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.frequency table exampleNotice 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 quartilecumulative frequency graph showing median, quartile one and quartile three.So 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.