[discia] GCSE Maths › Statistics › Box Plots

Box Plots

discia.org 10 questions · 35 marks
Name Date
  1. Either paper 4 marks

    The box plot shows information about the times taken by a group of students to solve a puzzle.

    05101520253035time (minutes)
    (a)

    State the median time.

    (b)

    Calculate the range of the times.

    (c)

    Calculate the interquartile range of the times.

    Show answer
    (a) \(25\ \text{minutes}\)
    (b) \(24\ \text{minutes}\)
    (c) \(11\ \text{minutes}\)
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  2. Either paper 5 marks

    Here are the numbers of goals scored by eleven hockey players last season.

    \(16,\ 19,\ 10,\ 30,\ 6,\ 33,\ 43,\ 38,\ 14,\ 27,\ 23\)

    (a)

    Find the median.

    (b)

    Find the interquartile range.

    (c)

    A box plot is to be drawn for this data.

    Write down the five values it needs.

    Show answer
    (a) \(23\ \text{goals}\)
    (b) \(19\ \text{goals}\)
    (c) \(6\), \(14\), \(23\), \(33\), \(43\)
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  3. Either paper 2 marks

    The box plot shows information about the marks scored by a class in a science test.

    05101520253035mark

    One of the students had a mark of \(14\) marks.

    Is that mark in the bottom 25% of the marks? Give a reason for your answer.

    Show answer
    No
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  4. Either paper 4 marks

    In a survey, 50 patients at each of four surgeries were timed from arriving to seeing a doctor.

    The box plots show the results.

    010203040506070waiting time (minutes)Elm RoadFairviewGreenlaneHillcrest
    (a)

    At which surgery were the waiting times most consistent, judged by the interquartile range?

    Give a reason for your answer.

    (b)

    On average, which surgery had the lowest waiting times?

    Give a reason for your answer.

    Show answer
    (a) Elm Road. The interquartile range for Elm Road is \(4\) minutes, which is smaller than the other three (the next smallest is \(7\) minutes).
    (b) Greenlane. The median for Greenlane is \(32\) minutes, which is lower than the other three (the next lowest is \(35\) minutes).
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  5. Either paper 4 marks

    The box plots show information about the waiting times at two health centres one morning.

    05101520253035waiting time (minutes)OakfieldRiverside
    (a)

    Find the interquartile range of the waiting times for Oakfield.

    (b)

    Compare the waiting times for Oakfield with the waiting times for Riverside.

    Make one comparison about the average and one about the spread.

    Show answer
    (a) \(8\ \text{minutes}\)
    (b) The median for Riverside is higher, \(21\) minutes against \(16\) minutes, so on average the waiting times for Riverside were greater. The interquartile range for Oakfield is smaller, \(8\) minutes against \(11\) minutes, so the waiting times for Oakfield were more consistent.
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  6. Either paper 3 marks

    The table shows information about the marks scored by a class in a test. No diagram has been drawn.

    Smallest mark\(7\) marks
    Lower quartile\(14\) marks
    Median\(19\) marks
    Range\(24\) marks
    Interquartile range\(10\) marks
    (a)

    Work out the largest mark.

    (b)

    Work out the upper quartile.

    (c)

    A box plot is to be drawn from this information.

    Write down, in order, the five values it needs.

    Show answer
    (a) \(31\ \text{marks}\)
    (b) \(24\ \text{marks}\)
    (c) \(7\), \(14\), \(19\), \(24\), \(31\)
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  7. Either paper 2 marks

    The box plot shows information about the marks scored by a class in a science test.

    051015202530354045mark

    Marcus looks at the box plot and says:

    "More students have a mark between the lower quartile and the median than between the median and the upper quartile, because that part of the box is wider."

    Is he correct? Explain your answer.

    Show answer
    No
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  8. Either paper 3 marks

    The box plot shows information about the heights of the tomato plants grown in a greenhouse trial.

    051015202530354045height (cm)

    Work out what percentage of the range is covered by the interquartile range.

    Show answer
    \(20\ \%\)
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  9. Either paper 5 marks
    The box plot shows information about the scores achieved by students on a quiz in 2022. 0510152025303540the scores achieved by students on a quiz The table shows information about the scores achieved by students on a quiz in 2021.
    marks
    Lower quartile19
    Median25
    Upper quartile31
    (a)

    In 2022, what was the lowest score?

    (b)

    Use the data to comment on this statement.

    "On average, scores were higher in 2022 than in 2021."

    (c)

    Use the data to comment on this statement.

    "The scores were equally consistent in 2022 and 2021."

    Show answer
    (a) \(15\ \text{marks}\)
    (b) Agree. The median for 2022 is \(28\) marks and the median for 2021 is \(25\) marks, so on average the scores were higher in 2022 than in 2021.
    (c) Agree. The interquartile range for 2022 is \(33 - 21 = 12\) marks and for 2021 it is \(31 - 19 = 12\) marks.
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  10. Either paper 3 marks
    Here is some information about the times, in minutes, that some students spent on homework one evening.
    Shortest time8 minutes
    Longest time30 minutes
    Upper quartile24 minutes
    Median18 minutes
    Interquartile range14 minutes
    Draw a box plot to show this information. 010203040Time (minutes)
    Show answer
    A box plot with minimum 8, lower quartile 10, median 18, upper quartile 24 and maximum 30 minutes
    010203040Time (minutes)
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discia.org Box Plots · sheet 1
Answers Box Plots · sheet 1
  1. (a) \(25\ \text{minutes}\)
    (b) \(24\ \text{minutes}\)
    (c) \(11\ \text{minutes}\)
  2. (a) \(23\ \text{goals}\)
    (b) \(19\ \text{goals}\)
    (c) \(6\), \(14\), \(23\), \(33\), \(43\)
  3. No
  4. (a) Elm Road. The interquartile range for Elm Road is \(4\) minutes, which is smaller than the other three (the next smallest is \(7\) minutes).
    (b) Greenlane. The median for Greenlane is \(32\) minutes, which is lower than the other three (the next lowest is \(35\) minutes).
  5. (a) \(8\ \text{minutes}\)
    (b) The median for Riverside is higher, \(21\) minutes against \(16\) minutes, so on average the waiting times for Riverside were greater. The interquartile range for Oakfield is smaller, \(8\) minutes against \(11\) minutes, so the waiting times for Oakfield were more consistent.
  6. (a) \(31\ \text{marks}\)
    (b) \(24\ \text{marks}\)
    (c) \(7\), \(14\), \(19\), \(24\), \(31\)
  7. No
  8. \(20\ \%\)
  9. (a) \(15\ \text{marks}\)
    (b) Agree. The median for 2022 is \(28\) marks and the median for 2021 is \(25\) marks, so on average the scores were higher in 2022 than in 2021.
    (c) Agree. The interquartile range for 2022 is \(33 - 21 = 12\) marks and for 2021 it is \(31 - 19 = 12\) marks.
  10. A box plot with minimum 8, lower quartile 10, median 18, upper quartile 24 and maximum 30 minutes
    010203040Time (minutes)
discia.org Box Plots · sheet 1