Data Handling and Presentation notes class 6th

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Class 6 Maths Chapter 4 | DHved Learning
DHVED LEARNING

Class 6 Mathematics

Chapter 4: Data Handling and Presentation

Understand data through tables, pictures and bar graphs.

1. Learning Objectives

After studying this chapter, you should be able to:

  • Understand what data means.
  • Collect and organise information.
  • Represent numbers using tally marks.
  • Prepare and read frequency tables.
  • Understand pictographs and their keys.
  • Read, interpret and draw bar graphs.
  • Answer questions using information presented in graphs.
Real-life connection: Schools use data to record attendance, compare examination results, count library books and understand students' favourite sports.

2. What Is Data?

Data is a collection of facts, numbers or information gathered for a particular purpose.

Example

Five students report the number of books they read last month: 2, 4, 3, 2, 5.

These numbers form a collection of data.

Raw data

Information in the form in which it is first collected.

Example: 2, 4, 3, 2, 5

Organised data

Information arranged systematically for easy understanding.

Example: a table showing how often each number occurs.

Why do we organise data?

  • To understand information quickly.
  • To compare different categories.
  • To identify the most and least common results.
  • To make decisions based on information.

3. Tally Marks and Frequency Tables

Tally marks help us count items quickly. We usually make four vertical strokes and cross them with a fifth stroke to represent a group of five.

Count Tally marks Frequency
One | 1
Two || 2
Three ||| 3
Four |||| 4
Five |||| with a diagonal stroke across the four 5
Remember: Frequency tells us how many times a value or category occurs.

Worked Example

A teacher records the favourite fruits of 12 students: Mango, Apple, Mango, Banana, Apple, Mango, Orange, Banana, Mango, Apple, Banana, Mango.

Fruit Tally marks Frequency
Mango ||||/ 5
Apple ||| 3
Banana ||| 3
Orange | 1
Total 12

Mango is the most popular fruit in this group. Orange is the least popular.

4. Pictographs

A pictograph represents data using pictures or symbols. Each picture represents a particular number of items.

Example: Books Read by Students

Key: 📘 = 2 books

Student Pictograph Number of books
Aman 📘 📘 4
Riya 📘 📘 📘 6
Rahul 📘 2
Neha 📘 📘 📘 📘 8
How to read a pictograph:
  1. Read the key carefully.
  2. Count the symbols in each row.
  3. Multiply the number of symbols by the value of each symbol.

For example, Neha has four symbols. Each symbol represents two books.

Number of books = 4 × 2 = 8 books

5. Bar Graphs

A bar graph represents data using rectangular bars. The height or length of each bar represents the value of a category.

Important Parts of a Bar Graph

  • Title: tells us what the graph represents.
  • Horizontal axis: usually shows categories.
  • Vertical axis: usually shows numbers or frequencies.
  • Scale: tells us the value represented by each division.
  • Bars: have heights proportional to their values.

Example: Favourite Activities of Students

A survey of students gives the following results:

Activity Number of students
Reading10
Music15
Art20
Sports30

Favourite Activities of Students

0 5 10 15 20 25 30 10 15 20 30 Reading Music Art Sports Favourite Activities Number of Students

Scale: Each division represents 5 students.

Understanding the Graph

  1. Reading is liked by 10 students.
  2. Music is liked by 15 students.
  3. Art is liked by 20 students.
  4. Sports is liked by 30 students.
Important graph check: The Sports bar reaches exactly the 30-student line. Every bar uses the same scale, and all bars start from zero.

Questions Based on the Graph

  1. Which activity is the most popular? Sports
  2. Which activity is the least popular? Reading
  3. How many students like Art? 20 students
  4. How many more students like Sports than Music? 30 − 15 = 15 students
  5. How many students were surveyed in total? 10 + 15 + 20 + 30 = 75 students

6. Practice Worksheet

Try answering the questions before opening the solutions.

Part A: Short Questions

  1. What is data?
  2. What is the purpose of tally marks?
  3. What does frequency mean?
  4. What is a pictograph?
  5. Name two important parts of a bar graph.

Part B: Numerical Questions

  1. The numbers of pencils owned by five students are 3, 5, 2, 3, 4. How many students own three pencils?
  2. In a pictograph, one star represents 4 books. What do 5 stars represent?
  3. A bar graph shows 25 students choosing cricket and 15 choosing football. How many more students choose cricket?
  4. The frequencies of four categories are 5, 10, 15 and 20. Find the total frequency.
  5. If each division on the vertical axis represents 5 students, what value is represented by 6 divisions above zero?
Show answers and explanations

Part A

  1. Data is a collection of facts, numbers or information.
  2. Tally marks help us record and count items efficiently.
  3. Frequency is the number of times a value or category occurs.
  4. A pictograph represents data using pictures or symbols.
  5. Examples: title, axes, scale and bars.

Part B

  1. Two students own three pencils.
  2. 5 × 4 = 20 books.
  3. 25 − 15 = 10 students.
  4. 5 + 10 + 15 + 20 = 50.
  5. 6 × 5 = 30 students.

7. Interactive Quiz

Choose one answer for each question, then click Check Answers.

1. What is data?

2. A complete group of tally marks usually represents:

3. What does frequency tell us?

4. Which representation uses pictures or symbols?

5. What does the scale of a graph tell us?

6. In a bar graph, the tallest bar usually represents:

7. Sports has 30 students and Music has 15. What is the difference?

8. If one symbol represents 2 books, four symbols represent:

9. What is the total of 10, 15, 20 and 30?

10. Each division represents 5 students. What do 6 divisions represent?

8. Quick Revision

  • Data: a collection of facts or information.
  • Tally marks: a quick method of recording counts.
  • Frequency: the number of times a value occurs.
  • Pictograph: data represented through pictures or symbols.
  • Bar graph: data represented using rectangular bars.
  • Scale: the value represented by each division.
  • Total frequency: the sum of all category frequencies.
  • Difference: subtract the smaller value from the larger value.
Study tip: Always check the title, axes, labels and scale before answering questions about a graph.

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