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Cumulative frequency Cambridge IGCSE Mathematics (9–1) revision

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In plain words

Cumulative means "running total". A cumulative frequency graph shows how many values are below each point, and its S-shaped curve makes it easy to read off the middle value and how spread out the data is.

Three things to know

  1. Cumulative frequency is a running total of the frequencies. Plot each total against the top of its group, and join the points with a smooth curve.
  2. Median: read across from half the total frequency. Lower quartile: from a quarter. Upper quartile: from three quarters.
  3. Interquartile range = upper quartile − lower quartile. It measures the spread of the middle half of the data, so it isn't affected by extreme values.

Worked example

A cumulative frequency graph shows the heights of 80 plants. At which cumulative frequencies do you read off the median and the quartiles?

  1. Median: half of 80 = 40.
  2. Lower quartile: a quarter of 80 = 20. Upper quartile: three quarters of 80 = 60.
  3. Read across from each to the curve, then down to the height axis.

Tips and tricks

  • Plot at the upper end of each group, not the middle.
  • To find how many are above a value, read the cumulative frequency there and subtract it from the total.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Cumulative frequency: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is cumulative frequency?
    • the largest frequency
    • a running total of the frequencies (the answer)
    • the mean frequency
    • the frequency squared

    Each value includes all the ones before it.

  2. For 120 values, at what cumulative frequency is the median?
    • 30
    • 60 (the answer)
    • 90
    • 120

    Half of 120.

  3. How is the interquartile range found?
    • largest − smallest
    • upper quartile − lower quartile (the answer)
    • median − lower quartile
    • upper quartile + lower quartile

    It is the spread of the middle half.

  4. For 80 values, at what cumulative frequency is the lower quartile?
    • 10
    • 20 (the answer)
    • 40
    • 60

    A quarter of 80.

  5. Where is each point plotted on a cumulative frequency graph?
    • at the middle of the group
    • at the lower end of the group
    • at the upper end of the group (the answer)
    • at the origin

    The running total has been reached by the top of the group.

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