Dual and stacked bar charts
Compare two subgroups with adjacent bars or show how subgroups make up a total.
Section Paper 2 · Extended · Non-calculator
Core and Extended. This is the separate 9–1 qualification 0980. Cambridge intends Core for grades 4–1 and Extended for grades 9–5; the eligible award bands are grades 5–1 for the Core papers and grades 9–3 for the Extended papers.
Before you begin
- Read simple bar charts.
- Add subgroup frequencies.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does a dual bar chart need to distinguish subgroups?
What you will learn
- Construct and interpret dual and stacked bar charts.
- Separate subgroup counts from combined totals.
Adjacent bars compare the same subgroup across categories
Class A has twelve boys and eight girls; class B has nine boys and fifteen girls. A dual bar chart puts two adjacent bars for each class using a shared frequency scale. A legend identifies the subgroup colours or patterns. This makes boy-to-boy and girl-to-girl comparisons straightforward.
The two bars in a class represent separate subgroup counts, not a total bar and one part. Keep all widths and spacing consistent. The class totals are twenty and twenty-four; compare proportions rather than raw counts if the question concerns composition across unequal class sizes.
Stacked segments build one combined total
A stacked chart for the same data places each class's subgroups above one another. Class A reaches twenty and class B reaches twenty-four. In class B, a boys segment from zero to nine and girls segment from nine to twenty-four means fifteen girls, not twenty-four girls.
Read a segment's height as upper boundary minus lower boundary. Only the bottom subgroup shares a common zero baseline, so comparing upper subgroups by eye can be harder than with dual bars. A percentage stacked chart has total height one hundred percent and answers a proportion question; label it distinctly from counts.
Pause and explain
A stacked segment extends from 9 to 24 on a frequency axis. What is its frequency?
Worked example
Class B's stacked bar has boys from 0 to 9 and girls from 9 to 24. Find girls and total.
Show the worked solution
- The girls segment height is 24−9 = 15.
- The top of the entire bar gives total twenty-four.
- The subgroup counts nine and fifteen add to that total.
Answer Girls 15; class total 24.
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.
Class A has twelve boys and eight girls. Find its stacked total.
Give me a hint
Add both subgroup counts.
Compare my reasoning
- The first segment is twelve high.
- The second adds eight.
- The stacked bar reaches twenty.
20.
Look for these in your work
- Added disjoint subgroups.
- Distinguished segment from total.
Class A has 8 girls of 20; B has 15 girls of 24. Compare girl percentages.
Give me a hint
Use each class's own total.
Compare my reasoning
- A has 8/20 = 40%.
- B has 15/24 = 62.5%.
- B has the larger girl proportion as well as count.
A 40%; B 62.5%.
Look for these in your work
- Used separate denominators.
- Compared the intended proportions.
Which chart better supports comparing girl counts across many classes: dual bars or girls stacked above unequal boy counts? Explain.
Give me a hint
Consider a shared baseline.
Compare my reasoning
- Dual girl bars share the zero baseline.
- Upper stacked segments start at different heights.
- Dual bars usually make direct subgroup-count comparison easier.
Dual bars, because corresponding subgroup heights share a baseline.
Look for these in your work
- Compared reading tasks.
- Explained the baseline advantage.
Common mistakes
- Reading a cumulative top as a segment count.
- Omitting subgroup labels.
- Mixing count and percentage scales.
What can you explain now?
Does the top of a stacked bar give the upper subgroup count alone?
Compare with the explanation
No; it gives the combined total.
Subtract the segment's lower boundary to recover that subgroup's own count.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, draw the same small table as dual and stacked bars and compare what each makes easiest to read.
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.