Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want cumulative frequency — building tables, drawing curves and reading medians and quartiles — to become a reliable source of marks instead of a graph they misread under exam pressure.
What query it owns: how to understand and revise cumulative frequency in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the cumulative frequency revision-guide angle, while Tutopiya’s Cumulative Frequency subtopic page owns the learning resource and the free Cumulative Frequency quiz owns the practice.

Cumulative frequency is one of the most tested ideas in the Statistics unit of Cambridge IGCSE Mathematics (0580/0607). Whenever a question involves grouped data and you need the median, quartiles or interquartile range — examiners expect you to build a cumulative frequency table, plot a curve and read values accurately. This guide explains exactly what cumulative frequency covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Cumulative frequency is a running total of frequencies up to each upper class boundary.
• Plot cumulative frequency against upper class boundary to draw a cumulative frequency curve (ogive).
• Read the median at n/2, lower quartile at n/4 and upper quartile at 3n/4 on the curve.
• Interquartile range = upper quartile − lower quartile; it measures spread of the middle 50%.

What is cumulative frequency in Cambridge IGCSE Maths?

Cumulative frequency tells you how many data values fall below a given boundary. For grouped data, you add frequencies successively and plot the totals against upper class boundaries. The resulting curve lets you estimate the median and quartiles without calculating every individual value — essential when data is grouped into classes.

You can read the full explanation, worked examples and notes on Tutopiya’s Cumulative Frequency subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Cumulative frequency table	Running total column	”Complete the cumulative frequency table.”
Upper class boundary	Top edge of each class interval	Plot CF against this, not mid-interval
Median from curve	Read at n/2 on CF axis	”Use the graph to estimate the median.”
Quartiles and IQR	Read at n/4 and 3n/4	”Find the interquartile range.”

How to use cumulative frequency — step by step

The safest method works for every table-and-curve question.

1. Write upper class boundaries for each class interval (e.g. 10–19 → boundary 19.5 if continuous).
2. Build the cumulative frequency column — each row adds the previous total plus the class frequency.
3. Plot points at (upper boundary, cumulative frequency) and join with a smooth curve.
4. Find n (total frequency). Mark n/2 on the CF axis for the median.
5. Draw a horizontal line from n/2 to the curve, then down to the x-axis for the median value.
6. Repeat at n/4 and 3n/4 for quartiles; subtract for IQR.

Once you have worked through a few, test yourself with the free Cumulative Frequency quiz — it tells you fast whether the method has actually stuck.

Table vs curve: which approach does the question want?

Students lose marks by plotting against class widths or misreading the scale. Use the question format to decide.

Situation	What to do	Typical signal words
Incomplete table	Add running totals	”Complete the cumulative frequency column.”
Draw the curve	Plot at upper boundaries	”Draw a cumulative frequency diagram.”
Read median / quartiles	n/2, n/4, 3n/4 method	”Use your graph to estimate …”
Compare distributions	Two curves on one grid	”Which class has the greater median?”

Cumulative frequency in past-paper wording: command words that matter

Most lost marks come from wrong boundaries or reading from the wrong position on the curve.

Command word / phrase	What the question wants	Typical stem
Complete the table	Fill in cumulative frequency column	”Complete the cumulative frequency table.”
Draw a cumulative frequency curve	Accurate plot and smooth join	”Draw a cumulative frequency curve.”
Use your graph to estimate	Read median or quartile from curve	”Estimate the median mass.”
Work out the interquartile range	Upper quartile − lower quartile	”Find the interquartile range.”
How many students scored more than …	Read CF and subtract from n	”How many scored above 60 marks?”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the plotting — is what method marks reward.

1. “The table shows the times taken by 80 students. Complete the cumulative frequency column.” Add frequencies running down: first entry = first frequency; each next = previous + class frequency. Reward: all entries correct, final total = 80.
2. “Draw a cumulative frequency curve and estimate the median time.” Plot at upper boundaries; read at 80/2 = 40 on CF axis. Reward: correct n/2 reading with construction lines shown.
3. “Use the graph to find how many students took longer than 45 minutes.” Read CF at 45 → subtract from n. Reward: n − CF at 45, not CF at 45 alone.

When you can recognise the wording instantly, work the full set on the Statistics topical past paper questions and the Cumulative Frequency quiz to lock the method in.

How cumulative frequency connects to the rest of Statistics

Cumulative frequency builds on Methods of Analysing Data when estimating the mean from grouped tables. It links to Statistical Charts and Diagrams through histograms and frequency polygons. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Plotting against class midpoints instead of upper class boundaries.
• Using n instead of n/2 when reading the median from the curve.
• Joining points with straight lines zigzagging instead of a smooth curve.
• Forgetting that the final cumulative frequency must equal total n.
• Confusing “how many above” with “how many below” when reading from the graph.

When you need more support

If cumulative frequency questions keep tripping you up — especially curve reading — work through the Statistics topical past paper questions and the Cumulative Frequency quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is cumulative frequency hard in Cambridge IGCSE Maths? No — the method is consistent. Marks are lost on wrong boundaries, misreading n/2, and confusing above/below readings.

What axis do I plot cumulative frequency against? Upper class boundary on the horizontal axis, cumulative frequency on the vertical axis.

How do I find the interquartile range from a curve? Read the lower quartile at n/4 and upper quartile at 3n/4, then subtract: IQR = Q₃ − Q₁.

How do I revise cumulative frequency effectively? Read the subtopic notes, practise one full table-to-curve question, then take the Cumulative Frequency quiz. Revisit boundary errors before moving on.

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