Discia GCSE Maths › Statistics › Box Plots

Box Plots worksheet

7 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

7 questions 26 marks Sheet 1
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  1. 4 marks

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

    A box plot drawn against a numbered scale: whiskers out to the smallest and largest values, a box from the lower quartile to the upper quartile, and the median marked by a line inside the box05101520253035time (minutes)
    (a)

    State the median time.

    (b)

    Calculate the range of the times.

    (c)

    Calculate the interquartile range of the times.

  2. 4 marks

    The box plots show information about the times taken by two classes to finish a puzzle.

    Two box plots drawn one above the other against the same numbered scale, so the two distributions can be compared directly0510152025303540time (minutes)Class AClass B
    (a)

    Find the interquartile range of the times for Class A.

    (b)

    Compare the times for Class A with the times for Class B.

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

  3. 3 marks

    The table shows information about the times taken by a group of students to solve a puzzle. No diagram has been drawn.

    Smallest time\(5\) minutes
    Lower quartile\(15\) minutes
    Median\(23\) minutes
    Range\(33\) minutes
    Interquartile range\(14\) minutes
    The box plot the five numbers describe, with each value written above it0510152025303540time (minutes)515232938
    (a)

    Work out the largest time.

    (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.

  4. 4 marks

    The box plot shows information about the heights of the plants in a greenhouse. There were 28 plants altogether.

    A box plot with the five values written above it: the smallest value, the lower quartile, the median, the upper quartile and the largest value05101520253035height (cm)1217232634
    (a)

    Work out how many of the plants had a height of more than \(26\) cm.

    (b)

    Work out how many of the plants had a height of less than \(23\) cm.

    (c)

    State the interquartile range.

  5. 4 marks

    The box plot shows information about the waiting times at a health centre one morning.

    A box plot drawn against a numbered scale: whiskers out to the smallest and largest values, a box from the lower quartile to the upper quartile, and the median marked by a line inside the box05101520253035waiting time (minutes)
    (a)

    State the median waiting time.

    (b)

    Work out the range of the waiting times.

    (c)

    Work out the interquartile range of the waiting times.

  6. 4 marks

    The box plots show information about the times taken by two classes to finish a puzzle.

    Two box plots drawn one above the other against the same numbered scale, so the two distributions can be compared directly05101520253035time (minutes)Class AClass B
    (a)

    Work out the interquartile range of the times for Class A.

    (b)

    Compare the times for Class A with the times for Class B.

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

  7. 3 marks

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

    Smallest mark\(9\) marks
    Lower quartile\(13\) marks
    Median\(17\) marks
    Range\(20\) marks
    Interquartile range\(8\) marks
    The box plot the five numbers describe, with each value written above it051015202530mark913172129
    (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.

Answers

  1. (a) \(25\ \text{minutes}\)
    (b) \(24\ \text{minutes}\)
    (c) \(11\ \text{minutes}\)
  2. (a) \(9\ \text{minutes}\)
    (b) The median for Class A is higher, \(23\) minutes against \(11\) minutes, so on average the times for Class A were greater. The interquartile range for Class B is smaller, \(6\) minutes against \(9\) minutes, so the times for Class B were more consistent.
  3. (a) \(38\ \text{minutes}\)
    (b) \(29\ \text{minutes}\)
    (c) \(5\), \(15\), \(23\), \(29\), \(38\)
  4. (a) \(7\ \text{plants}\)
    (b) \(14\ \text{plants}\)
    (c) \(9\ \text{cm}\)
  5. (a) \(21\ \text{minutes}\)
    (b) \(25\ \text{minutes}\)
    (c) \(14\ \text{minutes}\)
  6. (a) \(14\ \text{minutes}\)
    (b) The median for Class A is higher, \(20\) minutes against \(17\) minutes, so on average the times for Class A were greater. The interquartile range for Class B is smaller, \(11\) minutes against \(14\) minutes, so the times for Class B were more consistent.
  7. (a) \(29\ \text{marks}\)
    (b) \(21\ \text{marks}\)
    (c) \(9\), \(13\), \(17\), \(21\), \(29\)

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