Cumulative frequency diagrams and box plots are powerful tools for comparing data distributions. They're essential Higher GCSE topics.
Cumulative Frequency
Cumulative frequency is a running total of frequencies.
Drawing the Diagram
- Create a cumulative frequency column.
- Plot points at the upper class boundary vs. cumulative frequency.
- Join with a smooth curve.
Reading Off Values
- Median: read across from on the y-axis.
- Lower quartile (Q1): from .
- Upper quartile (Q3): from .
- Interquartile range (IQR): .
Box Plots
A box plot shows: minimum, Q1, median, Q3, maximum.
Drawing
Box from Q1 to Q3, line at median, whiskers to min and max.
Comparing Box Plots
Compare: medians (central tendency), IQR (spread), range.
Worked Example
| Time | Freq | Cum Freq |
|---|---|---|
| 0-10 | 5 | 5 |
| 10-20 | 12 | 17 |
| 20-30 | 18 | 35 |
| 30-40 | 10 | 45 |
| 40-50 | 5 | 50 |
. Median at → read off ≈ 24 minutes.
Q1 at 12.5 → ≈ 17 min. Q3 at 37.5 → ≈ 33 min. IQR = 16 min.
Practice Problems
- Draw a cumulative frequency curve from grouped data.
- Find the median and IQR from a cumulative frequency graph.
- Draw a box plot from: min=5, Q1=12, median=18, Q3=25, max=32.
Want to check your answers and get step-by-step solutions?
Key Takeaways
Plot cumulative frequency at upper class boundaries.
Read median at , Q1 at , Q3 at .
IQR = Q3 − Q1 measures spread.
Box plots allow quick comparison of distributions.