Drawing Cumulative Frequency Diagrams (Edexcel IGCSE Maths)

Spec point — 6.1B

Drawing cumulative frequency diagrams

What is a cumulative frequency diagram?

• A cumulative frequency diagram is a way of representing grouped continuous data

• A cumulative frequency diagram can be used to estimate other statistical values

  • For example the median, quartiles or percentiles

How do I draw a cumulative frequency diagram?

• This is best explained with an example

  • The times taken to complete a short general knowledge quiz taken by 50 students are shown in the table below: | Time taken ($s$seconds) | Frequency | |---|---| | $25\leq s<30$ | 3 | | $30\leq s<35$ | 8 | | $35\leq s<40$ | 17 | | $40\leq s<45$ | 12 | | $45\leq s<50$ | 7 | | $50\leq s<55$ | 3 | | Total | 50 |
  • Then the cumulative frequency is the running total of the frequencies | Time taken ($s$seconds) | Frequency | Cumulative Frequency | |---|---|---| | $25\leq s<30$ | 3 | 3 | | $30\leq s<35$ | 8 | 3 + 8 = 11 | | $35\leq s<40$ | 17 | 11 + 17 = 28 | | $40\leq s<45$ | 12 | 28 + 12 = 40 | | $45\leq s<50$ | 7 | 40 + 7 = 47 | | $50\leq s<55$ | 3 | 47 + 3 = 50 | | Total | 50 | |

• We can now draw the cumulative frequency diagram

  • The most important part is that cumulative frequency is plotted against the end(upper bound) of the class interval

    • The end of the class interval is the *x-*coordinate
    • The cumulative frequency is the *y-*coordinate
    • For the above example the first two points to plot would be (30, 3) and (35, 11)

  • To explain this, consider the second row ($30\leq s<35$)

    • The 8 students in this group could have taken any time between 30 and 35 seconds
    • They cannot all be guaranteed to have been accounted for until we reach 35 seconds

  • Once all points from the table are plotted, a point for the start needs to be added

    • This will be at the lowest time from the table
    • i.e. at 25 seconds with a cumulative frequency of 0
    • Plot the point (25, 0)

  • Join points up with a smooth curve (this takes some practice)

    • Make sure it goes through all of the marked points

  • In general a cumulative frequency diagram has a stretched-S-shape appearance

    • A cumulative frequency diagram will never come back towards the x-axis

• Here is the final cumulative frequency diagram for the quiz times

Example of a cumulative frequency diagram