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Cumulative Frequency
- The cumulative frequency is obtained by adding up the frequencies as you go along to give a 'running total'.
- For example,
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/944198_349070.png)
- 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.
- The points are plotted at the upper class boundary.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/195255_541788.png)
- 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 vertical axis.
There are no values below 20.5 cm.
- 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 S-shape.
- 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.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/899278_147854.png)
- Quartiles are associated with quarters.
- The interquartile range is the difference between the lower quartile and the upper quartile.
- From these values we can also estimate the interquartile range:
33 - 27 = 6 - Remember to use the total frequency, not the maximum value on the vertical axis. The values are always read from the horizontal axis.
That's the end of the topic!
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/522007_168269.png)
Drafted by Bonnie (Mathematics)