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Math 7

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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 7 · maddyhelps.com

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

  1. What is the median of 4, 9, 2, 7, 5?

    1. a) 5.4
    2. b) 2
    3. c) 5
    4. d) 7

  2. Two six-sided dice are rolled and the numbers are added. What is the probability that the sum is 7?

    1. a) 1/6
    2. b) 7/36
    3. c) 1/12
    4. d) 1/11

  3. A circle graph shows the favourite sports of 200 students. The basketball sector has a central angle of 54°. How many students chose basketball?

    1. a) 30
    2. b) 54
    3. c) 15
    4. d) 60

  4. What is the mean of 3, 5, 6, 10 and 11?

    1. a) 7
    2. b) 8
    3. c) 35
    4. d) 6

  5. A coin is flipped and a six-sided die is rolled. How many outcomes are in the sample space?

    1. a) 6
    2. b) 8
    3. c) 36
    4. d) 12

  6. In a circle graph, one sector shows 25% of the data. What is its central angle?

    1. a) 90°
    2. b) 45°
    3. c) 9°
    4. d) 25°

  7. In a survey of 40 students, 14 chose soccer. What central angle should the soccer sector have in a circle graph?

    1. a) 14°
    2. b) 35°
    3. c) 63°
    4. d) 126°

  8. A spinner has 4 equal sections: red, blue, green and yellow. In 100 spins it lands on red 29 times. Which statement is true?

    1. a) The theoretical probability of red has now changed to 29%.
    2. b) The experimental probability of red is 25%, and the theoretical probability is 29%.
    3. c) The experimental probability of red is 29%, and the theoretical probability is 25%.
    4. d) The spinner must be unfair, because red came up more than 25 times.

  9. The mean of 4, 6 and 8 is 6. A fourth number, 14, is added to the set. What is the new mean?

    1. a) 8
    2. b) 7
    3. c) 10
    4. d) 32

  10. Spinner A has three equal sections, 1, 2 and 3. Spinner B has two equal sections, 1 and 2. You spin both and add the numbers. What is the probability of a sum of 4?

    1. a) 2/5
    2. b) 1/4
    3. c) 1/6
    4. d) 1/3

Answer key · Data and probability

Math 7 · maddyhelps.com

  1. c) 5 — Put the numbers in order first: 2, 4, 5, 7, 9. The middle one is 5. Taking the middle of the list as it is written gives 2, and 5.4 is the mean.
  2. a) 1/6 — A table of the two dice has 36 equally likely outcomes, and 6 of them add to 7 (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1), so the probability is 6/36 = 1/6. 1/11 counts the 11 possible sums, 2 to 12, as if they were equally likely — but only one outcome makes 2, and six make 7.
  3. a) 30 — The sector is 54 ÷ 360 = 0.15 of the circle, or 15%, and 15% of 200 students is 30. 15 is the percent, not the number of students, and 60 divides 54 by 180 instead of 360.
  4. a) 7 — Add the numbers and share the total equally: 3 + 5 + 6 + 10 + 11 = 35, and 35 ÷ 5 = 7. 35 stops before dividing, 6 is the median and 8 is the range.
  5. d) 12 — Each of the 2 coin results can go with each of the 6 die results — heads with 1 to 6, then tails with 1 to 6 — so a table or tree diagram has 2 × 6 = 12 outcomes. Adding 2 + 6 = 8 counts the results of each separately, not the pairs, and 36 is the number for two dice.
  6. a) 90° — A whole circle is 360°, and the sector gets 25% of it: 0.25 × 360° = 90°, a quarter turn. 25° uses the percent as if it were degrees, and 45° takes 25% of 180° instead of 360°.
  7. d) 126° — 14 out of 40 is 14 ÷ 40 = 0.35, or 35%, and 35% of 360° is 0.35 × 360° = 126°. 35° stops at the percent and writes it as degrees, and 63° takes 35% of 180° — a circle graph is a full circle.
  8. c) The experimental probability of red is 29%, and the theoretical probability is 25%. — Experimental probability comes from what happened, 29 out of 100; theoretical probability comes from the equally likely sections, 1 out of 4 = 25%. Real results wander: 29 reds in 100 spins is not unusual for a fair spinner, and spinning cannot change the theoretical probability.
  9. a) 8 — The new total is 4 + 6 + 8 + 14 = 32, shared among 4 numbers: 32 ÷ 4 = 8. Averaging the old mean with the new number, (6 + 14) ÷ 2 = 10, counts the one new number as much as all three old ones. 7 is the new median.
  10. d) 1/3 — A table has 3 × 2 = 6 equally likely outcomes, and two of them add to 4: 2 + 2 and 3 + 1. So the probability is 2/6 = 1/3. 1/4 counts the four possible sums, 2 to 5, as if they were equally likely, and 1/6 finds only one of the two ways to make 4.