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Math 9

Math 9 · Worksheets

Probability and statistics

Ten questions of mixed difficulty, covering Probability and statistics. Print it, or work through it on screen — the answer key starts on its own page.

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Probability and statistics

Math 9 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. Which survey question is the most neutral?

    1. a) Most students love country. What about you?
    2. b) Don't you agree that rap is the best music?
    3. c) What is your favourite type of music?
    4. d) Is loud, noisy metal your favourite music?

  2. A weather forecast gives a 30% chance of rain tomorrow. What does this mean?

    1. a) On past days like tomorrow, it rained about 3 times in 10.
    2. b) It will not rain, since 30% is less than 50%.
    3. c) It is certain to rain tomorrow, but only lightly.
    4. d) It will rain for about 30% of the hours tomorrow.

  3. A reporter stands outside a mall and asks shoppers as they walk by, choosing people 'at random'. What kind of sample is this really?

    1. a) a convenience sample
    2. b) a systematic sample
    3. c) a simple random sample
    4. d) a stratified sample

  4. A survey about school supplies asks students to write their name and their family's income. The biggest issue with this survey is

    1. a) privacy
    2. b) timing
    3. c) use of language
    4. d) cost

  5. A coin is flipped 20 times and lands heads 14 times. What are the experimental and theoretical probabilities of heads?

    1. a) both are 7/10
    2. b) experimental 1/2, theoretical 7/10
    3. c) experimental 3/10, theoretical 1/2
    4. d) experimental 7/10, theoretical 1/2

  6. A principal surveys 60 of the 600 students in her school about a new timetable. The population is

    1. a) all 600 students in the school
    2. b) the students who liked the timetable
    3. c) the 540 students who were not surveyed
    4. d) the 60 students who were surveyed

  7. A school has 300 Grade 7, 250 Grade 8 and 200 Grade 9 students. A stratified sample of 75 students is chosen in proportion to the size of each grade. How many Grade 9 students are in the sample?

    1. a) 25
    2. b) 50
    3. c) 30
    4. d) 20

  8. A basketball player has made 42 of her last 60 free throws. Based on this, how many of her next 20 free throws is she most likely to make?

    1. a) 6
    2. b) 10
    3. c) 14
    4. d) 18

  9. A survey on whether city buses are too crowded is done at 11 a.m. on a Sunday. What is the main problem?

    1. a) timing: buses are quiet then, so crowding will be understated
    2. b) cost: surveying riders on buses is too expensive to do
    3. c) privacy: riders' names could be linked to their answers
    4. d) cultural sensitivity: the question may offend some riders

  10. Records show a river has flooded in 5 of the past 50 years. An insurance company uses this to price flood insurance. Which assumption is it making?

    1. a) The probability of a flood in any year is 5%.
    2. b) The river will flood exactly once every 10 years.
    3. c) A flood this year makes one next year less likely.
    4. d) Future years will be like the past 50 years.

Answer key · Probability and statistics

Math 9 · maddyhelps.com

  1. c) What is your favourite type of music? — A neutral question does not hint at an answer. 'Don't you agree' pushes people to say yes, telling people what most students think puts pressure on them, and 'loud, noisy' is loaded language that makes metal sound bad.
  2. a) On past days like tomorrow, it rained about 3 times in 10. — A probability forecast is based on many past days with similar conditions, about 3 in 10 of which had rain. It says nothing about how long or how hard it will rain, and 30% is not zero: rain is less likely than not, but it can still happen.
  3. a) a convenience sample — In a simple random sample, every member of the population has an equal chance of being chosen. People who are not at that mall at that time have no chance at all, so this is a convenience sample however randomly the reporter picks — calling it random because nobody was chosen on purpose is the trap.
  4. a) privacy — Family income is personal information, and a name on the form means the answers are not anonymous. Students may skip the question or not answer honestly — and income has nothing to do with school supplies anyway.
  5. d) experimental 7/10, theoretical 1/2 — Experimental probability comes from what happened: 14/20 = 7/10. Theoretical probability comes from the equally likely outcomes: one head out of two sides, 1/2. Over many more flips the experimental value should move closer to 1/2.
  6. a) all 600 students in the school — The population is the whole group the principal wants to know about: all 600 students. The 60 she actually asks are the sample, chosen to stand in for the population.
  7. d) 20 — Grade 9 is 200 of the 750 students, so it gets 200/750 × 75 = 20 places. Taking 25 from each grade ignores the sizes of the groups, and the point of a stratified sample is that each group is represented in proportion.
  8. c) 14 — Her experimental probability is 42/60 = 7/10, so expect about 7/10 × 20 = 14. Using 1/2 because a shot either goes in or does not gives 10, but making and missing are not equally likely — her record says so.
  9. a) timing: buses are quiet then, so crowding will be understated — When a survey is done can decide its answer. Sunday morning is one of the quietest times on a bus, so riders then have not seen the rush-hour crowding the question is about; nothing in the survey asks for names, and the question itself is not offensive.
  10. d) Future years will be like the past 50 years. — Using past floods to predict future ones assumes conditions stay the same — no new dams, no change in climate or land use. The probability is 5/50 = 10% a year, not 5%, and it is an average, not a schedule: one flood does not make the next one less likely.