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Form 5 Dispersion Practice

Form 5 · 60 practice questions with instant marking and worked solutions.

Dispersion is an important part of the Form 5 mathematics curriculum. This topic develops range, interquartile range, standard deviation and comparing distributions. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Dispersion has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The 60 original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Dispersion; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample. 8 of them are DSE Paper 1 style structured questions answered in parts (a), (b), (c), where later parts build on earlier ones.

Effective revision is more than recording a score. After completing the Dispersion set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Dispersion should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

This batch adds 20 questions, bringing the topic to 60. The new questions cover controlled variations of different concepts, with paired bilingual conditions, hints, worked solutions and reproducible checks.

Start practising

  1. 1 Basic
    Find the range of 7, 9, 13, 16. Choose the correct answer.
  2. 2 Basic
    Find the range of 8, 10, 14, 17. Give the numerical value only.

  3. 3 Basic
    Find the range of 9, 11, 15, 18. Show the essential working and give the numerical value.

    Reproducible diagram for Dispersion; values and labels are stated in the question

  4. 4 Basic
    In Dispersion, the value of $6,8,12,15$ is 10. Is this statement true?
  5. 5 Basic
    Consider the data 11, 16, 22, 27, 50, 51, 55, 57. Find the interquartile range. Choose the correct answer.
  6. 6 Basic
    Consider the data 30, 30, 30, 42, 42, 42. Find the standard deviation. Give the answer only.

  7. 7 Basic
    A data set has mean 64 and standard deviation 10. Each value $x$ becomes $y=\frac{1}{2}x-6$. Find the new mean. Show the essential working and give the answer.

  8. 8 Basic
    Class A has 18 students averaging 61; class B has 17 averaging 65. The combined mean is 63. Is this true?
  9. 9 Basic
    Consider the data 14, 17, 26, 34, 39, 40, 48, 58. Find the interquartile range (as a fraction in lowest terms). Choose the correct answer.
  10. 10 Basic
    Consider the data 48, 48, 48, 48, 60, 60, 60, 60. Find the standard deviation. Give the answer only.

  11. 11 Basic
    A data set has mean 34 and standard deviation 5. Each value $x$ becomes $y=2x-4$. Find the new mean. Show the essential working and give the answer.

  12. 12 Basic
    Class A has 15 students averaging 52; class B has 17 averaging 53. The combined mean is 105/2. Is this true?
  13. 13 Standard
    Find the range of 11, 13, 18, 21. Choose the correct answer.
  14. 14 Standard
    Find the range of 12, 14, 19, 22. Give the numerical value only.

  15. 15 Standard
    Find the range of 13, 15, 20, 23. Show the essential working and give the numerical value.

  16. 16 Standard
    In Dispersion, the value of $10,12,17,20$ is 10. Is this statement true?
  17. 17 Standard
    Consider the data 15, 18, 22, 27, 32, 49, 52, 58. Find the interquartile range (as a fraction in lowest terms). Choose the correct answer.
  18. 18 Standard
    Consider the data 40, 40, 44, 44. Find the standard deviation. Give the answer only.

  19. 19 Standard
    A data set has mean 70 and standard deviation 6. Each value $x$ becomes $y=2x+10$. Find the new mean. Show the essential working and give the answer.

  20. 20 Standard DSE long question
    Consider the data 13, 20, 23, 30, 40, 53, 57, 66. Answer each part; give the answer only.
    1. (a) Find the median.
    2. (b) Find the range.
    3. (c) Find the interquartile range (as a fraction in lowest terms).
  21. 21 Standard
    Consider the data 16, 22, 31, 32, 37, 41, 42, 45. Find the interquartile range. Choose the correct answer.
  22. 22 Standard
    Consider the data 43, 43, 43, 53, 53, 53. Find the standard deviation. Give the answer only.

  23. 23 Standard
    A data set has mean 46 and standard deviation 8. Each value $x$ becomes $y=-2x+13$. Find the new standard deviation. Show the essential working and give the answer.

  24. 24 Standard DSE long question
    Consider the data 15, 29, 39, 48, 49, 51, 54, 59. Answer each part; give the answer only.
    1. (a) Find the median (as a fraction in lowest terms).
    2. (b) Find the range.
    3. (c) Find the interquartile range (as a fraction in lowest terms).
  25. 25 Advanced
    Find the range of 15, 17, 23, 26. Choose the correct answer.
  26. 26 Advanced
    Find the range of 16, 18, 24, 27. Give the numerical value only.

  27. 27 Advanced
    Find the range of 17, 19, 25, 28. Show the essential working and give the numerical value.

  28. 28 Advanced
    In Dispersion, the value of $14,16,22,25$ is 12. Is this statement true?
  29. 29 Advanced
    Class A has 32 students averaging 80; class B has 29 averaging 53. Find the combined mean (as a fraction in lowest terms). Choose the correct answer.
  30. 30 Advanced
    Consider the data 28, 32, 35, 40, 41, 43, 56, 59. Find the interquartile range. Give the answer only.

  31. 31 Advanced
    Consider the data 40, 40, 56, 56. The standard deviation is 8. Is this true?
  32. 32 Advanced DSE long question
    Class A: 30 students, mean 65 (s.d. 5); class B: 29 students, mean 62. Answer each part; give the answer only.
    1. (a) Find the total score of class A.
    2. (b) Find the combined mean (as a fraction in lowest terms).
    3. (c) A class A student scores 75. Find the standard score within class A.
  33. 33 Advanced
    Class A has 31 students averaging 53; class B has 33 averaging 61. Find the combined mean (as a fraction in lowest terms). Choose the correct answer.
  34. 34 Advanced
    Consider the data 19, 27, 28, 37, 38, 43, 53, 54. Find the interquartile range (as a fraction in lowest terms). Give the answer only.

  35. 35 Advanced
    Consider the data 30, 30, 30, 34, 34, 34. The standard deviation is 2. Is this true?
  36. 36 Advanced DSE long question
    Class A: 29 students, mean 71 (s.d. 8); class B: 25 students, mean 67. Answer each part; give the answer only.
    1. (a) Find the total score of class A.
    2. (b) Find the combined mean (as a fraction in lowest terms).
    3. (c) A class A student scores 79. Find the standard score within class A.
  37. 37 Challenging
    Find the range of 19, 21, 28, 31. Choose the correct answer.
  38. 38 Challenging
    Find the range of 20, 22, 29, 32. Give the numerical value only.

  39. 39 Challenging
    Find the range of 21, 23, 30, 33. Show the essential working and give the numerical value.

  40. 40 Challenging
    In Dispersion, the value of $18,20,27,30$ is 12. Is this statement true?
  41. 41 Challenging
    A data set has mean 30 and standard deviation 11. Each value $x$ becomes $y=\frac{1}{2}x-6$. Find the new mean. Choose the correct answer.
  42. 42 Challenging
    Class A has 17 students averaging 71; class B has 22 averaging 66. Find the combined mean (as a fraction in lowest terms). Show the essential working and give the answer.

  43. 43 Challenging
    Consider the data 17, 20, 27, 34, 46, 47, 55, 56. The interquartile range is 39. Is this true?
  44. 44 Challenging DSE long question
    Consider the data 12, 22, 34, 37, 43, 44, 62, 63. Answer each part; give the answer only.
    1. (a) Find the median.
    2. (b) Find the range.
    3. (c) Find the interquartile range.
  45. 45 Challenging
    A data set has mean 44 and standard deviation 7. Each value $x$ becomes $y=-2x+10$. Find the new mean. Choose the correct answer.
  46. 46 Challenging
    Class A has 22 students averaging 65; class B has 17 averaging 70. Find the combined mean (as a fraction in lowest terms). Show the essential working and give the answer.

  47. 47 Challenging
    Consider the data 21, 26, 27, 32, 33, 34, 44, 59. The interquartile range is 38. Is this true?
  48. 48 Challenging DSE long question
    Consider the data 12, 15, 28, 29, 45, 49, 61, 66. Answer each part; give the answer only.
    1. (a) Find the median.
    2. (b) Find the range.
    3. (c) Find the interquartile range (as a fraction in lowest terms).
  49. 49 Elite
    Find the range of 23, 25, 33, 36. Choose the correct answer.
  50. 50 Elite
    Find the range of 24, 26, 34, 37. Give the numerical value only.

  51. 51 Elite
    Find the range of 25, 27, 35, 38. Show the essential working and give the numerical value.

  52. 52 Elite
    In Dispersion, the value of $22,24,32,35$ is 14. Is this statement true?
  53. 53 Elite
    Consider the data 61, 61, 61, 69, 69, 69. Find the standard deviation. Give the answer only.

  54. 54 Elite
    A data set has mean 59 and standard deviation 7. Each value $x$ becomes $y=\frac{1}{2}x+13$. Find the new mean (as a fraction in lowest terms). Show the essential working and give the answer.

  55. 55 Elite
    Class A has 20 students averaging 65; class B has 25 averaging 76. The combined mean is 640/9. Is this true?
  56. 56 Elite DSE long question
    Class A: 20 students, mean 58 (s.d. 8); class B: 24 students, mean 74. Answer each part; give the answer only.
    1. (a) Find the total score of class A.
    2. (b) Find the combined mean (as a fraction in lowest terms).
    3. (c) A class A student scores 74. Find the standard score within class A.
  57. 57 Elite
    Consider the data 66, 66, 66, 66, 78, 78, 78, 78. Find the standard deviation. Give the answer only.

  58. 58 Elite
    A data set has mean 63 and standard deviation 7. Each value $x$ becomes $y=3x-10$. Find the new standard deviation. Show the essential working and give the answer.

  59. 59 Elite
    Class A has 19 students averaging 71; class B has 27 averaging 57. The combined mean is 1444/23. Is this true?
  60. 60 Elite DSE long question
    Class A: 20 students, mean 68 (s.d. 10); class B: 32 students, mean 59. Answer each part; give the answer only.
    1. (a) Find the total score of class A.
    2. (b) Find the combined mean (as a fraction in lowest terms).
    3. (c) A class A student scores 88. Find the standard score within class A.

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Dispersion

This topic needs particular care with range, interquartile range, standard deviation and comparing distributions. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

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