Revision notes
Build running totals, draw an ogive and read off the median and quartiles of grouped data.
Mrs Okafor has grouped her class's test marks into classes like 1–10, 11–20 and so on. She can't list every mark, but a running total of the frequencies — and a smooth curve drawn from it — shows the median straight away.
The cumulative frequency of a class is the frequency of that class plus all the classes before it.
Marks 1–10: 4 students, 11–20: 7, 21–30: 9 give cumulative frequencies 4, 4 + 7 = 11 and 11 + 9 = 20.
The 11 tells you that 11 students scored 20 marks or less. The last cumulative frequency is always the total, n.
🔑 Key idea: Cumulative frequency = running total; the last one equals n.
Plot each cumulative frequency against the upper class boundary (for 1–10 that is 10.5), because by the end of the class everyone in it has been counted.
Start the curve at 0 on the lower boundary of the first class (0.5), then join the points with a smooth S-shaped curve called an ogive.
A running total can never go down, so the ogive always rises or stays level.
🔑 Key idea: Plot cumulative frequency against the upper class boundary and join with a smooth curve.
For grouped data on an ogive, read the median at n/2, the lower quartile Q₁ at n/4 and the upper quartile Q₃ at 3n/4.
With n = 40: median at 20, Q₁ at 10, Q₃ at 30. Go across to the curve, then down to read the mark.
The interquartile range is Q₃ − Q₁ (the spread of the middle half); the semi-interquartile range is half of it.
🔑 Key idea: Median at n/2, Q₁ at n/4, Q₃ at 3n/4; IQR = Q₃ − Q₁.
Marks in a test (marks: number of students) — 1–5: 3, 6–10: 9, 11–15: 8, 16–20: 10, 21–25: 10. What is the cumulative frequency of the class 6–10?
Step 1: Add up to this class
Running total: 3 + 9 = 12
Why? This counts every student who scored 10 marks or less.
Answer: 12
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.