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At GCSE you extend data representation to cumulative frequency graphs, box plots, histograms with frequency density, and more advanced comparison of distributions. You also study sampling methods and make inferences about populations.
Mean, median, mode and range from raw data and frequency tables — see KS3 lesson for details.
Mean from a grouped frequency table: Estimated mean = sum(f × midpoint) / sum(f)
Cumulative frequency is the running total of frequencies.
Plotting: plot (upper class boundary, cumulative frequency), then join with a smooth S-shaped curve.
| Height h (cm) | Frequency | Cumulative Frequency |
|---|---|---|
| 140 ≤ h < 150 | 4 | 4 |
| 150 ≤ h < 160 | 12 | 16 |
| 160 ≤ h < 170 | 20 | 36 |
| 170 ≤ h < 180 | 14 | 50 |
Reading off the graph:
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