NCERT Solutions for Class 6 Maths Chapter 9 Data Handling Exercise 9.3

Welcome, Class 6 students! In this guide, we will master Chapter 9, Exercise 9.3 of your NCERT textbook, which focuses on reading and interpreting bar graphs. Data handling is an essential mathematical skill that helps us make sense of large amounts of information quickly. Instead of reading long tables of numbers, a bar graph uses visual rectangular bars to represent quantities clearly. In this guide, you will learn how to look at a bar graph, identify its scale, read values from the horizontal and vertical axes, and perform calculations like finding the maximum, minimum, or total values. Mastering data handling ex 9 3 class 6 ncert will not only help you score full marks in your school exams but also lay a strong foundation for statistics in higher classes. Let's dive in with your YoLearn AI Tutor and learn with simple step-by-step explanations!

Understanding and Reading Bar Graphs

A bar graph is a visual representation of data using rectangular bars of uniform width. These bars can be drawn horizontally or vertically with equal spacing between them. The length of each bar represents a specific value or frequency. When analyzing a bar graph, the first step is to locate the axes: the horizontal axis (X-axis) and the vertical axis (Y-axis). One of these axes will represent the categories (like years, subjects, or cities), while the other axis will represent the numerical values. The most crucial part of reading any bar graph is understanding the 'Scale'. The scale tells us what one unit length of a bar actually represents in the real world (for example, 1 unit length = 5 bags of wheat, or 1 unit length = 100 students). By aligning the top of a bar with the marked scale on the vertical axis, you can instantly determine the quantity it represents. In Exercise 9.3, we focus heavily on extracting these values to answer comparison-based questions.

Step-by-Step Method to Interpret a Bar Graph

  1. Identify the Axes and Labels — Look at what information is plotted on the horizontal axis (usually categories) and what is on the vertical axis (usually quantities).
  2. Read the Scale — Check the scale definition, which is usually written at the top-right corner of the graph (e.g., 1 unit length = 10 units).
  3. Determine Individual Bar Values — Align the top edge of each bar with the markings on the scale axis to find its corresponding numerical value.
  4. Solve the Given Questions — Use the numerical values to compute totals, differences, find the maximum or minimum, and draw conclusions.

Solved Examples on Ex 9.3 Concepts

  • Example 1: A bar graph shows the wheat purchased by government during 1998-2002. Scale: 1 unit length = 5 thousand tonnes. The bar for 1998 is 3 units tall. Calculation: 3 units * 5 thousand tonnes = 15 thousand tonnes of wheat purchased in 1998.
  • Example 2: A bar graph displays student attendance. Scale: 1 unit length = 10 students. The bar for Friday is 4.5 units tall. Calculation: 4.5 units * 10 students = 45 students present on Friday.

Exam Tips: Avoiding Common Scale Mistakes

Always double-check the scale before writing your final answer! A common mistake made by Class 6 students is reading the height of the bar directly (e.g., '5 units') instead of multiplying it by the scale factor (e.g., if 1 unit = 100 tonnes, then 5 units is actually 500 tonnes). Always write down the unit of measurement (like 'tonnes', 'students', or 'rupees') along with your numerical answer to secure full step-marks.

Practice Questions with Solutions

  • Q: Based on a bar graph representing weekly bicycle sales (Scale: 1 unit length = 5 bicycles; Mon: 4 units, Tue: 6 units, Wed: 3 units, Thu: 5 units). Find the sales on Tuesday and the total sales for these four days. A: Step 1: Identify the scale: 1 unit length = 5 bicycles. Step 2: Read the units for Tuesday: Tuesday has 6 units. Therefore, sales on Tuesday = 6 5 = 30 bicycles. Step 3: Read units for all days: Mon = 4 5 = 20, Tue = 30, Wed = 3 5 = 15, Thu = 5 5 = 25. Step 4: Find total sales: 20 + 30 + 15 + 25 = 90 bicycles. Final answer: Tuesday sales = 30 bicycles; Total sales = 90 bicycles.
  • Q: A bar graph shows the number of trees planted by a school from 2018 to 2021. Scale: 1 unit length = 20 trees. Year 2018: 3 units, Year 2019: 5 units, Year 2020: 4 units, Year 2021: 7 units. In which year were the maximum trees planted and how many? A: Step 1: Observe the height of the bars for all years. The tallest bar is for the year 2021 with 7 unit lengths. Step 2: Calculate the actual number of trees for 2021 using the scale. Scale: 1 unit length = 20 trees. Step 3: Multiply units by scale: 7 units * 20 trees/unit = 140 trees. Final answer: The maximum number of trees (140 trees) were planted in the year 2021.
  • Q: Use the tree planting data from the previous question to find the difference between the trees planted in the year 2021 and the year 2018. A: Step 1: Find the number of trees planted in 2021. From the previous solution, trees in 2021 = 7 units 20 = 140 trees. Step 2: Find the number of trees planted in 2018. 2018 has 3 units. Trees in 2018 = 3 units 20 = 60 trees. Step 3: Calculate the difference: 140 - 60 = 80 trees. Final answer: The difference in trees planted between 2021 and 2018 is 80 trees.
  • Q: A graph shows marks scored by Rohit in different subjects out of 100. Scale: 1 unit length = 10 marks. Hindi: 6 units, English: 8 units, Maths: 9 units, Science: 7 units. What is the ratio of marks scored in Maths to marks scored in Hindi? A: Step 1: Find the marks scored in Maths. 9 units 10 = 90 marks. Step 2: Find the marks scored in Hindi. 6 units 10 = 60 marks. Step 3: Write down the ratio: Marks in Maths : Marks in Hindi = 90 : 60. Step 4: Simplify the ratio by dividing both numbers by their highest common factor (30): 90/30 : 60/30 = 3 : 2. Final answer: The ratio of marks scored in Maths to Hindi is 3:2.

Frequently Asked Questions

What is the scale of a bar graph?

The scale of a bar graph is a ratio that defines how many real-world units are represented by one unit length of a bar on the graph. For example, a scale of 1 unit = 10 students means a bar of height 5 units represents 50 students.

Why do we leave equal spaces between the bars in a bar graph?

We leave equal spaces between bars to make the graph clean, neat, and easy to read. This spacing ensures that each category remains distinct and visually independent from the others.

How do we find the total quantity from a bar graph?

To find the total quantity, identify the numerical value of each individual bar using the scale, and then add all these values together.