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Box plots practice questions with answers

Higher · Grade 6

A second set of box plots questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Ordered data: 3, 6, 8, 11, 13, 16, 19. Find the lower quartile.

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Answer: 6

  1. The median is the 4th value, 11.
  2. The lower quartile is the middle of 3, 6, 8, which is 6.
  • Method (1): The median is the 4th value, 11.
  • Accuracy (1): The lower quartile is the middle of 3, 6, 8, which is 6.

Question 2 Easy

Lower quartile 9 and upper quartile 25. Find the interquartile range.

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Answer: 16

  1. Subtract lower from upper quartile.
  2. 25 − 9 = 16.
  • Method (1): Subtract lower from upper quartile.
  • Accuracy (1): 25 − 9 = 16.

Question 3 Medium

The five-number summary is 4, 9, 13, 20, 28. State the median.

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Answer: 13

  1. The third number is the median.
  2. Median is 13.
  • Method (1): The third number is the median.
  • Accuracy (1): Median is 13.

Question 4 Medium

The five-number summary is 2, 6, 11, 15, 24. State the median.

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Answer: 11

  1. The third number is the median.
  2. Median is 11.
  • Method (1): The third number is the median.
  • Accuracy (1): Median is 11.

Question 5 Hard

The five-number summary is 1, 5, 8, 12, 18. State the range.

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Answer: 17

  1. Subtract minimum from maximum: 18 - 1 = 17.
  2. Range is 17.
  • Method (1): Subtract minimum from maximum: 18 - 1 = 17.
  • Accuracy (1): Range is 17.

Question 6 Hard

The five-number summary is 3, 7, 10, 16, 25. State the range.

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Answer: 22

  1. Subtract minimum from maximum: 25 - 3 = 22.
  2. Range is 22.
  • Method (1): Subtract minimum from maximum: 25 - 3 = 22.
  • Accuracy (1): Range is 22.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Lower quartile 12 and upper quartile 31. Find the interquartile range.

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Answer: 19

  1. Interquartile range = upper quartile - lower quartile.
  2. 31 - 12 = 19.
  • Method (1): Subtracts the quartiles: 31 - 12
  • Accuracy (1): 19

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Interquartile range is upper quartile minus

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Subtract lower quartile from upper quartile: UQ - LQ. Subtract lower quartile from upper quartile: UQ - LQ.

Check 2

Quartiles 9 and 20. The interquartile range is

  1. 11
  2. 12
  3. 29
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11 20 - 9 = 11.

Check 3

Quartiles 8 and 20. The interquartile range is

  1. 11
  2. 12
  3. 28
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12 20 minus 8 = 12.

Check 4

Ends 4 and 28. The range is

  1. 24
  2. 25
  3. 32
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24 28 minus 4 = 24.

Check 5

Ends 3 and 19. The range is

  1. 22
  2. 32
  3. 16
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16 19 minus 3 = 16.

Check 6

Five-number summary 4, 9, 13, 20, 28. The median is

  1. 13
  2. 12
  3. 26
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13 The middle value (third number) is 13.

Check 7

Five-number summary 2, 6, 11, 15, 24. The median is

  1. 6
  2. 11
  3. 24
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11 The middle value (third number) is 11.

Check 8

More spread means having a larger

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A larger IQR shows greater spread of the middle 50%. A larger IQR shows greater spread of the middle 50%.

Check 9

Interquartile ranges 12 and 7. The more spread set is

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12 is greater than 7, so set A is more spread. 12 is greater than 7, so set A is more spread.

Check 10

Interquartile ranges 5 and 9. The more spread set is

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9 is greater than 5, so set B is more spread. 9 is greater than 5, so set B is more spread.

Check 11

The third number in a five-number summary is the

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Minimum, lower quartile, median, upper quartile, maximum. Minimum, lower quartile, median, upper quartile, maximum.

Check 12

The first and last numbers in the summary make the

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Maximum minus minimum gives the full range. Maximum minus minimum gives the full range.

Check 13

Why is the interquartile range not the full range?

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It ignores the extreme top and bottom quarters. It ignores the extreme top and bottom quarters.

Check 14

Five-number summary 1, 5, 8, 12, 18. The range is

  1. 18
  2. 6
  3. 17
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17 18 minus 1 = 17.

Check 15

Where is the median represented on a box plot?

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The median is shown by a vertical line inside the central box. The median is shown by a vertical line inside the central box.

Keep going with Box plots

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