Bar Graph
Your teacher asks the class about their favourite fruit. Mango gets 12 votes, Apple gets 8, Banana gets 5, Grapes get 10, and Orange gets 7. Now, how do you show this information in a way that is easy to understand at a glance? You draw a bar graph.
A bar graph (also called a bar chart) uses rectangular bars to represent data. The length or height of each bar shows the value of the data it represents. Bar graphs make it very easy to compare different groups or categories at a single look.
You can see at one glance that Mango is the most popular (tallest bar) and Banana is the least popular (shortest bar). No need to study numbers carefully — the picture tells the story.
Bar graphs are one of the most common ways to display data in newspapers, textbooks, and on television. Weather reports use bar graphs to show rainfall. Schools use them to show student performance. Businesses use them to show sales.
In this chapter, you will learn how to read bar graphs, how to draw them step by step on graph paper, and how to answer questions based on the information shown in bar graphs. This topic is part of the Data Handling chapter in Grade 6 Maths (NCERT/CBSE).
What is Bar Graph - Grade 6 Maths (Data Handling)?
Definition: A bar graph is a pictorial representation of data using rectangular bars of equal width, where the length (or height) of each bar represents the value of the data.
Parts of a bar graph:
- Title: Tells what the bar graph is about.
- X-axis (horizontal axis): Shows the categories (items being compared).
- Y-axis (vertical axis): Shows the numerical values (using a scale).
- Bars: Rectangular bars of uniform width drawn for each category.
- Scale: The number each division on the Y-axis represents (e.g., 1 division = 5 units).
- Labels: Names on each axis telling what it represents.
Rules for drawing bar graphs:
- All bars must have the same width.
- There must be equal gaps between the bars.
- Bars can be drawn vertically (most common) or horizontally.
- The bars should NOT touch each other.
- Each bar must be labelled.
Bar Graph Formula
Steps to draw a bar graph:
1. Collect data → 2. Choose scale → 3. Draw axes → 4. Draw bars → 5. Label
Detailed steps:
- Organize the data in a table with categories and their values.
- Choose a suitable scale for the Y-axis. If values go up to 50, use scale 1 division = 5 or 10.
- Draw the X-axis (horizontal) and Y-axis (vertical) on graph paper.
- Mark the categories on the X-axis with equal spacing.
- Mark the scale values on the Y-axis (0, 5, 10, 15, ...).
- Draw a bar for each category. The height of the bar = the data value.
- Keep equal width and equal gaps for all bars.
- Write the title, axis labels, and scale.
Choosing the scale:
- If data values are small (under 20), use scale = 1.
- If values are medium (20 to 100), use scale = 5 or 10.
- If values are large (110+), use scale = 20, 25, 50, or 100.
Derivation and Proof
Bar graphs were invented to make data easier to understand. Before bar graphs, data was only shown in tables of numbers. Tables are accurate, but it is hard to compare numbers quickly in a table.
Why are bar graphs useful?
- You can see the highest and lowest values immediately (tallest and shortest bars).
- You can compare categories side by side.
- They are more visual and engaging than plain numbers.
Bar graph vs Pictograph:
- A pictograph uses pictures/symbols to represent data. Each symbol represents a fixed number of items.
- A bar graph uses bars whose height represents the exact value.
- Bar graphs are more precise because you can read exact values from the scale, while pictographs can be approximate.
Vertical vs Horizontal bar graphs:
- In a vertical bar graph, bars go upwards. Categories are on the X-axis and values on the Y-axis.
- In a horizontal bar graph, bars go sideways. Categories are on the Y-axis and values on the X-axis.
- Both show the same information. Use horizontal bars when category names are long.
Types and Properties
Type 1: Reading a bar graph
- Given a bar graph, answer questions about the data.
- Example: Which category has the highest value? What is the value of Category B?
Type 2: Drawing a bar graph from data
- Given a data table, draw a bar graph on graph paper.
- Choose an appropriate scale, draw axes, and draw bars.
Type 3: Comparison questions
- How much more is A than B? Which category has the least value?
Type 4: Finding totals and differences from a bar graph
- Find the total of all values, or the difference between two values.
Type 5: Missing data problems
- Given a bar graph with one bar missing, use other information to find the missing value.
Solved Examples
Example 1: Example 1: Reading a Bar Graph
Problem: A bar graph shows the number of books read by 5 students: Anu — 8, Bela — 12, Charu — 6, Diya — 15, Ela — 10. Answer: (a) Who read the most books? (b) Who read the fewest? (c) How many more books did Diya read than Charu?
Solution:
- (a) Diya read the most books (15).
- (b) Charu read the fewest (6).
- (c) Diya − Charu = 15 − 6 = 9 more books.
Example 2: Example 2: Drawing a Bar Graph
Problem: Draw a bar graph for the following data showing marks scored by Rahul in different subjects: Hindi — 70, English — 85, Maths — 95, Science — 80, Social Studies — 65.
Solution:
Step 1: Choose scale. Marks range from 65 to 95. Use scale: 1 division = 10 marks. Y-axis: 0, 10, 20, ..., 100.
Step 2: Draw X-axis with subjects: Hindi, English, Maths, Science, Social Studies.
Step 3: Draw bars:
- Hindi: height = 70
- English: height = 85
- Maths: height = 95
- Science: height = 80
- Social Studies: height = 65
Step 4: Add title: "Marks Scored by Rahul". Label X-axis: "Subjects", Y-axis: "Marks".
Example 3: Example 3: Choosing the Right Scale
Problem: The population of 4 villages is: Village A — 2500, Village B — 4000, Village C — 3500, Village D — 1500. What scale should be used for the bar graph?
Solution:
The values range from 1500 to 4000. They are in thousands.
Suitable scale: 1 division = 500
Y-axis markings: 0, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000.
This gives 8 divisions on the Y-axis, which fits nicely on a page.
Example 4: Example 4: Comparison Question
Problem: A bar graph shows the runs scored by 5 batsmen in a match: Rohit — 45, Virat — 80, KL — 35, Jadeja — 55, Pant — 70. (a) Who scored the highest? (b) Find the difference between the highest and lowest scores. (c) How many runs did all 5 score together?
Solution:
- (a) Virat scored the highest (80 runs).
- (b) Highest = 80, Lowest = 35. Difference = 80 − 35 = 45 runs.
- (c) Total = 45 + 80 + 35 + 55 + 70 = 285 runs.
Example 5: Example 5: Favourite Sport Survey
Problem: In a survey of 200 students, their favourite sport was recorded: Cricket — 75, Football — 50, Badminton — 35, Basketball — 25, Swimming — 15. Draw a bar graph and find what fraction of students chose Cricket.
Solution:
Scale: 1 division = 10 students. Y-axis: 0, 10, 20, ..., 80.
Draw 5 bars with heights 75, 50, 35, 25, and 15.
Fraction who chose Cricket:
- 75/200 = 15/40 = 3/8
Answer: 3/8 of the students chose Cricket.
Example 6: Example 6: Temperature Data
Problem: The maximum temperature (in °C) on five days of a week was: Monday — 32, Tuesday — 35, Wednesday — 30, Thursday — 28, Friday — 33. From the bar graph, find: (a) the hottest day (b) the coolest day (c) the average temperature.
Solution:
- (a) Tuesday was the hottest (35°C).
- (b) Thursday was the coolest (28°C).
- (c) Average = (32 + 35 + 30 + 28 + 33) ÷ 5 = 158 ÷ 5 = 31.6°C.
Example 7: Example 7: Production Data
Problem: A factory produced the following number of toys each month: January — 400, February — 350, March — 500, April — 450, May — 300. What scale is suitable? Which month had the lowest production?
Solution:
Scale: Values range from 300 to 500. Use 1 division = 50.
Y-axis: 0, 50, 100, ..., 500.
Lowest production: May with 300 toys.
Example 8: Example 8: Finding Missing Data
Problem: A bar graph shows enrolment in 5 classes. Total enrolment is 200. Class A — 50, Class B — 45, Class C — 35, Class D — ?, Class E — 30. Find the enrolment of Class D.
Solution:
- Total = 200
- Known total = 50 + 45 + 35 + 30 = 160
- Class D = 200 − 160 = 40
Answer: Class D has 40 students.
Example 9: Example 9: Comparing Two Bars
Problem: In a bar graph, the bar for "Apples sold" reaches 120 on the Y-axis and the bar for "Oranges sold" reaches 90. How many more apples were sold than oranges? What is the ratio of oranges to apples sold?
Solution:
- Difference = 120 − 90 = 30 more apples
- Ratio of oranges to apples = 90 : 120 = 3 : 4 (dividing by HCF 30)
Answer: 30 more apples were sold. The ratio is 3 : 4.
Example 10: Example 10: Interpreting Scale
Problem: In a bar graph, the Y-axis has a scale of 1 division = 20 students. A bar reaches up to the 7th division line. How many students does this bar represent?
Solution:
- Each division = 20 students
- Bar reaches 7th division = 7 × 20 = 140 students
Answer: The bar represents 140 students.
Real-World Applications
Bar graphs are used in many real-life situations:
- Weather reports: TV channels show bar graphs of temperature or rainfall over a week to help you see patterns.
- Business: Companies use bar graphs to compare monthly sales, profits, or the number of products sold.
- Sports: Bar graphs compare runs scored by different batsmen, goals by different teams, or medals won by countries in the Olympics.
- School: Teachers use bar graphs to compare average marks of students across subjects or attendance across months.
- Elections: Bar graphs show the number of votes each candidate received, making it easy to see who won.
- Population data: Census reports use bar graphs to compare population across cities, states, or age groups.
Key Points to Remember
- A bar graph uses rectangular bars to represent data visually.
- All bars must have equal width and equal gaps between them.
- The height (or length) of each bar shows the value of that category.
- The Y-axis has a scale — each division represents a fixed number of units.
- Choosing the right scale is important — it should fit all values on the page.
- Bar graphs make it easy to compare data at a glance.
- Bars can be vertical (most common) or horizontal.
- Every bar graph must have a title, axis labels, and scale.
- Bar graphs are more precise than pictographs because you can read exact values.
- The tallest bar shows the maximum value; the shortest shows the minimum.
Practice Problems
- Draw a bar graph for the number of students in each section: A — 40, B — 35, C — 45, D — 38, E — 42.
- A bar graph shows the rainfall (in mm) for 5 months. Which month had the highest rainfall?
- From a bar graph, read the values and find the total of all bars.
- What scale would you choose for data values: 150, 225, 300, 175, 250?
- A bar graph shows the favourite colours of 80 students. If Red = 25, Blue = 20, Green = ?, Yellow = 15, and the rest chose Green, find the value for Green.
- The heights of 5 bars are 30, 45, 25, 50, and 35. Find the difference between the tallest and shortest bar.
- Can a bar graph have bars of different widths? Why or why not?
- Convert this pictograph data into a bar graph: Mango = 6 symbols (each = 5), Apple = 4 symbols, Banana = 3 symbols.
Frequently Asked Questions
Q1. What is a bar graph?
A bar graph is a chart that uses rectangular bars to show data. The height of each bar represents the value of the data for that category. It is used to compare different groups or categories.
Q2. What is the difference between a bar graph and a pictograph?
A pictograph uses pictures or symbols to represent data (each symbol = a fixed number). A bar graph uses rectangular bars whose height equals the exact value. Bar graphs are more precise because values can be read accurately from the scale.
Q3. How do you choose a scale for a bar graph?
Look at the range of your data values. Choose a scale so that the highest value fits on the graph paper. If values go up to 50, you could use 1 division = 5 or 10. If values go up to 500, use 1 division = 50 or 100.
Q4. Can bars in a bar graph touch each other?
No. In a standard bar graph (for discrete/categorical data), bars should NOT touch each other. Equal gaps are left between bars. This is different from a histogram (used for continuous data), where bars do touch.
Q5. What is the purpose of a bar graph?
The main purpose is to make data easy to understand and compare. By looking at the heights of bars, you can quickly see which category is the largest, smallest, or how they compare to each other.
Q6. Can a bar graph be drawn horizontally?
Yes. In a horizontal bar graph, bars extend from left to right instead of bottom to top. Categories are on the Y-axis and values on the X-axis. Horizontal bar graphs are useful when category names are long.
Q7. What must every bar graph have?
Every bar graph must have: a title (what the graph shows), labelled X-axis and Y-axis, a scale on the value axis, bars of equal width with equal gaps, and clear labels for each bar.
Q8. How do you read the value of a bar in a bar graph?
Look at the top of the bar and read across to the Y-axis (or down to the X-axis in a horizontal bar graph). The number where the top of the bar meets the scale is the value.
