The cumulative frequency is a running total of how many results you have had so far. 

For example, in the second histogram example, 5 people scored 25% or less. To find how many people scored 45% or less, we would need to add a further 8 students to this. Therefore 13 students scored 45% or less. Using the same process, 20 students scored 55% or less. Adding a cumulative frequency row to the table  gives:

The final cumulative frequency will be the total number of students.

The cumulative frequency can be drawn on a graph. One area of confusion with these graphs, is what value to plot on the x-axis. You plot each frequency against the largest value (Not the midpoint of the group). So you plot the points (25,5),(45,13),(55,20),(65,32),(70,42),(80,52),(100,58)

The points are joined with straight lines, to form the distinctive shape of a cumulative frequency graph.

What is the point of cumulative frequency? Well it allows you to easily gauge the performance/value of a specific section of the population. For example, if you want to know the scores being achieved by the top 20% of students, you simply go to 80% of the cumulative frequency (46.4), go across to the line and then down to the score

This tells you that the top 20% of students, are scoring more than 74.4%.

Finding the Median

The most common value to find from a cumulative frequency curve, is the median, the value of the middle person. In this case, there are 58 students. Does make the 29th student the middle student? No, because the 29th person has 28 below and 29 above. Equally, the 30th person has 29 below and only 28 above. Instead we will take the 29.5th person (This will be explained in more detail later).

In the next section, on finding averages, we will see how to calculate medians, but a graph gives a good indication.

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