Cumulative Frequency (Cambridge International IGCSE Mathematics)

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.