Cumulative Frequency (Cambridge (CIE) IGCSE Maths)

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.