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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,

- 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.

- 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.

- 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!

Drafted by Bonnie (Mathematics)