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.
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.
- Drawing a Cumulative Frequency Graph
This is best explained with an example.
eg 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.
Version 1 – an extra column in the original table:
Version 2 – a new table with the class intervals all starting at the same value – the lowest in the data – for this example this is 25 but will often be 0.
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).