Read component counts and totals in a compound bar chart
Use a key to identify stacked components · Read a component by subtracting its boundary heights · Compare component shares as well as totals
Section E10.3 · Extended · Statistical charts and distributions
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Frequency counts
- Percentages
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Use a key to identify stacked components
- Read a component by subtracting its boundary heights
- Compare component shares as well as totals
Height at the top is cumulative
In the illustrative library-loan chart, March has 15 fiction and 10 non-fiction loans, April 20 and 15, May 10 and 20. Totals are 25,35,30. A non-fiction segment starting above a fiction segment has height equal to top minus bottom. Its top coordinate alone gives the total, not the non-fiction count.
Counts and shares answer different questions
March’s fiction share is 15/25=60%, April’s 20/35≈57.1%, May’s 10/30≈33.3%. April has more fiction loans than March but a smaller fiction share. For ordinary frequency compound bars, the overall bar heights can differ; for a percentage chart, read the percentage scale and its stated totals.
Sources for this lesson
Pause and explain
Does the April top height 35 mean 35 non-fiction loans?
Worked example
Read the April total and non-fiction count from the chart.
Show the worked solution
- The top is 35 loans and the lower segment ends at 20.
- Non-fiction height=35−20=15.
Answer 35 total; 15 non-fiction.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Read the March fiction, non-fiction and total loan counts from the chart.
Give me a hint
Use both segment boundaries.
Compare my reasoning
- Fiction reaches 15.
- The top is 25, so non-fiction is 10.
Fiction 15; non-fiction 10; total 25.
Look for these in your work
- Use the chart key
- Subtract the stacked boundaries
Compare fiction shares for March and April in the chart.
Give me a hint
Divide the component by its own bar total.
Compare my reasoning
- March is 15/25=60%.
- April is 20/35=4/7≈57.1%.
March has the larger fiction share, although April has more fiction loans.
Look for these in your work
- Use the correct totals
- Distinguish count from share
A compound bar has a lower segment of 12 and a total height of 30. Find the upper count and its share of the total.
Give me a hint
Subtract the lower height.
Compare my reasoning
- Upper count=30−12=18.
- Share=18/30=60%.
18; 60%.
Look for these in your work
- Read the upper segment as a difference
- Use total as the percentage base
Common mistakes
- An upper segment’s top is not its individual count.
- Compare proportions with the relevant total.
What can you explain now?
Does the April top height 35 mean 35 non-fiction loans?
Compare with the explanation
No; subtract the fiction boundary 20 to get 15.
The top of a stacked bar represents the combined total.
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Make it stick
Does the April top height 35 mean 35 non-fiction loans?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.