Skip to content

Form 5 Statistical Applications Practice

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

Statistical Applications is an important part of the Form 5 mathematics curriculum. This topic develops mean, median, mode, sampling and interpretation. 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 Statistical Applications 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 Statistical Applications; 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 Statistical Applications 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.

Statistical Applications 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
    In Statistical Applications, calculate $7,9,11,13$. Choose the correct answer.
  2. 2 Basic
    In Statistical Applications, calculate $8,10,12,14$. Give the numerical value only.

  3. 3 Basic
    In Statistical Applications, calculate $9,11,13,15$. Show the essential working and give the numerical value.

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

  4. 4 Basic
    In Statistical Applications, the value of $6,8,10,12$ is 10. Is this statement true?
  5. 5 Basic
    A test has mean 61 and standard deviation 5. Ming scores 64. Find Ming's standard score (as a fraction in lowest terms). Choose the correct answer.
  6. 6 Basic
    Class A has 19 students averaging 57; class B has 33 averaging 63. Find the combined mean (as a fraction in lowest terms). Give the answer only.

  7. 7 Basic
    The mean of 10 numbers is 63. The number 59 is added. Find the new mean (as a fraction in lowest terms). Show the essential working and give the answer.

  8. 8 Basic
    A data set has mean 56 and standard deviation 4. Each value $x$ becomes $y=3x-4$. The new mean is 52. Is this true?
  9. 9 Basic
    A test has mean 53 and standard deviation 4. Ming scores 51. Find Ming's standard score (as a fraction in lowest terms). Choose the correct answer.
  10. 10 Basic
    Class A has 33 students averaging 61; class B has 24 averaging 78. Find the combined mean (as a fraction in lowest terms). Give the answer only.

  11. 11 Basic
    The mean of 9 numbers is 59. The number 55 is added. Find the new mean (as a fraction in lowest terms). Show the essential working and give the answer.

  12. 12 Basic
    A data set has mean 70 and standard deviation 11. Each value $x$ becomes $y=-2x-10$. The new mean is 60. Is this true?
  13. 13 Standard
    In Statistical Applications, calculate $11,13,15,17$. Choose the correct answer.
  14. 14 Standard
    In Statistical Applications, calculate $12,14,16,18$. Give the numerical value only.

  15. 15 Standard
    In Statistical Applications, calculate $13,15,17,19$. Show the essential working and give the numerical value.

  16. 16 Standard
    In Statistical Applications, the value of $10,12,14,16$ is 13. Is this statement true?
  17. 17 Standard
    Consider the data 30, 30, 42, 42. Find the standard deviation. Choose the correct answer.
  18. 18 Standard
    A test has mean 44 and standard deviation 12. Ming scores 33. Find Ming's standard score (as a fraction in lowest terms). Give the answer only.

  19. 19 Standard
    Class A has 26 students averaging 58; class B has 26 averaging 78. Find the combined mean. Show the essential working and give the answer.

  20. 20 Standard DSE long question
    Class A: 33 students, mean 75 (s.d. 8); class B: 24 students, mean 56. Answer each part; give the answer only.
    1. (a) Find the total score of class A.
    2. (b) Find the combined mean.
    3. (c) A class A student scores 83. Find the standard score within class A.
  21. 21 Standard
    Consider the data 72, 72, 72, 72, 88, 88, 88, 88. Find the standard deviation. Choose the correct answer.
  22. 22 Standard
    A test has mean 55 and standard deviation 12. Ming scores 67. Find Ming's standard score. Give the answer only.

  23. 23 Standard
    Class A has 24 students averaging 51; class B has 35 averaging 80. Find the combined mean (as a fraction in lowest terms). Show the essential working and give the answer.

  24. 24 Standard DSE long question
    Class A: 28 students, mean 68 (s.d. 5); class B: 26 students, mean 72. 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 78. Find the standard score within class A.
  25. 25 Advanced
    In Statistical Applications, calculate $15,17,19,21$. Choose the correct answer.
  26. 26 Advanced
    In Statistical Applications, calculate $16,18,20,22$. Give the numerical value only.

  27. 27 Advanced
    In Statistical Applications, calculate $17,19,21,23$. Show the essential working and give the numerical value.

  28. 28 Advanced
    In Statistical Applications, the value of $14,16,18,20$ is 18. Is this statement true?
  29. 29 Advanced
    The mean of 12 numbers is 46. The number 94 is added. Find the new mean (as a fraction in lowest terms). Choose the correct answer.
  30. 30 Advanced
    A data set has mean 40 and standard deviation 11. Each value $x$ becomes $y=-2x+10$. Find the new standard deviation. Give the answer only.

  31. 31 Advanced
    Consider the data 73, 73, 73, 73, 81, 81, 81, 81. The standard deviation is 4. Is this true?
  32. 32 Advanced DSE long question
    Consider the data 10, 37, 38, 39, 49, 63, 68, 69. Answer each part; give the answer only.
    1. (a) Find the median.
    2. (b) Find the range.
    3. (c) Find the interquartile range.
  33. 33 Advanced
    The mean of 9 numbers is 52. The number 66 is added. Find the new mean (as a fraction in lowest terms). Choose the correct answer.
  34. 34 Advanced
    A data set has mean 58 and standard deviation 7. Each value $x$ becomes $y=2x-4$. Find the new mean. Give the answer only.

  35. 35 Advanced
    Consider the data 55, 55, 55, 65, 65, 65. The standard deviation is 5. Is this true?
  36. 36 Advanced DSE long question
    Consider the data 13, 21, 24, 32, 37, 44, 52, 60. 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).
  37. 37 Challenging
    In Statistical Applications, calculate $19,21,23,25$. Choose the correct answer.
  38. 38 Challenging
    In Statistical Applications, calculate $20,22,24,26$. Give the numerical value only.

  39. 39 Challenging
    In Statistical Applications, calculate $21,23,25,27$. Show the essential working and give the numerical value.

  40. 40 Challenging
    In Statistical Applications, the value of $18,20,22,24$ is 21. Is this statement true?
  41. 41 Challenging
    A test has mean 49 and standard deviation 12. Ming scores 38. Find Ming's standard score (as a fraction in lowest terms). Choose the correct answer.
  42. 42 Challenging
    Class A has 23 students averaging 55; class B has 24 averaging 62. Find the combined mean (as a fraction in lowest terms). Show the essential working and give the answer.

  43. 43 Challenging
    The mean of 9 numbers is 70. The number 37 is added. The new mean is 107/2. Is this true?
  44. 44 Challenging DSE long question
    Class A: 25 students, mean 69 (s.d. 8); class B: 21 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 77. Find the standard score within class A.
  45. 45 Challenging
    A test has mean 54 and standard deviation 8. Ming scores 51. Find Ming's standard score (as a fraction in lowest terms). Choose the correct answer.
  46. 46 Challenging
    Class A has 26 students averaging 80; class B has 34 averaging 70. Find the combined mean (as a fraction in lowest terms). Show the essential working and give the answer.

  47. 47 Challenging
    The mean of 5 numbers is 65. The number 51 is added. The new mean is 58. Is this true?
  48. 48 Challenging DSE long question
    Class A: 34 students, mean 65 (s.d. 8); class B: 29 students, mean 70. 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 81. Find the standard score within class A.
  49. 49 Elite
    In Statistical Applications, calculate $23,25,27,29$. Choose the correct answer.
  50. 50 Elite
    In Statistical Applications, calculate $24,26,28,30$. Give the numerical value only.

  51. 51 Elite
    In Statistical Applications, calculate $25,27,29,31$. Show the essential working and give the numerical value.

  52. 52 Elite
    In Statistical Applications, the value of $22,24,26,28$ is 26. Is this statement true?
  53. 53 Elite
    A data set has mean 47 and standard deviation 5. Each value $x$ becomes $y=2x+4$. Find the new standard deviation. Give the answer only.

  54. 54 Elite
    Consider the data 73, 73, 73, 83, 83, 83. Find the standard deviation. Show the essential working and give the answer.

  55. 55 Elite
    A test has mean 65 and standard deviation 5. Ming scores 62. Ming's standard score is -3/5. Is this true?
  56. 56 Elite DSE long question
    Consider the data 10, 19, 21, 25, 38, 40, 68, 69. 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.
  57. 57 Elite
    A data set has mean 43 and standard deviation 12. Each value $x$ becomes $y=3x-2$. Find the new standard deviation. Give the answer only.

  58. 58 Elite
    Consider the data 71, 71, 79, 79. Find the standard deviation. Show the essential working and give the answer.

  59. 59 Elite
    A test has mean 53 and standard deviation 5. Ming scores 59. Ming's standard score is 6/5. Is this true?
  60. 60 Elite DSE long question
    Consider the data 19, 21, 23, 30, 35, 43, 47, 55. 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.

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

Common mistakes

Common mistakes in Statistical Applications

This topic needs particular care with mean, median, mode, sampling and interpretation. 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.

More Form 5 topics

Form 5 mixed revision → My mistakes →

Keep missing the same type?

Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.

Book a Trial WhatsApp us
WhatsApp