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.