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Math 8

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Data and probability

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

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Data and probability

Math 8 · maddyhelps.com

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

  1. Which of these can make a circle graph misleading?

    1. a) giving the graph a clear title
    2. b) labelling each sector with its name and percent
    3. c) tilting it in 3-D so front sectors look bigger
    4. d) ordering the sectors from largest to smallest

  2. A spinner has 4 equal sections, and 1 of them is red. A bag holds 3 green marbles and 2 yellow ones. What is the probability of spinning red and then drawing a green marble?

    1. a) 15%
    2. b) 25%
    3. c) 60%
    4. d) 85%

  3. A survey let each student choose every sport they play: 60% chose hockey, 45% soccer and 30% basketball. Why can't these results go in one circle graph?

    1. a) They add to 135%, because some students chose more than one sport.
    2. b) A circle graph cannot show more than two categories.
    3. c) They add to 135%, so the survey results must contain a mistake.
    4. d) They can: each sector's angle is just its percent in degrees.

  4. A company's sales fell for two years, then rose for the last three months. Its ad shows a line graph of only those three months. What makes the graph misleading?

    1. a) It hides the longer trend by choosing a short time range.
    2. b) The line graph should have been a circle graph.
    3. c) Its numbers must be wrong, since sales went up.
    4. d) Its horizontal axis has uneven intervals between months.

  5. A coin is flipped and a six-sided die is rolled. What is the probability of getting heads and a 6?

    1. a) 2/3
    2. b) 1/8
    3. c) 1/6
    4. d) 1/12

  6. Which graph is best for showing how a puppy's mass changed over its first 12 months?

    1. a) a line graph
    2. b) a pictograph
    3. c) a double bar graph
    4. d) a circle graph

  7. In a pictograph, each symbol stands for 8 students. The row for Grade 8 shows 3¾ symbols. How many Grade 8 students does it show?

    1. a) 24
    2. b) 32
    3. c) 27
    4. d) 30

  8. A basketball player makes 80% of her free throws, and each shot is independent of the others. What is the probability that she makes two shots in a row?

    1. a) 160%
    2. b) 80%
    3. c) 64%
    4. d) 40%

  9. Two bars on a bar graph show 92 and 96. The vertical axis starts at 90, not 0. How many times as tall as the 92 bar does the 96 bar look?

    1. a) 3 times as tall
    2. b) 4 times as tall
    3. c) about 1.04 times as tall
    4. d) 2 times as tall

  10. A fair coin has landed heads 5 times in a row. What is the probability that the next flip is heads?

    1. a) 1/6
    2. b) 1/64
    3. c) 1/32
    4. d) 1/2

Answer key · Data and probability

Math 8 · maddyhelps.com

  1. c) tilting it in 3-D so front sectors look bigger — A tilted 3-D circle graph stretches the sectors nearest you and squashes the ones at the back, so equal percents stop looking equal. Labels, a title and a sensible order make a graph easier to read honestly — they are what a fair graph should have.
  2. a) 15% — The spinner and the bag do not affect each other, so multiply: 1/4 × 3/5 = 3/20 = 0.15 = 15%. Adding the chances, 25% + 60% = 85%, gives more than either one alone, but needing both to happen can only make it less likely. 60% and 25% are each chance on its own.
  3. a) They add to 135%, because some students chose more than one sport. — A circle graph shows the parts of one whole, so its percents must add to exactly 100%. Here 60 + 45 + 30 = 135%, because many students play more than one sport and were counted more than once — the survey is not wrong, but its results are not parts of one whole. A bar graph would show them fairly.
  4. a) It hides the longer trend by choosing a short time range. — Every number on the graph can be correct and it still misleads: showing only the three months of growth hides two years of falling sales, so the story looks like the opposite of what happened. Nothing in the description suggests uneven intervals, and a circle graph cannot show change over time at all.
  5. d) 1/12 — The coin does not affect the die, so the events are independent and you multiply: 1/2 × 1/6 = 1/12. A table of the 12 equally likely outcomes shows the same thing — only one of them is heads with a 6. Adding 1/2 + 1/6 = 2/3 gives more than either chance alone, but needing both to happen can only make it less likely.
  6. a) a line graph — A line graph shows change over time: the months go along the bottom and the line rises as the puppy grows. A circle graph shows the parts of one whole, and the puppy's masses in different months are not parts of anything. A double bar graph compares two sets of data, and here there is only one.
  7. d) 30 — 3 whole symbols stand for 3 × 8 = 24 students, and ¾ of a symbol stands for ¾ × 8 = 6 more: 24 + 6 = 30. 24 ignores the part symbol, 32 counts it as a whole one, and 27 reads ¾ of a symbol as 3 students.
  8. c) 64% — Independent events multiply: 0.8 × 0.8 = 0.64, or 64%. It is less than 80% because a miss on either shot spoils the pair — answering 80% treats two shots as if they were one. 160% adds the chances and gives a probability over 100%, which is impossible.
  9. a) 3 times as tall — Drawn from 90, the bars are 92 − 90 = 2 and 96 − 90 = 6 units tall, so the 96 bar looks 6 ÷ 2 = 3 times as tall. The real values are only about 1.04 times apart — 96 is about 4% more than 92 — which is how the bars would look with the axis starting at 0. That gap is what makes the graph misleading.
  10. d) 1/2 — The coin has no memory: each flip is independent, so the next one is heads with probability 1/2, whatever came before. 1/64 = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 is the chance of six heads in a row worked out before any flips — but five of those have already happened, so only one flip is still uncertain.