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Cumulative frequency graphs and box plots are powerful tools for summarising and comparing distributions. These are Higher-tier staples on the Edexcel GCSE, though some Foundation questions also appear.
| Term | Definition |
|---|---|
| Cumulative frequency | A running total of frequencies |
| Cumulative frequency graph | An S-shaped curve plotted using upper class boundaries vs cumulative frequency |
| Box plot (box-and-whisker diagram) | A diagram showing the minimum, Q1, median, Q3 and maximum |
| Median | The middle value (50th percentile); read from the cumulative frequency graph at n/2 |
| Lower quartile (Q1) | 25th percentile; read at n/4 |
| Upper quartile (Q3) | 75th percentile; read at 3n/4 |
| Interquartile range (IQR) | Q3 − Q1 |
Add a cumulative frequency column by keeping a running total of the frequencies.
Worked Example: The table shows the time (t minutes) taken by 80 students to complete a task.
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