Cumulative Frequency (Edexcel IGCSE Maths A (Modular))

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Cumulative Frequency

What is cumulative frequency?

  • Cumulative refers to a “running total" or "adding up as you go along”

  • So in a table of grouped data

    • cumulative frequency means all of the frequencies for the different groups totalled up to the end of the group in a given row

  • When working out cumulative frequencies you may see tables presented in two ways

    • A regular grouped data table with an extra column for cumulative frequencies

      • E.g. rows labelled 0 ≤ x < 20, 20 ≤ x < 40, 40 ≤ x < 60, etc

        Group

        Frequency

        Cumulative frequency

        0 ≤ x < 20

        14

        14

        20 ≤ x < 40

        25

        39

        (because 14+25=39)

        40 ≤ x < 60

        29

        68

        (because 14+25+29=68)

        60 ≤ x < 80

        12

        80

        (because 14+25+29+12=80)

    • or a separate table where every group is relabelled as starting at the beginning (often zero)

      • E.g. rows labelled 0 ≤ x < 20, 0 ≤ x < 40, 0 ≤ x < 60, etc.

      • Or x < 20, x < 40, x < 60, etc.

        Group

        Cumulative frequency

        0 ≤ x < 20

        (or x < 20)

        14

        0 ≤ x < 40

        (or x < 40)

        39

        0 ≤ x < 60

        (or x < 60)

        68

        0 ≤ x < 80

        (or x < 80)

        80

    • In the second type of table, you can subtract to find the individual frequencies

      • E.g. the frequency of the 20 ≤ x < 40 class interval is 39-14=25

      • The frequency of the 40 ≤ x < 60 class interval is 68-39=29, etc.

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Roger B

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Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.