GCSE · Cumulative frequency & box plots

Cumulative frequency diagramsExam-style questions

How to build a running total from a grouped frequency table, why every point is plotted at the upper class boundary rather than the midpoint, and how to read estimates off the curve in both directions.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    The cumulative frequency graph gives information about the times, in minutes, that 6060 students took to finish a puzzle.510152025303540102030405060Time (minutes)Cumulative frequency(a) Use the graph to find an estimate for the median time. (1 mark)
    (b) Use the graph to find an estimate for the interquartile range of the times. (2 marks)
    (c) Use the graph to find an estimate for the number of students who took longer than 2525 minutes. (1 mark)
    Level 3 · 4 marksTry it
  2. 2
    The table shows the amounts spent in one week by 80 shoppers at a supermarket.
    Amount spent, xx (£)Frequency
    0<x≤200 < x \le 208
    20<x≤4020 < x \le 4022
    40<x≤6040 < x \le 6026
    60<x≤8060 < x \le 8017
    80<x≤10080 < x \le 1007
    (a) Write down the cumulative frequency for each of the five classes.

    (b) Draw a cumulative frequency diagram for this information.

    (c) Use your diagram to estimate the number of shoppers who spent £50 or less.
    Level 3 · 5 marksTry it
  3. 3
    The cumulative frequency diagram shows the number of hours that each of 100 students spent revising in one month.51015202520406080100Revision time (hours)Cumulative frequency(a) Use the diagram to estimate the number of students who revised for 12 hours or less.

    (b) 7575 of the students revised for less than hh hours. Use the diagram to estimate the value of hh.

    (c) Explain why your answer to part (a) can only be an estimate.
    Level 3 · 5 marksTry it
  4. 4
    The cumulative frequency graph shows the times, in minutes, taken by 8080 students to travel to school.1020304050601020304050607080Time (minutes)Cumulative frequency(a) Estimate the median time. [1]

    (b) Estimate the interquartile range. [2]

    (c) Estimate the number of students who took longer than 4545 minutes. [1]
    Level 3 · 4 marksTry it