Edexcel IGCSE Maths

Revision Notes

6.3.1 Cumulative Frequency

What does cumulative frequency mean?

  • Cumulative basically means “adding up as you go along”
  • So cumulative frequency means all of the frequencies for the different classes, totalled
  • This allows us to draw a cumulative frequency graph, from which we can find useful information such as the median and quartiles

What do I need to know?

  • You will either be asked to draw a cumulative frequency graph or analyse one
  • It is also possible to draw a box plot from a cumulative frequency graph and you could be asked to compare the data with another set of data (see Box Plots)

1. Drawing a cumulative frequency graph

  • This is best explained with an example
  • For example, the times taken to complete a short general knowledge quiz taken by 50 students are shown in the table below:

Cumulative Frequency RN 1, downloadable IGCSE & GCSE Maths revision notes

  • When asked to find the cumulative frequencies you may be given another table – or the table above will have an extra column on it
  • You should be aware of both possibilities although the process is the same

Cumulative Frequency RN 2, downloadable IGCSE & GCSE Maths revision notes

  • Note the cumulative frequencies are found in exactly the same way whichever version you may come across but we’ve shown two different ways of thinking about it
  • Now you have your cumulative frequencies you can draw a graph from it
  • The key here is that cumulative frequencies are plotted against the end (upper bound) of the class interval
  • This is because you can’t say, for example, you have covered all 11 students (2nd row of table) until you have reached 35 seconds
  • After 30 seconds (start) only 3 people had finished the quiz and you cannot tell how many had finished by 32.5 seconds (midpoint)

CF1 General Knowledge, IGCSE & GCSE Maths revision notes

Worked Example

Cumulative Frequency Example 1, IGCSE & GCSE Maths revision notes

CF2 Length of phone calls, IGCSE & GCSE Maths revision notes

(a)

Q1a-Finding-Q1,Q2,Q3

Cumulative Frequency Worked Example 2

(b)

Q1b 12min Cut Off, IGCSE & GCSE Maths revision notes

Cumulative Frequency Worked Example 3

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