Dual & compound bar charts
🎯 In this topic you will
- Draw and interpret dual bar charts
- Draw and interpret compound bar charts
🧠 Key Words
- compound bar chart
- dual bar chart
Show Definitions
- compound bar chart: A bar chart that shows multiple pieces of information in each bar, often stacked or divided.
- dual bar chart: A bar chart that displays two sets of data side by side for easy comparison.
You already know how to draw and use bar charts. You use a bar chart to show one set of data.
If you want to show more than one set of data, you can use a dual bar chart or a compound bar chart.
- Dual bar chart: the different sets of data are shown side by side (two bars next to each other for each category).
- Compound bar chart: the different sets of data are combined into one bar (stacked on top of each other) for each category.
Example. Both charts below would display how many CDs and DVDs three students have.
| Student | CDs | DVDs | Total (for compound bar) |
| Amber | 8 | 2 | 10 |
| Wenkai | 9 | 5 | 14 |
| Karl | 2 | 7 | 9 |
How to choose:
- Use a dual bar chart when you want to compare CDs vs DVDs for each student directly.
- Use a compound (stacked) bar chart when you want to compare total collections, while still showing each part’s contribution.
❓ EXERCISES
1. This dual bar chart shows the number of matches won and lost by four players at a tennis tournament.
a. Which player won the most number of matches?
b. Which player lost the most number of matches?
c. How many more matches did Ahu win than Duyen?
d. Make two other comments about what the bar chart shows.
e. Did all the players play the same number of matches? Explain how you worked out your answer.
🔎 Reasoning Tip
For part d, for example, you could:
- Compare the number of matches won or lost between different players
- Or compare the number of matches won and lost by one player
👀 Show answer
1a. Beth won the most matches (7).
1b. Duyen lost the most matches (7).
1c. Ahu won 4 matches, Duyen won 2 matches → Ahu won 2 more matches than Duyen.
1d.
• Cho won and lost the same number of matches (5 each).
• Beth lost the fewest matches (2).
1e. Yes, they all played 9 matches each. For each player: wins + losses = 9.
2. This two-way table shows the hair colour of the girls and boys in Miss Awan’s class.
| Brown hair | Black hair | Other hair colour | |
|---|---|---|---|
| Girls | 8 | 6 | 2 |
| Boys | 4 | 9 | 1 |
a. Copy and complete the dual bar chart to show this information.
b. Make two comments about what the bar chart shows.
👀 Show answer
2a. Completed bar chart matches the table above.
2b.
• More girls have brown hair than boys.
• More boys have black hair than girls.
3. The two-way table shows how the students in class 7P travel to school.
| Walk | Car | Bus | Bicycle | |
|---|---|---|---|---|
| Girls | 10 | 2 | 4 | 3 |
| Boys | 5 | 1 | 8 | 5 |
a. Draw a dual bar chart to show this information.
b. Make two comments about what the bar chart shows.
👀 Show answer
3a. Dual bar chart reflects the table values above.
3b.
• More girls walk to school compared to boys.
• More boys travel by bus and bicycle than girls.
🧠 Think like a Mathematician
Task: Evaluate different methods for finding how many millilitres of vinegar are in the salad dressing using the compound bar chart.
Scenario: The compound bar chart shows the ingredients in 50 mL of salad dressing (oil, vinegar, soy sauce, herbs). Sofia counts the scale sections for vinegar and multiplies: 7 sections × 2 mL = 14 mL of vinegar.
Questions:
👀 show answer
- a) Sofia’s method is correct: she used the scale to measure the vinegar section and multiplied by 2 mL per division to get 14 mL.
- b) Other possible methods: - Measure directly from the bar chart scale (30 mL to 44 mL = 14 mL). - Work out vinegar as a fraction of the total 50 mL if ratios were known. - Estimate using proportional reasoning (vinegar bar is just under a third of the oil bar).
- c) The best method is to use the scale directly (Sofia’s method), as it is accurate and uses the information already shown on the chart. Fraction or ratio methods are useful if exact numbers are given instead of a bar chart.
❓ EXERCISES
5. This compound bar chart shows the number of hours of triathlon training Luiz and Marcos do one week.
a. How many hours does:
i Luiz swim? ii Marcos run?
b. How many more hours does Marcos cycle than Luiz?
c. How many more hours does Luiz run than Marcos?
👀 Show answer
5a(i). Luiz swims about 3 hours.
5a(ii). Marcos runs about 5 hours.
5b. Marcos cycles 15 hours, Luiz cycles 10 hours → Marcos cycles 5 more hours.
5c. Luiz runs 10 hours, Marcos runs 5 hours → Luiz runs 5 more hours.
6. Chinara and Adaku compare their scores from five mental maths tests. The compound bar chart shows their test scores.
a. In which test did Chinara and Adaku get the same score?
b. In which tests did Chinara get a higher score than Adaku?
c. Arun says: “Chinara scored three more than Adaku in test 1.”
Write down two comments that are similar to Arun’s that compare the test results of Chinara and Adaku.
d. Do you think Chinara or Adaku is better at mental maths? Explain your answer.
e. In each test there was a total possible score of 10. Write Adaku’s total score for the five tests as a:
i fraction ii percentage
🔎 Reasoning Tip
A triathlon is a competition in which people swim, then cycle, then run.
👀 Show answer
6a. They got the same score in test 3.
6b. Chinara scored higher in tests 1 and 5.
6c.
• In test 2, Adaku scored two more than Chinara.
• In test 5, Chinara scored four more than Adaku.
6d. Chinara is slightly better overall, because her total score is higher (34 vs 30).
6e(i). Adaku’s total = 30 out of 50 = $\tfrac{30}{50}=\tfrac{3}{5}$.
6e(ii). Percentage = $(30 \div 50)\times 100 = 60\%$.
7. This two-way table shows the number of holidays sold by a travel agency in a period of two weeks.
| Beach | Sport | City | Safari | |
|---|---|---|---|---|
| Week 1 | 10 | 5 | 4 | 1 |
| Week 2 | 5 | 1 | 8 | 2 |
Copy the compound bar chart shown and use the information in the two-way table to complete the chart.
👀 Show answer
Week 1 totals: Beach 10, Sport 5, City 4, Safari 1.
Week 2 totals: Beach 5, Sport 1, City 8, Safari 2.
The compound bar chart should show taller stacks for Week 1 than Week 2.
8. The compound bar chart shows the number of football matches won, lost and drawn by three teams.
Copy this two-way table and use the information in the chart to complete the table.
| Won | Lost | Drawn | Total | |
|---|---|---|---|---|
| Barcelona | 18 | 12 | 5 | 35 |
| Real Madrid | 15 | 10 | 10 | 35 |
| Valencia | 12 | 10 | 8 | 30 |
| Total | 45 | 32 | 23 | 100 |
👀 Show answer
From the chart, totals were read directly:
Barcelona: Won 18, Lost 12, Drawn 5 → Total 35.
Real Madrid: Won 15, Lost 10, Drawn 10 → Total 35.
Valencia: Won 12, Lost 10, Drawn 8 → Total 30.
Overall totals: Won 45, Lost 32, Drawn 23, Total 100.
9. This two-way table shows the number of cakes sold by a café one Saturday and Sunday.
| Type of cake | ||
|---|---|---|
| chocolate | vanilla | |
| Saturday | 18 | 7 |
| Sunday | 9 | 14 |
a.i Draw a dual bar chart to show this information. ii Make one comment on what your chart shows.
b.i Draw a compound (stacked) bar chart to show this information. ii Make one comment on what your chart shows.
c. Which chart do you think is the best to use to display this information? Give reasons for your answer.
👀 Show answer
9a(ii). From a dual bar chart (two bars per flavour, one for each day):
• Chocolate sells more on Saturday (18) than Sunday (9).
• Vanilla sells more on Sunday (14) than Saturday (7).
9b(ii). From a compound/stacked chart (one stack per day):
• Totals: Saturday = 25, Sunday = 23 → Saturday sold slightly more cakes overall.
9c.Best chart depends on the purpose:
• To compare flavours between days clearly, the dual bar chart is best (side-by-side comparison).
• To compare total sales by day and show the day’s make-up, the compound bar chart is best (stack height shows total, segments show flavour split).
In this context, if the task is general comparison of both days and flavours, start with the dual bar chart and mention the totals (25 vs 23).
⚠️ Be careful!
- Use one consistent scale: the vertical axis must use equal intervals across all bars; don’t change scale between categories or datasets.
- Keep bar widths & gaps equal: uneven widths/gaps distort comparisons in dual charts.
- Align categories perfectly: for dual bars, the two bars for a category must be adjacent and centered on the same tick/label.
- Add a clear legend/key: always label which color/pattern is which dataset (e.g., CDs vs DVDs).
- Start bars at zero: do not truncate the vertical axis; otherwise differences appear exaggerated.
- Stack correctly in compound charts: draw the second part on top of the first; the top of the stack shows the total.
- Totals check (compound): top height of each stacked bar must equal the sum of its parts (e.g., $\text{CDs}+\text{DVDs}$).
- Compare the right thing: in a dual chart, compare bar heights within the same category; in a compound chart, compare totals via overall bar heights.
- Don’t mix counts with percentages: convert all data to the same unit before drawing or interpreting.
- Read gridlines exactly: estimate to the nearest tick; avoid reading between uneven gridlines.