M4.7.3 For the adult
Cumulative frequency
A bus company times 80 journeys and sorts the times into classes. How can one graph show the middle time, and how many journeys took under 25 minutes?
What this chapter teaches
A cumulative frequency is a running total, plotted at the upper boundary of each class and joined with straight lines. The median and quartiles are read at n ÷ 2, n ÷ 4 and 3n ÷ 4. The interquartile range, Q3 − Q1, is the spread of the middle half.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why is a cumulative frequency plotted at the upper boundary of a class, not at its middle?
- For 80 values, where do you read the lower quartile, the median and the upper quartile?
- Why can the interquartile range tell us more about spread than the range does?
After the chapter, the learner can
- Draw a cumulative frequency graph
- Read the median and quartiles from the graph
- Find the interquartile range
What they copy into their notebook
Cumulative frequency is a running total, plotted at the upper boundary. Read the median at n ÷ 2, Q1 at n ÷ 4, Q3 at 3n ÷ 4. IQR = Q3 − Q1.