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Form 6 Statistics and Probability Synthesis Practice

Form 6 · 60 practice questions with instant marking and worked solutions.

Statistics and Probability Synthesis is an important part of the Form 6 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 Statistics and Probability Synthesis 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 Statistics and Probability Synthesis; 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 Statistics and Probability Synthesis 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.

Statistics and Probability Synthesis 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 Statistics and Probability Synthesis, calculate $7,9,11,13$. Choose the correct answer.
  2. 2 Basic
    In Statistics and Probability Synthesis, calculate $8,10,12,14$. Give the numerical value only.

  3. 3 Basic
    In Statistics and Probability Synthesis, calculate $9,11,13,15$. Show the essential working and give the numerical value.

    Reproducible diagram for Statistics and Probability Synthesis; values and labels are stated in the question

  4. 4 Basic
    In Statistics and Probability Synthesis, the value of $6,8,10,12$ is 10. Is this statement true?
  5. 5 Basic
    A bag has 6 red and 3 blue balls. Two are drawn at random without replacement. Find the probability that they are of different colours (as a fraction in lowest terms). Choose the correct answer.
  6. 6 Basic
    2 books are chosen from 7 different books. Find the number of selections. Give the answer only.

  7. 7 Basic
    Consider the data 18, 19, 29, 33, 42, 50, 52, 58. Find the interquartile range. Show the essential working and give the answer.

  8. 8 Basic
    A test has mean 45 and standard deviation 5. Ming scores 50. Ming's standard score is -1. Is this true?
  9. 9 Basic
    A bag has 4 red and 4 blue balls. Two are drawn at random without replacement. Find the probability that they are of different colours (as a fraction in lowest terms). Choose the correct answer.
  10. 10 Basic
    3 books are chosen from 8 different books. Find the number of selections. Give the answer only.

  11. 11 Basic
    Consider the data 10, 12, 18, 24, 29, 38, 51, 52. Find the interquartile range (as a fraction in lowest terms). Show the essential working and give the answer.

  12. 12 Basic
    A test has mean 67 and standard deviation 5. Ming scores 58. Ming's standard score is 9/5. Is this true?
  13. 13 Standard
    In Statistics and Probability Synthesis, calculate $11,13,15,17$. Choose the correct answer.
  14. 14 Standard
    In Statistics and Probability Synthesis, calculate $12,14,16,18$. Give the numerical value only.

  15. 15 Standard
    In Statistics and Probability Synthesis, calculate $13,15,17,19$. Show the essential working and give the numerical value.

  16. 16 Standard
    In Statistics and Probability Synthesis, the value of $10,12,14,16$ is 13. Is this statement true?
  17. 17 Standard
    Class A has 33 students averaging 57; class B has 20 averaging 64. Find the combined mean (as a fraction in lowest terms). Choose the correct answer.
  18. 18 Standard
    A shooter hits the target with probability $\frac{1}{4}$ each time, independently. He shoots 4 times. Find the probability of at least one hit (as a fraction in lowest terms). Give the answer only.

  19. 19 Standard
    Of 45 students, 23 are in the basketball team and 12 of those are also in the swimming team. A basketball player is chosen at random. Find the probability that the student is also a swimmer (as a fraction in lowest terms). Show the essential working and give the answer.

  20. 20 Standard DSE long question
    A bag has 6 red and 3 blue balls. Two are drawn without replacement. Answer each part; give the answer only.
    1. (a) Find the probability that the first is red (as a fraction in lowest terms).
    2. (b) Find the probability that both are red (as a fraction in lowest terms).
    3. (c) Find the probability of at least one blue ball (as a fraction in lowest terms).
  21. 21 Standard
    Class A has 32 students averaging 70; class B has 19 averaging 66. Find the combined mean (as a fraction in lowest terms). Choose the correct answer.
  22. 22 Standard
    A shooter hits the target with probability $\frac{1}{3}$ each time, independently. He shoots 2 times. Find the probability of at least one hit (as a fraction in lowest terms). Give the answer only.

  23. 23 Standard
    Of 52 students, 24 are in the basketball team and 2 of those are also in the swimming team. A basketball player is chosen at random. Find the probability that the student is also a swimmer (as a fraction in lowest terms). Show the essential working and give the answer.

  24. 24 Standard DSE long question
    A bag has 4 red and 4 blue balls. Two are drawn without replacement. Answer each part; give the answer only.
    1. (a) Find the probability that the first is red (as a fraction in lowest terms).
    2. (b) Find the probability that both are red (as a fraction in lowest terms).
    3. (c) Find the probability of at least one blue ball (as a fraction in lowest terms).
  25. 25 Advanced
    In Statistics and Probability Synthesis, calculate $15,17,19,21$. Choose the correct answer.
  26. 26 Advanced
    In Statistics and Probability Synthesis, calculate $16,18,20,22$. Give the numerical value only.

  27. 27 Advanced
    In Statistics and Probability Synthesis, calculate $17,19,21,23$. Show the essential working and give the numerical value.

  28. 28 Advanced
    In Statistics and Probability Synthesis, the value of $14,16,18,20$ is 18. Is this statement true?
  29. 29 Advanced
    Consider the data 25, 25, 25, 41, 41, 41. Find the standard deviation. Choose the correct answer.
  30. 30 Advanced
    A bag has 6 red and 2 blue balls. Two are drawn at random without replacement. Find the probability that they are of different colours (as a fraction in lowest terms). Give the answer only.

  31. 31 Advanced
    2 books are chosen from 9 different books. The number of selections is 36. Is this true?
  32. 32 Advanced DSE long question
    Consider the data 18, 21, 25, 38, 45, 46, 62, 67. 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.
  33. 33 Advanced
    Consider the data 71, 71, 83, 83. Find the standard deviation. Choose the correct answer.
  34. 34 Advanced
    A bag has 4 red and 4 blue balls. Two are drawn at random without replacement. Find the probability that both are red (as a fraction in lowest terms). Give the answer only.

  35. 35 Advanced
    2 books are chosen from 6 different books. The number of selections is 15. Is this true?
  36. 36 Advanced DSE long question
    Consider the data 11, 12, 16, 28, 35, 39, 47, 61. 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.
  37. 37 Challenging
    In Statistics and Probability Synthesis, calculate $19,21,23,25$. Choose the correct answer.
  38. 38 Challenging
    In Statistics and Probability Synthesis, calculate $20,22,24,26$. Give the numerical value only.

  39. 39 Challenging
    In Statistics and Probability Synthesis, calculate $21,23,25,27$. Show the essential working and give the numerical value.

  40. 40 Challenging
    In Statistics and Probability Synthesis, the value of $18,20,22,24$ is 21. Is this statement true?
  41. 41 Challenging
    Consider the data 19, 24, 31, 34, 37, 43, 44, 51. Find the interquartile range. Choose the correct answer.
  42. 42 Challenging
    A test has mean 55 and standard deviation 4. Ming scores 68. Find Ming's standard score (as a fraction in lowest terms). Show the essential working and give the answer.

  43. 43 Challenging
    Class A has 25 students averaging 55; class B has 27 averaging 55. The combined mean is 110. Is this true?
  44. 44 Challenging DSE long question
    Class A: 26 students, mean 56 (s.d. 8); class B: 26 students, mean 75. 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 64. Find the standard score within class A.
  45. 45 Challenging
    Consider the data 10, 26, 28, 39, 43, 48, 49, 56. Find the interquartile range (as a fraction in lowest terms). Choose the correct answer.
  46. 46 Challenging
    A test has mean 49 and standard deviation 4. Ming scores 52. Find Ming's standard score (as a fraction in lowest terms). Show the essential working and give the answer.

  47. 47 Challenging
    Class A has 17 students averaging 65; class B has 20 averaging 65. The combined mean is 130. Is this true?
  48. 48 Challenging DSE long question
    Class A: 35 students, mean 71 (s.d. 8); class B: 28 students, mean 57. 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.
  49. 49 Elite
    In Statistics and Probability Synthesis, calculate $23,25,27,29$. Choose the correct answer.
  50. 50 Elite
    In Statistics and Probability Synthesis, calculate $24,26,28,30$. Give the numerical value only.

  51. 51 Elite
    In Statistics and Probability Synthesis, calculate $25,27,29,31$. Show the essential working and give the numerical value.

  52. 52 Elite
    In Statistics and Probability Synthesis, the value of $22,24,26,28$ is 26. Is this statement true?
  53. 53 Elite
    A shooter hits the target with probability $\frac{1}{2}$ each time, independently. He shoots 4 times. Find the probability of at least one hit (as a fraction in lowest terms). Give the answer only.

  54. 54 Elite
    Of 52 students, 29 are in the basketball team and 2 of those are also in the swimming team. A basketball player is chosen at random. Find the probability that the student is also a swimmer (as a fraction in lowest terms). Show the essential working and give the answer.

  55. 55 Elite
    Consider the data 63, 63, 63, 79, 79, 79. The standard deviation is 8. Is this true?
  56. 56 Elite DSE long question
    A group of 3 is chosen from 7 boys and 3 girls. Answer each part; give the answer only.
    1. (a) Find the total number of ways.
    2. (b) Find the number of ways with exactly 2 girls.
    3. (c) Find the number of ways with at least one girl.
  57. 57 Elite
    A shooter hits the target with probability $\frac{1}{4}$ each time, independently. He shoots 2 times. Find the probability of at least one hit (as a fraction in lowest terms). Give the answer only.

  58. 58 Elite
    Of 26 students, 10 are in the basketball team and 5 of those are also in the swimming team. A basketball player is chosen at random. Find the probability that the student is also a swimmer (as a fraction in lowest terms). Show the essential working and give the answer.

  59. 59 Elite
    Consider the data 32, 32, 32, 48, 48, 48. The standard deviation is 8. Is this true?
  60. 60 Elite DSE long question
    A group of 3 is chosen from 6 boys and 5 girls. Answer each part; give the answer only.
    1. (a) Find the total number of ways.
    2. (b) Find the number of ways with exactly 1 girl.
    3. (c) Find the number of ways with at least one girl.

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

Common mistakes

Common mistakes in Statistics and Probability Synthesis

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.

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