Bar Graphs (Grade 5)
A bar graph uses rectangular bars to represent data visually. Each bar's height (or length) shows the value of the data it represents. Bar graphs make it easy to compare quantities at a glance.
In Class 5, you learn to read, interpret, and draw bar graphs. You also learn about double bar graphs that compare two sets of data side by side.
Bar graphs are used in newspapers, textbooks, and presentations to show data such as population, marks, rainfall, and sales figures.
What is Bar Graphs - Class 5 Maths (Data Handling)?
A bar graph (or bar chart) is a graphical representation of data using rectangular bars of equal width. The bars can be drawn vertically or horizontally.
Parts of a bar graph:
- Title — describes what the graph shows
- X-axis (horizontal) — shows categories (items being compared)
- Y-axis (vertical) — shows values (numbers/quantities)
- Bars — rectangular blocks representing data values
- Scale — the intervals marked on the Y-axis (e.g., 0, 10, 20, 30...)
Types and Properties
Types of Bar Graphs:
- Vertical bar graph: Bars stand upright. The most common type.
- Horizontal bar graph: Bars lie flat (left to right). Useful when category names are long.
- Double bar graph: Two bars placed side by side for each category. Used to compare two data sets (e.g., boys vs girls, Test 1 vs Test 2).
Solved Examples
Example 1: Example 1: Reading a Bar Graph
Problem: The bar graph shows runs scored by 4 players in a cricket match.
| Player | Runs |
|---|---|
| Aman | 45 |
| Rahul | 60 |
| Kavi | 35 |
| Dev | 55 |
(a) Who scored the most runs? (b) What is the difference between the highest and lowest scores?
Solution:
(a) Rahul scored the most runs: 60.
(b) Difference = 60 − 35 = 25 runs.
Answer: (a) Rahul (b) 25 runs
Example 2: Example 2: Total from a Bar Graph
Problem: The bar graph shows the number of books read by students in a month: Ria = 8, Priya = 12, Aditi = 6, Meera = 10. Find the total books read.
Solution:
Step 1: Add all values: 8 + 12 + 6 + 10 = 36
Answer: Total books read = 36
Example 3: Example 3: Choosing a Scale
Problem: The data shows students in 4 sections: A = 40, B = 35, C = 50, D = 45. What scale should be used for the bar graph?
Solution:
Step 1: The values range from 35 to 50.
Step 2: A suitable scale is 1 division = 5 students.
Step 3: Y-axis: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Answer: Use a scale of 1 division = 5 students.
Example 4: Example 4: Drawing Steps
Problem: Draw a bar graph for favourite fruits: Mango = 15, Apple = 10, Banana = 8, Guava = 12.
Solution:
Step 1: Draw X-axis (fruits) and Y-axis (number of students).
Step 2: Choose scale: 1 division = 2 students. Y-axis goes 0 to 16.
Step 3: Draw bars: Mango up to 15, Apple up to 10, Banana up to 8, Guava up to 12.
Step 4: Label axes and give a title: "Favourite Fruits of Class 5".
Answer: The bar graph has 4 bars with Mango as the tallest bar.
Example 5: Example 5: Double Bar Graph
Problem: Marks of two students in 3 subjects:
| Subject | Ria | Aman |
|---|---|---|
| Maths | 85 | 78 |
| Science | 72 | 80 |
| English | 90 | 88 |
Who scored more in total?
Solution:
Step 1: Ria's total = 85 + 72 + 90 = 247
Step 2: Aman's total = 78 + 80 + 88 = 246
Answer: Ria scored more by 1 mark.
Example 6: Example 6: Finding Average from a Bar Graph
Problem: A bar graph shows rainfall (in mm) over 4 months: June = 120, July = 200, August = 180, September = 100. Find the average rainfall.
Solution:
Step 1: Total = 120 + 200 + 180 + 100 = 600 mm
Step 2: Average = 600 ÷ 4 = 150 mm
Answer: Average rainfall = 150 mm
Example 7: Example 7: Finding the Difference
Problem: Priya sold 25 chapatis on Monday and 40 chapatis on Tuesday at her canteen. How many more were sold on Tuesday?
Solution:
Step 1: Difference = 40 − 25 = 15
Answer: 15 more chapatis were sold on Tuesday.
Example 8: Example 8: Scale Interpretation
Problem: In a bar graph, each division on the Y-axis represents 50 people. A bar reaches up to the 7th division. How many people does the bar represent?
Solution:
Step 1: Value = Number of divisions × Scale
Step 2: Value = 7 × 50 = 350
Answer: The bar represents 350 people.
Example 9: Example 9: Missing Data from Bar Graph
Problem: A bar graph shows scores of 5 students. The total of all scores is 350. Four students scored 80, 65, 90, and 70. What did the 5th student score?
Solution:
Step 1: Sum of 4 scores = 80 + 65 + 90 + 70 = 305
Step 2: 5th score = 350 − 305 = 45
Answer: The 5th student scored 45.
Key Points to Remember
- A bar graph represents data using rectangular bars of equal width.
- Bars can be vertical or horizontal.
- The scale determines the value of each division on the axis.
- All bars must have equal gaps between them.
- A double bar graph compares two data sets using two bars per category.
- To draw a bar graph: choose a scale, draw axes, label them, draw bars, and add a title.
- Always read the scale carefully before interpreting values.
Practice Problems
- A bar graph shows the number of students in 5 clubs: Art = 25, Music = 30, Science = 20, Sports = 45, Dance = 35. Which club has the most students?
- Draw a bar graph for the following data — Favourite sport: Cricket = 18, Football = 12, Badminton = 15, Kabaddi = 9.
- In a bar graph, the Y-axis scale is 1 division = 20. A bar reaches the 6th line. What value does it show?
- The rainfall in 4 cities is: Delhi = 80 mm, Mumbai = 250 mm, Chennai = 120 mm, Bengaluru = 90 mm. Find the difference between the highest and lowest rainfall.
- A double bar graph shows boys and girls in 3 sections. Section A: Boys = 22, Girls = 28. Section B: Boys = 25, Girls = 25. Section C: Boys = 30, Girls = 20. Which section has equal numbers?
- From the above data, find the total number of girls across all sections.
- Explain why a scale of 1 division = 100 would be a poor choice if all values are between 5 and 30.
Frequently Asked Questions
Q1. What is a bar graph?
A bar graph is a chart that uses rectangular bars to show data. The height or length of each bar represents the value of the data for that category.
Q2. How do you choose the right scale for a bar graph?
Look at the data values. The scale should make the largest value fit on the graph without making it too tall. Common scales are 1, 2, 5, 10, 20, 50, or 100 per division.
Q3. What is a double bar graph?
A double bar graph shows two bars for each category, placed side by side. It is used to compare two data sets, such as marks in two tests or boys vs girls.
Q4. What is the difference between a bar graph and a pictograph?
A pictograph uses pictures or symbols to represent data. A bar graph uses rectangular bars. Bar graphs are more precise because you can read exact values from the scale.
Q5. Can bars in a bar graph touch each other?
In a standard bar graph, bars have equal gaps between them. In a histogram (studied in higher classes), bars touch each other because the data is continuous.
Q6. How do you find the total from a bar graph?
Read the value of each bar from the scale and add them all together.
Q7. Can a bar graph show negative values?
At the Class 5 level, bar graphs show only positive values. In higher classes, bars can extend below the X-axis to show negative values.
Q8. Why are bar graphs useful?
Bar graphs make it easy to compare data at a glance. You can quickly see which category has the highest or lowest value without reading each number.
