IGCSE Maths Cumulative Frequency & Box Plots Notes
Cumulative frequency adds up frequencies as you go. The graph is used to estimate the median, quartiles and interquartile range.
Key concepts
- Cumulative frequency
- Running total of frequencies, plotted at the upper class boundary.
- Median & quartiles
- Read off at ½, ¼ and ¾ of the total frequency.
- Box plot
- Shows minimum, lower quartile, median, upper quartile and maximum.
Key formulas
Interquartile range
IQR = upper quartile − lower quartile
Median position
at n/2 on the cumulative axis
Worked example
60 values are recorded. At what cumulative frequency is the lower quartile read?
- 1Lower quartile is at ¼ of the total.
- 2¼ × 60 = 15.
- 3Read across from cumulative frequency 15.
Answer: Read at cumulative frequency 15
Common mistakes
✗ Plotting at midpoints, not upper boundaries.
✓ Plot cumulative frequency at the upper class boundary.
✗ Reading quartiles from the wrong axis.
✓ Use fractions of the total frequency, then read across to the value.
✗ Computing IQR from min and max.
✓ IQR uses the quartiles, not the extremes.
Quick check
Try these, then reveal the answers.
IQR from Q1 = 20, Q3 = 35?Reveal answer
15
Median position for n = 80?Reveal answer
40
Plot cumulative frequency at the … boundary?Reveal answer
Upper
Exam tips
- Join cumulative frequency points with a smooth curve.
- Use dashed construction lines to show how you read the median and quartiles.
- Compare box plots by median and IQR together.
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Frequently asked questions
Where do I plot cumulative frequency points?+
At the upper boundary of each class interval, against the running total of frequencies.
What does a box plot show?+
The minimum, lower quartile, median, upper quartile and maximum — a five-number summary of the data.
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