# 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: • 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
• 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)

### Worked Example

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