Count = 5.
  4. Do the maths. 25 ÷ 5 = 5.
  5. Answer. 5
Answer: 5
Watch outThe mean can be a decimal.
Q40.Find the mean of 10, 14, 18, 22, 26.
(1 mark)
  1. Read it. Find the mean of 10, 14, 18, 22, 26.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. Sum = 90. Count = 5.
  4. Do the maths. 90 ÷ 5 = 18.
  5. Answer. 18
Answer: 18
Watch outThe mean can be a decimal.
Band C
Section — Mixed measures
Mean, median, mode and range
Q41.Find the mean of 4, 8, 12.
(1 mark)
  1. Read it. Find the mean of 4, 8, 12.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 4, 8, 12
  4. Do the maths. Sum = 24, count = 3. 24 ÷ 3 = 8.
  5. Answer. 8
Answer: 8
Watch outUse the mean rule.
Q42.Find the mean of 3, 5, 7, 9.
(1 mark)
  1. Read it. Find the mean of 3, 5, 7, 9.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 3, 5, 7, 9
  4. Do the maths. Sum = 24, count = 4. 24 ÷ 4 = 6.
  5. Answer. 6
Answer: 6
Watch outUse the mean rule.
Q43.Find the mean of 10, 20, 30, 40, 50.
(1 mark)
  1. Read it. Find the mean of 10, 20, 30, 40, 50.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 10, 20, 30, 40, 50
  4. Do the maths. Sum = 150, count = 5. 150 ÷ 5 = 30.
  5. Answer. 30
Answer: 30
Watch outUse the mean rule.
Q44.Find the mean of 2, 4, 6, 8.
(1 mark)
  1. Read it. Find the mean of 2, 4, 6, 8.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 2, 4, 6, 8
  4. Do the maths. Sum = 20, count = 4. 20 ÷ 4 = 5.
  5. Answer. 5
Answer: 5
Watch outUse the mean rule.
Q45.Find the mean of 6, 10, 14, 18.
(1 mark)
  1. Read it. Find the mean of 6, 10, 14, 18.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 6, 10, 14, 18
  4. Do the maths. Sum = 48, count = 4. 48 ÷ 4 = 12.
  5. Answer. 12
Answer: 12
Watch outUse the mean rule.
Q46.Find the median of 4, 1, 3, 5, 2.
(1 mark)
  1. Read it. Find the median of 4, 1, 3, 5, 2.
  2. The fact. Sort then take middle (odd) or mean of two middles (even).
  3. The numbers. 4, 1, 3, 5, 2
  4. Do the maths. Sort: 1, 2, 3, 4, 5. Middle = 3.
  5. Answer. 3
Answer: 3
Watch outUse the median rule.
Q47.Find the median of 7, 12, 3, 8, 5.
(1 mark)
  1. Read it. Find the median of 7, 12, 3, 8, 5.
  2. The fact. Sort then take middle (odd) or mean of two middles (even).
  3. The numbers. 7, 12, 3, 8, 5
  4. Do the maths. Sort: 3, 5, 7, 8, 12. Middle = 7.
  5. Answer. 7
Answer: 7
Watch outUse the median rule.
Q48.Find the median of 1, 3, 5, 7.
(1 mark)
  1. Read it. Find the median of 1, 3, 5, 7.
  2. The fact. Sort then take middle (odd) or mean of two middles (even).
  3. The numbers. 1, 3, 5, 7
  4. Do the maths. Sort: 1, 3, 5, 7. Mean of two middles (3, 5) = 4.
  5. Answer. 4
Answer: 4
Watch outUse the median rule.
Q49.Find the median of 10, 20, 30, 40.
(1 mark)
  1. Read it. Find the median of 10, 20, 30, 40.
  2. The fact. Sort then take middle (odd) or mean of two middles (even).
  3. The numbers. 10, 20, 30, 40
  4. Do the maths. Sort: 10, 20, 30, 40. Mean of two middles (20, 30) = 25.
  5. Answer. 25
Answer: 25
Watch outUse the median rule.
Q50.Find the median of 8, 3, 10, 5, 12.
(1 mark)
  1. Read it. Find the median of 8, 3, 10, 5, 12.
  2. The fact. Sort then take middle (odd) or mean of two middles (even).
  3. The numbers. 8, 3, 10, 5, 12
  4. Do the maths. Sort: 3, 5, 8, 10, 12. Middle = 8.
  5. Answer. 8
Answer: 8
Watch outUse the median rule.
Q51.Find the mode of 2, 4, 4, 6, 8.
(1 mark)
  1. Read it. Find the mode of 2, 4, 4, 6, 8.
  2. The fact. Mode = most common value.
  3. The numbers. 2, 4, 4, 6, 8
  4. Do the maths. Count each value; most common is 4.
  5. Answer. 4
Answer: 4
Watch outUse the mode rule.
Q52.Find the mode of 5, 7, 7, 7, 9.
(1 mark)
  1. Read it. Find the mode of 5, 7, 7, 7, 9.
  2. The fact. Mode = most common value.
  3. The numbers. 5, 7, 7, 7, 9
  4. Do the maths. Count each value; most common is 7.
  5. Answer. 7
Answer: 7
Watch outUse the mode rule.
Q53.Find the mode of 1, 3, 3, 5, 5, 5, 7.
(1 mark)
  1. Read it. Find the mode of 1, 3, 3, 5, 5, 5, 7.
  2. The fact. Mode = most common value.
  3. The numbers. 1, 3, 3, 5, 5, 5, 7
  4. Do the maths. Count each value; most common is 5.
  5. Answer. 5
Answer: 5
Watch outUse the mode rule.
Q54.Find the mode of 2, 6, 6, 6, 8, 10.
(1 mark)
  1. Read it. Find the mode of 2, 6, 6, 6, 8, 10.
  2. The fact. Mode = most common value.
  3. The numbers. 2, 6, 6, 6, 8, 10
  4. Do the maths. Count each value; most common is 6.
  5. Answer. 6
Answer: 6
Watch outUse the mode rule.
Q55.Find the mode of 4, 4, 7, 9, 12.
(1 mark)
  1. Read it. Find the mode of 4, 4, 7, 9, 12.
  2. The fact. Mode = most common value.
  3. The numbers. 4, 4, 7, 9, 12
  4. Do the maths. Count each value; most common is 4.
  5. Answer. 4
Answer: 4
Watch outUse the mode rule.
Q56.Find the range of 3, 7, 1, 5, 9.
(1 mark)
  1. Read it. Find the range of 3, 7, 1, 5, 9.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 3, 7, 1, 5, 9
  4. Do the maths. Biggest = 9, smallest = 1. 9 - 1 = 8.
  5. Answer. 8
Answer: 8
Watch outUse the range rule.
Q57.Find the range of 12, 20, 5, 15, 8.
(1 mark)
  1. Read it. Find the range of 12, 20, 5, 15, 8.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 12, 20, 5, 15, 8
  4. Do the maths. Biggest = 20, smallest = 5. 20 - 5 = 15.
  5. Answer. 15
Answer: 15
Watch outUse the range rule.
Q58.Find the range of 4, 4, 4, 10.
(1 mark)
  1. Read it. Find the range of 4, 4, 4, 10.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 4, 4, 4, 10
  4. Do the maths. Biggest = 10, smallest = 4. 10 - 4 = 6.
  5. Answer. 6
Answer: 6
Watch outUse the range rule.
Q59.Find the range of 25, 45, 15, 35, 55.
(1 mark)
  1. Read it. Find the range of 25, 45, 15, 35, 55.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 25, 45, 15, 35, 55
  4. Do the maths. Biggest = 55, smallest = 15. 55 - 15 = 40.
  5. Answer. 40
Answer: 40
Watch outUse the range rule.
Q60.Find the range of 2, 8, 6, 4, 10.
(1 mark)
  1. Read it. Find the range of 2, 8, 6, 4, 10.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 2, 8, 6, 4, 10
  4. Do the maths. Biggest = 10, smallest = 2. 10 - 2 = 8.
  5. Answer. 8
Answer: 8
Watch outUse the range rule.
Band D
Section — Mode and range with dot plots
Read the visual
Q61.Find the mode of 2, 5, 3, 5, 8, 5, 6.
23568
(1 mark)
  1. Read it. Find the mode of 2, 5, 3, 5, 8, 5, 6.
  2. The fact. Mode = value with tallest column of dots.
  3. The numbers. 2, 5, 3, 5, 8, 5, 6
  4. Do the maths. Most common value: 5.
  5. Answer. 5
Answer: 5
Watch outLook for the tallest stack.
Q62.Find the mode of 1, 4, 4, 4, 7, 9.
1479
(1 mark)
  1. Read it. Find the mode of 1, 4, 4, 4, 7, 9.
  2. The fact. Mode = value with tallest column of dots.
  3. The numbers. 1, 4, 4, 4, 7, 9
  4. Do the maths. Most common value: 4.
  5. Answer. 4
Answer: 4
Watch outLook for the tallest stack.
Q63.Find the mode of 3, 6, 6, 9, 6, 12.
36912
(1 mark)
  1. Read it. Find the mode of 3, 6, 6, 9, 6, 12.
  2. The fact. Mode = value with tallest column of dots.
  3. The numbers. 3, 6, 6, 9, 6, 12
  4. Do the maths. Most common value: 6.
  5. Answer. 6
Answer: 6
Watch outLook for the tallest stack.
Q64.Find the mode of 8, 8, 11, 15, 8, 20.
8111520
(1 mark)
  1. Read it. Find the mode of 8, 8, 11, 15, 8, 20.
  2. The fact. Mode = value with tallest column of dots.
  3. The numbers. 8, 8, 11, 15, 8, 20
  4. Do the maths. Most common value: 8.
  5. Answer. 8
Answer: 8
Watch outLook for the tallest stack.
Q65.Find the mode of 2, 7, 2, 5, 2, 9.
2579
(1 mark)
  1. Read it. Find the mode of 2, 7, 2, 5, 2, 9.
  2. The fact. Mode = value with tallest column of dots.
  3. The numbers. 2, 7, 2, 5, 2, 9
  4. Do the maths. Most common value: 2.
  5. Answer. 2
Answer: 2
Watch outLook for the tallest stack.
Q66.Find the range of 12, 5, 18, 8, 15.
58121518range = 13
(1 mark)
  1. Read it. Find the range of 12, 5, 18, 8, 15.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 12, 5, 18, 8, 15
  4. Do the maths. Biggest = 18. Smallest = 5. Range = 18 - 5 = 13.
  5. Answer. 13
Answer: 13
Watch outRange is measured across the dot plot.
Q67.Find the range of 3, 15, 8, 22, 6.
3681522range = 19
(1 mark)
  1. Read it. Find the range of 3, 15, 8, 22, 6.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 3, 15, 8, 22, 6
  4. Do the maths. Biggest = 22. Smallest = 3. Range = 22 - 3 = 19.
  5. Answer. 19
Answer: 19
Watch outRange is measured across the dot plot.
Q68.Find the range of 4, 4, 4, 10, 12, 8.
481012range = 8
(1 mark)
  1. Read it. Find the range of 4, 4, 4, 10, 12, 8.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 4, 4, 4, 10, 12, 8
  4. Do the maths. Biggest = 12. Smallest = 4. Range = 12 - 4 = 8.
  5. Answer. 8
Answer: 8
Watch outRange is measured across the dot plot.
Q69.Find the range of 7, 14, 21, 28.
7142128range = 21
(1 mark)
  1. Read it. Find the range of 7, 14, 21, 28.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 7, 14, 21, 28
  4. Do the maths. Biggest = 28. Smallest = 7. Range = 28 - 7 = 21.
  5. Answer. 21
Answer: 21
Watch outRange is measured across the dot plot.
Q70.Find the range of 2, 5, 8, 11, 14.
2581114range = 12
(1 mark)
  1. Read it. Find the range of 2, 5, 8, 11, 14.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 2, 5, 8, 11, 14
  4. Do the maths. Biggest = 14. Smallest = 2. Range = 14 - 2 = 12.
  5. Answer. 12
Answer: 12
Watch outRange is measured across the dot plot.
Band D
Section — Median without diagrams
Sort in your head
Q71.Find the median of 3, 1, 5.
(1 mark)
  1. Read it. Find the median of 3, 1, 5.
  2. The fact. Sort then pick middle.
  3. The numbers. 3 values.
  4. Do the maths. Sort: 1, 3, 5. Middle = 3.
  5. Answer. 3
Answer: 3
Watch outAlways sort before picking middle.
Q72.Find the median of 10, 2, 6, 4, 8.
(1 mark)
  1. Read it. Find the median of 10, 2, 6, 4, 8.
  2. The fact. Sort then pick middle.
  3. The numbers. 5 values.
  4. Do the maths. Sort: 2, 4, 6, 8, 10. Middle = 6.
  5. Answer. 6
Answer: 6
Watch outAlways sort before picking middle.
Q73.Find the median of 15, 5, 25, 10, 20.
(1 mark)
  1. Read it. Find the median of 15, 5, 25, 10, 20.
  2. The fact. Sort then pick middle.
  3. The numbers. 5 values.
  4. Do the maths. Sort: 5, 10, 15, 20, 25. Middle = 15.
  5. Answer. 15
Answer: 15
Watch outAlways sort before picking middle.
Q74.Find the median of 7, 3, 9, 5, 11.
(1 mark)
  1. Read it. Find the median of 7, 3, 9, 5, 11.
  2. The fact. Sort then pick middle.
  3. The numbers. 5 values.
  4. Do the maths. Sort: 3, 5, 7, 9, 11. Middle = 7.
  5. Answer. 7
Answer: 7
Watch outAlways sort before picking middle.
Q75.Find the median of 2, 4, 6, 8, 10, 12, 14.
(1 mark)
  1. Read it. Find the median of 2, 4, 6, 8, 10, 12, 14.
  2. The fact. Sort then pick middle.
  3. The numbers. 7 values.
  4. Do the maths. Sort: 2, 4, 6, 8, 10, 12, 14. Middle = 8.
  5. Answer. 8
Answer: 8
Watch outAlways sort before picking middle.
Q76.Find the median of 1, 3, 5, 7.
(1 mark)
  1. Read it. Find the median of 1, 3, 5, 7.
  2. The fact. Sort then pick middle.
  3. The numbers. 4 values.
  4. Do the maths. Sort: 1, 3, 5, 7. Mean of 3 and 5 = 4.
  5. Answer. 4
Answer: 4
Watch outAlways sort before picking middle.
Q77.Find the median of 10, 20, 30, 40, 50, 60.
(1 mark)
  1. Read it. Find the median of 10, 20, 30, 40, 50, 60.
  2. The fact. Sort then pick middle.
  3. The numbers. 6 values.
  4. Do the maths. Sort: 10, 20, 30, 40, 50, 60. Mean of 30 and 40 = 35.
  5. Answer. 35
Answer: 35
Watch outAlways sort before picking middle.
Q78.Find the median of 4, 8, 12, 16.
(1 mark)
  1. Read it. Find the median of 4, 8, 12, 16.
  2. The fact. Sort then pick middle.
  3. The numbers. 4 values.
  4. Do the maths. Sort: 4, 8, 12, 16. Mean of 8 and 12 = 10.
  5. Answer. 10
Answer: 10
Watch outAlways sort before picking middle.
Q79.Find the median of 3, 5, 7, 9, 11, 13.
(1 mark)
  1. Read it. Find the median of 3, 5, 7, 9, 11, 13.
  2. The fact. Sort then pick middle.
  3. The numbers. 6 values.
  4. Do the maths. Sort: 3, 5, 7, 9, 11, 13. Mean of 7 and 9 = 8.
  5. Answer. 8
Answer: 8
Watch outAlways sort before picking middle.
Q80.Find the median of 2, 4, 6, 8, 10, 12, 14, 16.
(1 mark)
  1. Read it. Find the median of 2, 4, 6, 8, 10, 12, 14, 16.
  2. The fact. Sort then pick middle.
  3. The numbers. 8 values.
  4. Do the maths. Sort: 2, 4, 6, 8, 10, 12, 14, 16. Mean of 8 and 10 = 9.
  5. Answer. 9
Answer: 9
Watch outAlways sort before picking middle.
Band E
Section — Larger sets and tricky answers
Decimal means and bigger data
Q81.Find the mean of 3, 5, 4, 7, 5, 6, 4, 5.
35475645Sum = 3 + 5 + 4 + 7 + 5 + 6 + 4 + 5 = 39Mean = 39 ÷ 8 = 4.875
(1 mark)
  1. Read it. Find the mean of 3, 5, 4, 7, 5, 6, 4, 5.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 3, 5, 4, 7, 5, 6, 4, 5
  4. Do the maths. Sum = 39, count = 8. 39 ÷ 8 = 4.875.
  5. Answer. 4.875
Answer: 4.875
Watch outUse the correct rule for this measure.
Q82.Find the mean of 6, 9, 12, 15, 18.
69121518Sum = 6 + 9 + 12 + 15 + 18 = 60Mean = 60 ÷ 5 = 12
(1 mark)
  1. Read it. Find the mean of 6, 9, 12, 15, 18.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 6, 9, 12, 15, 18
  4. Do the maths. Sum = 60, count = 5. 60 ÷ 5 = 12.
  5. Answer. 12
Answer: 12
Watch outUse the correct rule for this measure.
Q83.Find the mean of 1, 2, 3, 4, 5, 6, 7.
1234567Sum = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28Mean = 28 ÷ 7 = 4
(1 mark)
  1. Read it. Find the mean of 1, 2, 3, 4, 5, 6, 7.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 1, 2, 3, 4, 5, 6, 7
  4. Do the maths. Sum = 28, count = 7. 28 ÷ 7 = 4.
  5. Answer. 4
Answer: 4
Watch outUse the correct rule for this measure.
Q84.Find the mean of 10, 15, 20, 25, 30.
1015202530Sum = 10 + 15 + 20 + 25 + 30 = 100Mean = 100 ÷ 5 = 20
(1 mark)
  1. Read it. Find the mean of 10, 15, 20, 25, 30.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 10, 15, 20, 25, 30
  4. Do the maths. Sum = 100, count = 5. 100 ÷ 5 = 20.
  5. Answer. 20
Answer: 20
Watch outUse the correct rule for this measure.
Q85.Find the mean of 8, 8, 12, 16, 20, 24.
8812162024Sum = 8 + 8 + 12 + 16 + 20 + 24 = 88Mean = 88 ÷ 6 = 14.667
(1 mark)
  1. Read it. Find the mean of 8, 8, 12, 16, 20, 24.
  2. The fact. Mean = sum ÷ count.
  3. The numbers. 8, 8, 12, 16, 20, 24
  4. Do the maths. Sum = 88, count = 6. 88 ÷ 6 = 14.667.
  5. Answer. 14.667
Answer: 14.667
Watch outUse the correct rule for this measure.
Q86.Find the median of 45, 12, 78, 33, 91, 26, 55.
Original:45127833912655sortSorted:12263345557891↑ median
(1 mark)
  1. Read it. Find the median of 45, 12, 78, 33, 91, 26, 55.
  2. The fact. Sort then middle (odd) or mean of two middles (even).
  3. The numbers. 45, 12, 78, 33, 91, 26, 55
  4. Do the maths. Sort: 12, 26, 33, 45, 55, 78, 91. Middle = 45.
  5. Answer. 45
Answer: 45
Watch outUse the correct rule for this measure.
Q87.Find the median of 15, 8, 22, 4, 30, 12, 18, 25.
Original:15822430121825sortSorted:48121518222530↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 15, 8, 22, 4, 30, 12, 18, 25.
  2. The fact. Sort then middle (odd) or mean of two middles (even).
  3. The numbers. 15, 8, 22, 4, 30, 12, 18, 25
  4. Do the maths. Sort: 4, 8, 12, 15, 18, 22, 25, 30. Mean of 15 and 18 = 16.5.
  5. Answer. 16.5
Answer: 16.5
Watch outUse the correct rule for this measure.
Q88.Find the median of 3, 7, 1, 9, 5, 11, 13, 15.
Original:37195111315sortSorted:13579111315↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 3, 7, 1, 9, 5, 11, 13, 15.
  2. The fact. Sort then middle (odd) or mean of two middles (even).
  3. The numbers. 3, 7, 1, 9, 5, 11, 13, 15
  4. Do the maths. Sort: 1, 3, 5, 7, 9, 11, 13, 15. Mean of 7 and 9 = 8.
  5. Answer. 8
Answer: 8
Watch outUse the correct rule for this measure.
Q89.Find the median of 50, 20, 80, 30, 100, 40, 90.
Original:502080301004090sortSorted:203040508090100↑ median
(1 mark)
  1. Read it. Find the median of 50, 20, 80, 30, 100, 40, 90.
  2. The fact. Sort then middle (odd) or mean of two middles (even).
  3. The numbers. 50, 20, 80, 30, 100, 40, 90
  4. Do the maths. Sort: 20, 30, 40, 50, 80, 90, 100. Middle = 50.
  5. Answer. 50
Answer: 50
Watch outUse the correct rule for this measure.
Q90.Find the median of 6, 2, 12, 4, 16, 8, 20, 10.
Original:621241682010sortSorted:246810121620↑ two middles → mean
(1 mark)
  1. Read it. Find the median of 6, 2, 12, 4, 16, 8, 20, 10.
  2. The fact. Sort then middle (odd) or mean of two middles (even).
  3. The numbers. 6, 2, 12, 4, 16, 8, 20, 10
  4. Do the maths. Sort: 2, 4, 6, 8, 10, 12, 16, 20. Mean of 8 and 10 = 9.
  5. Answer. 9
Answer: 9
Watch outUse the correct rule for this measure.
Q91.Find the mode of 12, 15, 18, 15, 21, 15, 24.
1215182124
(1 mark)
  1. Read it. Find the mode of 12, 15, 18, 15, 21, 15, 24.
  2. The fact. Mode = most common value.
  3. The numbers. 12, 15, 18, 15, 21, 15, 24
  4. Do the maths. Count of each value; 15 appears 3 times.
  5. Answer. 15
Answer: 15
Watch outUse the correct rule for this measure.
Q92.Find the mode of 4, 8, 8, 12, 8, 16, 8.
481216
(1 mark)
  1. Read it. Find the mode of 4, 8, 8, 12, 8, 16, 8.
  2. The fact. Mode = most common value.
  3. The numbers. 4, 8, 8, 12, 8, 16, 8
  4. Do the maths. Count of each value; 8 appears 4 times.
  5. Answer. 8
Answer: 8
Watch outUse the correct rule for this measure.
Q93.Find the mode of 3, 7, 3, 11, 3, 15, 3, 19.
37111519
(1 mark)
  1. Read it. Find the mode of 3, 7, 3, 11, 3, 15, 3, 19.
  2. The fact. Mode = most common value.
  3. The numbers. 3, 7, 3, 11, 3, 15, 3, 19
  4. Do the maths. Count of each value; 3 appears 4 times.
  5. Answer. 3
Answer: 3
Watch outUse the correct rule for this measure.
Q94.Find the mode of 22, 22, 25, 30, 22, 40.
22253040
(1 mark)
  1. Read it. Find the mode of 22, 22, 25, 30, 22, 40.
  2. The fact. Mode = most common value.
  3. The numbers. 22, 22, 25, 30, 22, 40
  4. Do the maths. Count of each value; 22 appears 3 times.
  5. Answer. 22
Answer: 22
Watch outUse the correct rule for this measure.
Q95.Find the mode of 5, 10, 10, 15, 20, 10, 25.
510152025
(1 mark)
  1. Read it. Find the mode of 5, 10, 10, 15, 20, 10, 25.
  2. The fact. Mode = most common value.
  3. The numbers. 5, 10, 10, 15, 20, 10, 25
  4. Do the maths. Count of each value; 10 appears 3 times.
  5. Answer. 10
Answer: 10
Watch outUse the correct rule for this measure.
Q96.Find the range of 45, 12, 78, 33, 91, 26.
122633457891range = 79
(1 mark)
  1. Read it. Find the range of 45, 12, 78, 33, 91, 26.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 45, 12, 78, 33, 91, 26
  4. Do the maths. 91 - 12 = 79.
  5. Answer. 79
Answer: 79
Watch outUse the correct rule for this measure.
Q97.Find the range of 100, 250, 50, 300, 150.
50100150250300range = 250
(1 mark)
  1. Read it. Find the range of 100, 250, 50, 300, 150.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 100, 250, 50, 300, 150
  4. Do the maths. 300 - 50 = 250.
  5. Answer. 250
Answer: 250
Watch outUse the correct rule for this measure.
Q98.Find the range of 15, 8, 42, 22, 30, 12.
81215223042range = 34
(1 mark)
  1. Read it. Find the range of 15, 8, 42, 22, 30, 12.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 15, 8, 42, 22, 30, 12
  4. Do the maths. 42 - 8 = 34.
  5. Answer. 34
Answer: 34
Watch outUse the correct rule for this measure.
Q99.Find the range of 7, 3, 22, 18, 11, 5, 25.
35711182225range = 22
(1 mark)
  1. Read it. Find the range of 7, 3, 22, 18, 11, 5, 25.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 7, 3, 22, 18, 11, 5, 25
  4. Do the maths. 25 - 3 = 22.
  5. Answer. 22
Answer: 22
Watch outUse the correct rule for this measure.
Q100.Find the range of 66, 12, 89, 45, 33, 78.
123345667889range = 77
(1 mark)
  1. Read it. Find the range of 66, 12, 89, 45, 33, 78.
  2. The fact. Range = biggest - smallest.
  3. The numbers. 66, 12, 89, 45, 33, 78
  4. Do the maths. 89 - 12 = 77.
  5. Answer. 77
Answer: 77
Watch outUse the correct rule for this measure.

Answer key — all 100

The rule and the working for each question.

QAnswerTypeWorking
Q18mean40 ÷ 5 = 8.
Q25mean25 ÷ 5 = 5.
Q320mean60 ÷ 3 = 20.
Q44mean16 ÷ 4 = 4.
Q510mean40 ÷ 4 = 10.
Q66mean18 ÷ 3 = 6.
Q75mean20 ÷ 4 = 5.
Q86mean30 ÷ 5 = 6.
Q95mean15 ÷ 3 = 5.
Q1013mean52 ÷ 4 = 13.
Q1120mean60 ÷ 3 = 20.
Q1212mean36 ÷ 3 = 12.
Q137mean35 ÷ 5 = 7.
Q1410mean30 ÷ 3 = 10.
Q153mean15 ÷ 5 = 3.
Q1635mean140 ÷ 4 = 35.
Q1713mean39 ÷ 3 = 13.
Q1810mean40 ÷ 4 = 10.
Q1915mean75 ÷ 5 = 15.
Q2014mean42 ÷ 3 = 14.
Q215medianSort: 3, 4, 5, 7, 9. Middle value = 5.
Q225medianSort: 1, 3, 5, 6, 8. Middle value = 5.
Q235medianSort: 2, 4, 5, 7, 9. Middle value = 5.
Q2412medianSort: 5, 10, 12, 15, 20. Middle value = 12.
Q2512medianSort: 7, 8, 10, 12, 15, 18, 20. Middle value = 12.
Q265medianSort: 2, 4, 6, 8. Two middles: 4 and 6. Median = (4 + 6) ÷ 2 = 5.
Q274medianSort: 1, 3, 5, 7. Two middles: 3 and 5. Median = (3 + 5) ÷ 2 = 4.
Q2825medianSort: 10, 20, 30, 40. Two middles: 20 and 30. Median = (20 + 30) ÷ 2 = 25.
Q295medianSort: 2, 4, 6, 8. Two middles: 4 and 6. Median = (4 + 6) ÷ 2 = 5.
Q3017.5medianSort: 5, 10, 15, 20, 25, 30. Two middles: 15 and 20. Median = (15 + 20) ÷ 2 = 17.5.
Q315mean20 ÷ 4 = 5.
Q328mean40 ÷ 5 = 8.
Q336mean30 ÷ 5 = 6.
Q3412mean48 ÷ 4 = 12.
Q357mean28 ÷ 4 = 7.
Q364mean16 ÷ 4 = 4.
Q378.333mean25 ÷ 3 = 8.333.
Q3810.5mean42 ÷ 4 = 10.5.
Q395mean25 ÷ 5 = 5.
Q4018mean90 ÷ 5 = 18.
Q418meanSum = 24, count = 3. 24 ÷ 3 = 8.
Q426meanSum = 24, count = 4. 24 ÷ 4 = 6.
Q4330meanSum = 150, count = 5. 150 ÷ 5 = 30.
Q445meanSum = 20, count = 4. 20 ÷ 4 = 5.
Q4512meanSum = 48, count = 4. 48 ÷ 4 = 12.
Q463medianSort: 1, 2, 3, 4, 5. Middle = 3.
Q477medianSort: 3, 5, 7, 8, 12. Middle = 7.
Q484medianSort: 1, 3, 5, 7. Mean of two middles (3, 5) = 4.
Q4925medianSort: 10, 20, 30, 40. Mean of two middles (20, 30) = 25.
Q508medianSort: 3, 5, 8, 10, 12. Middle = 8.
Q514modeCount each value; most common is 4.
Q527modeCount each value; most common is 7.
Q535modeCount each value; most common is 5.
Q546modeCount each value; most common is 6.
Q554modeCount each value; most common is 4.
Q568rangeBiggest = 9, smallest = 1. 9 - 1 = 8.
Q5715rangeBiggest = 20, smallest = 5. 20 - 5 = 15.
Q586rangeBiggest = 10, smallest = 4. 10 - 4 = 6.
Q5940rangeBiggest = 55, smallest = 15. 55 - 15 = 40.
Q608rangeBiggest = 10, smallest = 2. 10 - 2 = 8.
Q615modeMost common value: 5.
Q624modeMost common value: 4.
Q636modeMost common value: 6.
Q648modeMost common value: 8.
Q652modeMost common value: 2.
Q6613rangeBiggest = 18. Smallest = 5. Range = 18 - 5 = 13.
Q6719rangeBiggest = 22. Smallest = 3. Range = 22 - 3 = 19.
Q688rangeBiggest = 12. Smallest = 4. Range = 12 - 4 = 8.
Q6921rangeBiggest = 28. Smallest = 7. Range = 28 - 7 = 21.
Q7012rangeBiggest = 14. Smallest = 2. Range = 14 - 2 = 12.
Q713medianSort: 1, 3, 5. Middle = 3.
Q726medianSort: 2, 4, 6, 8, 10. Middle = 6.
Q7315medianSort: 5, 10, 15, 20, 25. Middle = 15.
Q747medianSort: 3, 5, 7, 9, 11. Middle = 7.
Q758medianSort: 2, 4, 6, 8, 10, 12, 14. Middle = 8.
Q764medianSort: 1, 3, 5, 7. Mean of 3 and 5 = 4.
Q7735medianSort: 10, 20, 30, 40, 50, 60. Mean of 30 and 40 = 35.
Q7810medianSort: 4, 8, 12, 16. Mean of 8 and 12 = 10.
Q798medianSort: 3, 5, 7, 9, 11, 13. Mean of 7 and 9 = 8.
Q809medianSort: 2, 4, 6, 8, 10, 12, 14, 16. Mean of 8 and 10 = 9.
Q814.875meanSum = 39, count = 8. 39 ÷ 8 = 4.875.
Q8212meanSum = 60, count = 5. 60 ÷ 5 = 12.
Q834meanSum = 28, count = 7. 28 ÷ 7 = 4.
Q8420meanSum = 100, count = 5. 100 ÷ 5 = 20.
Q8514.667meanSum = 88, count = 6. 88 ÷ 6 = 14.667.
Q8645medianSort: 12, 26, 33, 45, 55, 78, 91. Middle = 45.
Q8716.5medianSort: 4, 8, 12, 15, 18, 22, 25, 30. Mean of 15 and 18 = 16.5.
Q888medianSort: 1, 3, 5, 7, 9, 11, 13, 15. Mean of 7 and 9 = 8.
Q8950medianSort: 20, 30, 40, 50, 80, 90, 100. Middle = 50.
Q909medianSort: 2, 4, 6, 8, 10, 12, 16, 20. Mean of 8 and 10 = 9.
Q9115modeCount of each value; 15 appears 3 times.
Q928modeCount of each value; 8 appears 4 times.
Q933modeCount of each value; 3 appears 4 times.
Q9422modeCount of each value; 22 appears 3 times.
Q9510modeCount of each value; 10 appears 3 times.
Q9679range91 - 12 = 79.
Q97250range300 - 50 = 250.
Q9834range42 - 8 = 34.
Q9922range25 - 3 = 22.
Q10077range89 - 12 = 77.
/ 100

Answer key & mark scheme

QAnswerRule usedWorking
Q114Linear sequence: continue by common differenced = +3; 11 + 3 = 14
Q213Linear sequence: continue by common differenced = +2; 11 + 2 = 13
Q317Linear sequence: continue by common differenced = +4; 13 + 4 = 17
Q430Linear sequence: continue by common differenced = +5; 25 + 5 = 30
Q519Linear sequence: continue by common differenced = +3; 16 + 3 = 19
Q628Linear sequence: continue by common differenced = +6; 22 + 6 = 28
Q728Linear sequence: continue by common differenced = +7; 21 + 7 = 28
Q817Linear sequence: continue by common differenced = +2; 15 + 2 = 17
Q935Linear sequence: continue by common differenced = +8; 27 + 8 = 35
Q1024Linear sequence: continue by common differenced = +3; 21 + 3 = 24
Q1122Linear sequence: continue by common differenced = +4; 18 + 4 = 22
Q1235Linear sequence: continue by common differenced = +5; 30 + 5 = 35
Q1336Linear sequence: continue by common differenced = +7; 29 + 7 = 36
Q1438Linear sequence: continue by common differenced = +9; 29 + 9 = 38
Q1527Linear sequence: continue by common differenced = +4; 23 + 4 = 27
Q1623Linear sequence: continue by common differenced = +5; 18 + 5 = 23
Q1732Linear sequence: continue by common differenced = +3; 29 + 3 = 32
Q1838Linear sequence: continue by common differenced = +6; 32 + 6 = 38
Q1933Linear sequence: continue by common differenced = +8; 25 + 8 = 33
Q2014Linear sequence: continue by common differenced = +2; 12 + 2 = 14
Q2190Linear sequence: continue by common differenced = +10; 80 + 10 = 90
Q2280Linear sequence: continue by common differenced = -5; 85 − 5 = 80
Q2348Linear sequence: continue by common differenced = +7; 41 + 7 = 48
Q2414Linear sequence: continue by common differenced = -4; 18 − 4 = 14
Q25105Linear sequence: continue by common differenced = +15; 90 + 15 = 105
Q2652Linear sequence: continue by common differenced = +11; 41 + 11 = 52
Q2732Linear sequence: continue by common differenced = -7; 39 − 7 = 32
Q2849Linear sequence: continue by common differenced = +9; 40 + 9 = 49
Q2948Linear sequence: continue by common differenced = -8; 56 − 8 = 48
Q3073Linear sequence: continue by common differenced = +12; 61 + 12 = 73
Q3131Linear sequence: find term by extendinga₁ = 4, d = +3; term 10 = 31
Q3236Linear sequence: find term by extendinga₁ = 1, d = +5; term 8 = 36
Q3351Linear sequence: find term by extendinga₁ = 7, d = +4; term 12 = 51
Q3450Linear sequence: find term by extendinga₁ = 2, d = +6; term 9 = 50
Q3552Linear sequence: find term by extendinga₁ = 10, d = +3; term 15 = 52
Q3668Linear sequence: find term by extendinga₁ = 5, d = +7; term 10 = 68
Q3766Linear sequence: find term by extendinga₁ = 3, d = +9; term 8 = 66
Q3858Linear sequence: find term by extendinga₁ = 8, d = +5; term 11 = 58
Q3977Linear sequence: find term by extendinga₁ = 1, d = +4; term 20 = 77
Q4078Linear sequence: find term by extendinga₁ = 6, d = +8; term 10 = 78
Q4132Geometric sequence: multiply by ratior = 2; 16 × 2 = 32
Q42243Geometric sequence: multiply by ratior = 3; 81 × 3 = 243
Q43625Geometric sequence: multiply by ratior = 5; 125 × 5 = 625
Q4464Geometric sequence: multiply by ratior = 2; 32 × 2 = 64
Q4580Geometric sequence: multiply by ratior = 2; 40 × 2 = 80
Q46162Geometric sequence: multiply by ratior = 3; 54 × 3 = 162
Q4796Geometric sequence: multiply by ratior = 2; 48 × 2 = 96
Q4810000Geometric sequence: multiply by ratior = 10; 1000 × 10 = 10000
Q49768Geometric sequence: multiply by ratior = 4; 192 × 4 = 768
Q501250Geometric sequence: multiply by ratior = 5; 250 × 5 = 1250
Q514Common difference7 − 3 = 4
Q527Common difference17 − 10 = 7
Q5311Common difference13 − 2 = 11
Q54-5Common difference15 − 20 = -5
Q559Common difference14 − 5 = 9
Q5631Check membership in linear sequenced = +4; lands exactly on 31
Q570Check membership in linear sequenced = +4; misses 30
Q5850Check membership in linear sequenced = +6; lands exactly on 50
Q590Check membership in linear sequenced = +7; misses 60
Q6033Check membership in linear sequenced = +4; lands exactly on 33
Q6125Square numbers: n × n5 × 5 = 25
Q6236Square numbers: n × n6 × 6 = 36
Q6349Square numbers: n × n7 × 7 = 49
Q6464Square numbers: n × n8 × 8 = 64
Q6581Square numbers: n × n9 × 9 = 81
Q6615Triangular numbers: gap grows by 1next gap = +5; 10 + 5 = 15
Q6721Triangular numbers: gap grows by 1next gap = +6; 15 + 6 = 21
Q6821Triangular numbers: gap grows by 1next gap = +6; 15 + 6 = 21
Q6928Triangular numbers: gap grows by 1next gap = +7; 21 + 7 = 28
Q7036Triangular numbers: gap grows by 1next gap = +8; 28 + 8 = 36
Q7113Fibonacci-style: term = sum of two before5 + 8 = 13
Q7226Fibonacci-style: term = sum of two before10 + 16 = 26
Q7321Fibonacci-style: term = sum of two before8 + 13 = 21
Q7439Fibonacci-style: term = sum of two before15 + 24 = 39
Q7565Fibonacci-style: term = sum of two before25 + 40 = 65
Q7629Fibonacci-style: term = sum of two before11 + 18 = 29
Q7734Fibonacci-style: term = sum of two before13 + 21 = 34
Q7837Fibonacci-style: term = sum of two before14 + 23 = 37
Q7955Fibonacci-style: term = sum of two before21 + 34 = 55
Q8076Fibonacci-style: term = sum of two before29 + 47 = 76
Q8113Dot pattern: linear sequenced = +3; pattern 5 = 13
Q8217Dot pattern: linear sequenced = +3; pattern 6 = 17
Q8327Dot pattern: linear sequenced = +4; pattern 7 = 27
Q8422Dot pattern: linear sequenced = +2; pattern 10 = 22
Q8525Dot pattern: linear sequenced = +4; pattern 6 = 25
Q8630Dot pattern: linear sequenced = +4; pattern 8 = 30
Q8725Dot pattern: linear sequenced = +4; pattern 7 = 25
Q8823Dot pattern: linear sequenced = +5; pattern 5 = 23
Q8928Dot pattern: linear sequenced = +6; pattern 5 = 28
Q9031Dot pattern: linear sequenced = +5; pattern 7 = 31
Q9132Identify sequence type (geometric ×2)Next term = 32
Q9248Identify sequence type (geometric ×2)Next term = 48
Q9325Identify sequence type (square)Next term = 25
Q9415Identify sequence type (triangular)Next term = 15
Q9513Identify sequence type (fibonacci)Next term = 13
Q9671Linear sequence: find term by extendinga₁ = 5, d = +6; term 12 = 71
Q9775Linear sequence: find term by extendinga₁ = 3, d = +8; term 10 = 75
Q9899Linear sequence: find term by extendinga₁ = 1, d = +7; term 15 = 99
Q99100Linear sequence: find term by extendinga₁ = 10, d = +9; term 11 = 100
Q10092Linear sequence: find term by extendinga₁ = 4, d = +11; term 9 = 92
Improve Tuition · George Street, Batley, West Yorkshire WF17 5AR · improvetuition.org
Teacher-led tuition since 2007. We are committed to safeguarding and promoting the welfare of every child in our care.