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Cumulative frequency diagrams
The cumulative frequency is obtained by adding up the frequencies as you go along to give a
Drawing a cumulative frequency diagram
The table shows the lengths (in cm) of 32 cucumbers.
Before drawing the cumulative frequency diagram, we need to work out the cumulative
frequencies. This is done by adding the frequencies in turn.
Length Frequency Cumulative Frequency
21 24 3 3
25 28 7 10 (= 3 + 7)
29 32 12 22 (= 3 + 7 + 12)
33 36 6 28 (= 3 + 7 + 12 + 6)
37 40 4 32 (= 3 + 7 + 12 + 6 + 4)
The points are plotted at the upper class boundary. In this example the upper class
boundaries are 24.5, 28.5, 32.5, 36.5 and 40.5. Cumulative frequency is plotted on the
There are no values below 20.5cm.
Remember, cumulative frequency graphs are always plotted using the highest value in each
group of data and the cumulative frequency is always plotted up a graph, never across.
The cumulative frequency diagram always has this characteristic Sshape.
Finding the median and quartiles
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When looking at a cumulative frequency curve you will need to know how to find its median,
lower and upper quartiles and the interquartile range.
By drawing horizontal lines to represent 1/4 of the total frequency, 1/2 of the total frequency
and 3/4 of the total frequency, we can read estimates of the lower quartile, median and upper
quartile from the horizontal axis.
Quartiles are associated with quarters. The interquartile range is the difference between the
lower quartile and the upper quartile.…read more