Double Bar Graph
You already know how a bar graph shows data using bars. A double bar graph (also called a comparative bar graph) shows two sets of data side by side so you can compare them easily.
For example, if you want to compare the marks of two students across five subjects, you draw two bars for each subject — one for each student — right next to each other. This makes comparison quick and visual.
In Class 7 NCERT Maths, you will learn how to read, draw, and interpret double bar graphs.
What is Double Bar Graph - Grade 7 Maths (Data Handling)?
Definition: A double bar graph is a bar graph that displays two sets of data on the same graph using two different coloured (or shaded) bars placed side by side for each category.
- Each pair of bars represents one category.
- A legend (or key) shows which colour or pattern represents which data set.
- The bars can be drawn vertically or horizontally.
Double Bar Graph Formula
Steps to draw a double bar graph:
- Draw two axes — the horizontal axis (x-axis) for categories and the vertical axis (y-axis) for values.
- Choose a suitable scale for the y-axis (e.g., 1 unit = 10 marks).
- For each category, draw two bars side by side — one for each data set.
- Use different colours or patterns for the two data sets.
- Add a legend to show what each colour represents.
- Give the graph a title.
- Label both axes.
Types and Properties
Reading a double bar graph:
- Compare within a category: Look at the two bars for a single category. The taller bar has the higher value.
- Compare across categories: Look at how the bars change from one category to another.
- Find totals: Add the values of both bars for each category.
- Find differences: Subtract the shorter bar from the taller bar for each category.
Vertical vs Horizontal:
- In a vertical double bar graph, bars go upward from the x-axis.
- In a horizontal double bar graph, bars go sideways from the y-axis.
- Both show the same information — the choice depends on convenience.
Solved Examples
Example 1: Reading a Double Bar Graph
Problem: A double bar graph shows marks of Riya and Aman in 4 subjects:
- Maths: Riya = 85, Aman = 78
- Science: Riya = 72, Aman = 80
- English: Riya = 90, Aman = 88
- Hindi: Riya = 68, Aman = 75
(a) In which subject did Riya score the highest?
(b) In which subject did Aman score more than Riya?
Solution:
(a) Riya scored the highest in English (90 marks).
(b) Aman scored more than Riya in Science (80 > 72) and Hindi (75 > 68).
Example 2: Comparing Boys and Girls
Problem: Number of students in 3 classes:
- Class 7A: Boys = 22, Girls = 18
- Class 7B: Boys = 20, Girls = 25
- Class 7C: Boys = 24, Girls = 21
Find: (a) Which class has the most girls? (b) Which class has more boys than girls?
Solution:
(a) Class 7B has the most girls (25).
(b) Classes 7A (22 > 18) and 7C (24 > 21) have more boys than girls.
Example 3: Finding the Difference
Problem: Production of two factories (in thousands):
- January: Factory A = 30, Factory B = 25
- February: Factory A = 35, Factory B = 40
- March: Factory A = 28, Factory B = 32
In which month was the difference in production the greatest?
Solution:
- January: |30 − 25| = 5
- February: |35 − 40| = 5
- March: |28 − 32| = 4
Answer: January and February both have the greatest difference of 5 thousand units.
Example 4: Drawing a Double Bar Graph (Steps)
Problem: Draw a double bar graph for the runs scored by two teams:
- Match 1: Team A = 180, Team B = 165
- Match 2: Team A = 200, Team B = 210
- Match 3: Team A = 150, Team B = 175
Solution (Steps):
- Draw x-axis (Matches) and y-axis (Runs).
- Scale: 1 unit = 20 runs. Mark 0, 20, 40, ..., 220 on y-axis.
- For Match 1, draw a blue bar (Team A = 180) and a red bar (Team B = 165) side by side.
- Repeat for Match 2 and Match 3.
- Add legend: Blue = Team A, Red = Team B.
- Title: "Runs Scored by Two Teams".
Example 5: Total from a Double Bar Graph
Problem: Monthly expenses of two families:
- Food: Family X = Rs. 5000, Family Y = Rs. 6000
- Rent: Family X = Rs. 8000, Family Y = Rs. 7000
- Transport: Family X = Rs. 3000, Family Y = Rs. 4000
Find the total expenses of each family.
Solution:
Family X total = 5000 + 8000 + 3000 = Rs. 16,000
Family Y total = 6000 + 7000 + 4000 = Rs. 17,000
Answer: Family X spends Rs. 16,000 and Family Y spends Rs. 17,000 in total.
Example 6: Choosing the Right Scale
Problem: Population of two villages (in hundreds): Village P = 12, 15, 18, 22 (over 4 years). Village Q = 10, 14, 20, 25. What scale should you use?
Solution:
The values range from 10 to 25 (in hundreds).
A good scale would be: 1 unit = 2 (hundreds), marking 0, 2, 4, 6, ..., 26 on the y-axis.
This ensures all bars fit and the differences between bars are clearly visible.
Example 7: Interpreting Trends
Problem: Sales of two products over 4 quarters:
- Q1: Product A = 100, Product B = 80
- Q2: Product A = 110, Product B = 95
- Q3: Product A = 105, Product B = 115
- Q4: Product A = 95, Product B = 130
What trend do you notice?
Solution:
Product A started higher but decreased over time. Product B started lower but steadily increased. Product B overtook Product A in Q3.
Answer: Product B shows a rising trend while Product A shows a declining trend.
Example 8: Double Bar Graph with Equal Values
Problem: In a sports day, School X and School Y won medals:
- Gold: X = 5, Y = 5
- Silver: X = 8, Y = 6
- Bronze: X = 3, Y = 7
In which category did both schools win the same number of medals?
Solution:
In the Gold category, both schools won 5 medals each (equal bars).
Answer: Both schools won the same number of Gold medals.
Real-World Applications
Real-life uses of double bar graphs:
- School: Comparing marks of two students, or attendance of boys and girls in different classes.
- Business: Comparing sales of two products, expenses of two branches, or revenue across two years.
- Sports: Comparing runs, goals, or points of two teams across matches.
- Census data: Comparing populations of two cities or districts across different years.
- Weather: Comparing rainfall or temperature of two cities month by month.
Key Points to Remember
- A double bar graph displays two data sets side by side for easy comparison.
- Each category has two bars — one for each data set.
- A legend (key) is essential to identify which bar represents which data set.
- Choose an appropriate scale so all bars fit on the graph.
- Bars should have equal width and equal gaps between groups.
- Double bar graphs make it easy to compare values within and across categories.
- They can be drawn vertically or horizontally.
- Always give the graph a title and label both axes.
Practice Problems
- Draw a double bar graph for the favourite sports of boys and girls in a class: Cricket (Boys: 12, Girls: 5), Football (Boys: 8, Girls: 4), Badminton (Boys: 6, Girls: 10), Swimming (Boys: 4, Girls: 8).
- From the above graph, which sport is most popular among girls?
- The marks of two students in 4 subjects are: Maths (A: 90, B: 85), Science (A: 75, B: 80), English (A: 88, B: 92), Hindi (A: 70, B: 65). In how many subjects did Student A score more than Student B?
- If both bars in a category are the same height, what does it mean?
- Why is a legend necessary in a double bar graph?
Frequently Asked Questions
Q1. What is a double bar graph?
A double bar graph is a graph that shows two sets of data using two bars placed side by side for each category. It helps compare the two data sets visually.
Q2. How is a double bar graph different from a simple bar graph?
A simple bar graph shows one set of data with one bar per category. A double bar graph shows two sets of data with two bars per category, making comparison between the two sets easy.
Q3. Why do we need a legend in a double bar graph?
The legend tells the reader which colour or pattern represents which data set. Without a legend, you cannot tell which bars belong to which group.
Q4. Can a double bar graph have more than two data sets?
When three or more data sets are shown, it is called a grouped bar graph (or multiple bar graph). The idea is the same, but with three or more bars per category.
Q5. How do you choose the scale for a double bar graph?
Look at the largest value in both data sets. Choose a scale so that the largest bar fits comfortably on the graph. Common scales are 1 unit = 5, 10, 20, or 50, depending on the data.
Q6. Can double bar graphs be horizontal?
Yes. Horizontal double bar graphs have categories on the y-axis and values on the x-axis. The bars extend sideways. They show the same information as vertical ones.
