# Cumulative Frequency

Cumulative frequency means you just keep a running total as you go along.

Example: The table below shows the lengths of 32 bananas. Draw a cumulative frequency graph and estimate the median interquartile range.Notice the cumulative frequency column is just a running total of the frequency column…so if you’re asked to do this in an exam it will be a piece of cake!

To Draw The Graph

• Put cumulative freuquency on the y axis, and height (or whatever you are dealing with in the question) on the x axis.
• Plot points using the highest value in each class
• Plot a point at 0 for the lowest point in the lowest class
• Join the points with a smooth curve

To Find The Median And Interquartile Range

• Go halfway up the values of the cumulative frequency on the y axis. Here the values go up to 32, so you would go to 16. Then go across to the curve and then down to the x axis to read the height value
• For the upper quartile do the same but this time go three quarters up the y axis (i.e. 24)
• For the lower quartile do the same but this time go a quarter up the y axis (i.e. 8)
• To find the interquartile range take the value of the lower quartile away from the value for the upper quartileSo here you can see:

Median = 30.5
upper quartile = 33.5
lower quartile = 27.5
interquartile range = 33.5 – 27.5 = 6

Note: If in an exam they ask you to estimate the number of values less than a given value just go along the bottom scale to this number then up to the curve and along to cumulative frequency.