Read and Interpret Cumulative Frequency Graphs

What is cumulative frequency?

 

 

Cumulative frequency is how many data points there are equal to or less than a certain value.

We find it by adding up ('accumulating') all the frequencies up to that point.

 

So for example, we could have:

 

Hours (h)	Frequency	Cumulative Frequency
0 ≤ h < 2	5	5
2 ≤ h < 4	8	5 + 8 = 13
4 ≤ h < 6	10	13 + 10 = 23
6 ≤ h < 8	7	23 + 7 = 30
8 ≤ h < 10	3	30 + 3 = 33

 

In cumulative frequency graphs, we have the cumulative frequency on the y-axis and what we are measuring on the x-axis (e.g. number of hours spent studying here):

 

 

We can use this graph to find estimates for cumulative frequencies and quartiles.

 

Let's say we wanted to find the estimate for how many students study up to 3 hours, i.e. the cumulative frequency for 3.

Then we just draw a line from 3 to the curve and then to the y-axis!

 

 

The cumulative frequency for 3 is approximately 9 - so there are 9 students who study up to 3 hours!

 

We can also find quartiles.

 

For example, we know that the lower quartile is the value such that a quarter (25%) of the data is below or equal to it.

Here, we can see that we have 33 data points in total (the y-coordinate of the last point).

 

A quarter of 33 is:

33 ÷ 4 = 8.25

 

So the lower quartile will be the value that corresponds to the cumulative frequency of 8.25:

 

 

That value seems to be just under 3 - so the estimate of the lower quartile is 2.8!

 

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