We use cumulative frequencies to describe intervals and ranges of data. For example, consider the boxes with between 27 and 29 raisins, inclusively, which are represented in blue on the line plot:
The number of boxes with between 27 and 29 raisins (12) is easy to determine from this line plot, but in problems with very large data sets, this might not be the case.
Here's how a cumulative frequency table can be used to answer the question of how many boxes have between 27 and 29 raisins, inclusively. First, look at the number of boxes with counts of 29 or smaller. There are 15 of these, represented in red on the frequency table and line plot:
Remove the boxes that have fewer than 27 raisins. There are three of these, highlighted in green on the frequency table and line plot:
The number of remaining boxes is:
15 - 3 = 12
Therefore, there are 12 boxes that contain between 27 and 29 raisins.