GCSE · Cumulative frequency & box plots

Box plotsExam-style questions

What each of the five marks on a box plot means, why the box holds the middle 50% of the data, and why a longer section means the data there is more spread out — never that there is more of it.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    The box plots give information about the marks scored in the same test by the students at School P and by the students at School Q.

    School P:10203040506070MarkSchool Q:10203040506070Mark(a) Compare the distribution of the marks at School P with the distribution of the marks at School Q.

    (b) 160160 students at School P took the test. Work out how many of them scored more than 5050 marks.
    Level 4 · 4 marksTry it
  2. 2
    The box plot gives information about the times, in minutes, that 8080 customers spent in a café one afternoon. One of the times is shown as a cross.1020304050607080Time (minutes)(a) Write down the longest of these times that is not an outlier.

    (b) Work out the interquartile range of the times.

    (c) Zak says, "The range of these times is 3535 minutes."

    Explain why Zak is wrong.
    Level 4 · 4 marksTry it
  3. 3
    The cumulative frequency graph gives information about the marks scored by 8080 students in a test.102030405060701020304050607080MarkCumulative frequencyThe lowest mark scored was 1212 and the highest mark scored was 6868.

    (a) Use the graph to draw a box plot for the marks.

    (b) Work out the interquartile range of the marks.
    Level 4 · 4 marksTry it
  4. 4
    A factory has two machines, AA and BB, that fill bags with pasta.

    The table gives information about the masses, in grams, of a sample of bags filled by machine AA.
    Mass (grams)
    Heaviest bag512512
    Upper quartile506506
    Median503503
    Interquartile range77
    Range1818
    (a) On the grid, draw a box plot for machine AA.

    Machine AA490495500505510515Mass (grams)(3 marks)

    The box plot below gives information about the masses of a sample of bags filled by machine BB.

    Machine BB490495500505510515Mass (grams)(b) Compare the distribution of the masses of the bags filled by machine AA with the distribution of the masses of the bags filled by machine BB.

    (2 marks)
    Level 4 · 5 marksTry it
  5. 5
    There are 4040 books on a shelf in a library.

    The table gives information about the numbers of pages in these books.
    Number of pages
    Fewest pages112112
    Lower quartile168168
    Median196196
    Upper quartile284284
    Most pages412412
    (a) Draw a box plot for this information.100150200250300350400450Number of pages(3 marks)
    (b) Work out an estimate for the number of these books with more than 168168 pages.

    (1 mark)

    Rhys says,

    "More of these books have between 196196 and 284284 pages than have between 168168 and 196196 pages."
    (c) Is Rhys correct? Give a reason for your answer.

    (1 mark)
    Level 4 · 5 marksTry it