Cumulative frequency tables

Cumulative frequency is a running total of the frequencies. This can be represented on a graph by plotting the upper boundary of the groups.


Look at this table:

Two column table of 'X' and 'Frequency'

To create a cumulative frequency table all we need to do is add the frequencies together as we progress down the column.

Two column table of 'X' and 'Cumulative frequency'

You can see that there is a total frequency of 20 as this is the number in the last column. While the cumulative frequency column may be harder to interpret, it allows us to construct an effective graphical representation of the data.

This table shows the scores that were obtained by students in an English class:

Two column table of 'English score' and 'Frequency'

This table is very similar to the first table but you may have noticed that the class intervals are not the same. The first and last groups cover 20 possible numbers while the central two groups cover only 10 possible outcomes.

Two column table of 'English score' and 'Cumuative frequency'
The cumulative frequency table is constructed in exactly the same way as before. The process is the same even though the class width is different.
Two column table of 'Height (cm)' and 'Frequency'

Create a cumulative frequency table for the following information:

Two column table of 'Height (cm)' and 'Cumulative Frequency'

This table shows continuous data. Continuous data is data that can have any numerical value such as height or weight. Shoe size and colour would be two examples of discrete data. Data is grouped at the upper class boundary, eg 99.5, 129.5, 139.5 and 200.5.