CBSE Class 6 Mathematics Chapter 9: Data Handling NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Mathematics Chapter 9: Data Handling introduces students to the essential skills of organizing and interpreting information. The NCERT Solutions offer clear, step-by-step guidance on collecting, recording, and representing data using methods like tally marks and tables. Learners will discover how to analyze this organized information to answer questions, such as determining the frequency of various data points or identifying the most and least common items. These solutions aim to establish a solid foundation in data analysis, which is vital for grasping more advanced mathematical ideas in the future. Engaging with these exercises will sharpen problem-solving abilities and effectively prepare students for their exams by reinforcing key data handling techniques.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 9: Data Handling

Chapter summary

Chapter 9, Data Handling, for Class 6 Mathematics focuses on the basics of data organization and representation. The NCERT Solutions cover exercises that involve using tally marks to count frequencies of data points, creating tables to summarize information, and interpreting these tables to answer questions about minimum, maximum, and equal occurrences. This chapter equips students with essential skills for managing and understanding numerical and categorical data.

Learning outcomes

  • Understand the concept of data and its importance.
  • Learn to organize data using tally marks.
  • Create frequency tables for given data sets.
  • Interpret data presented in tables to answer questions.
  • Identify the minimum and maximum frequency of data points.
  • Determine data points that occur an equal number of times.

Topics covered

Paper topics

  • Data
  • Data Organization
  • Tally Marks
  • Frequency
  • Frequency Table
  • Data Interpretation
  • Mathematics
  • Class 6
  • CBSE
  • Data Handling
  • Statistics Basics
  • Data Representation

Important topics

  • Using Tally Marks
  • Creating Frequency Tables
  • Interpreting Data Tables
  • Finding Minimum and Maximum Frequencies
  • Identifying Equal Frequencies

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Questions and Solutions

Question 1

In a mathematics test, 40 students obtained the following marks. Arrange these marks in a table using tally marks.

8 1 3 7 5 6 5 4 4 2

4 9 5 3 1 7 6 5 2 7

7 3 8 4 8 2 9 5 8 6

7 4 5 6 6 9 4 4 6 6

  1. Find how many students obtained marks equal to or more than 7?
  2. How many students obtained marks below 4?
Solution:

To organize the marks obtained by 40 students, we will create a table using tally marks to count the frequency of each score.

Marks Tally Marks Number of Students
1 II 2
2 III 3
3 III 3
4 IIII II 7
5 IIII I 6
6 IIII II 6
7 IIII I 5
8 IIII 4
9 III 3

Let's verify the total number of students: 2 + 3 + 3 + 7 + 6 + 6 + 5 + 4 + 3 = 40. This matches the given total number of students.

  1. To find the number of students who obtained marks equal to or more than 7, we add the number of students who scored 7, 8, and 9: Number of students = (Students with 7 marks) + (Students with 8 marks) + (Students with 9 marks) = 5 + 4 + 3 = 12 students.
  2. To find the number of students who obtained marks below 4, we add the number of students who scored 1, 2, and 3: Number of students = (Students with 1 mark) + (Students with 2 marks) + (Students with 3 marks) = 2 + 3 + 3 = 8 students.

Answer:

  1. Twelve students obtained marks equal to or more than 7.
  2. Eight students obtained marks below 4.

Question 2

Following is the choice of sweets of 30 students of Class VI.

Ladoo, Barfi, Ladoo, jalebi, Ladoo, Rashulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi, Jalebi, Rashulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo, Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo

  1. Arrange the names of sweets in a table using tally marks.
  2. Which sweet is preferred by most of the students?
Solution:

We need to count the frequency of each type of sweet chosen by the 30 students and represent it using tally marks in a table.

Sweets Tally Marks Number of Students
Ladoo IIII IIII I 11
Barfi III 3
Jalebi IIII II 7
Rasgulla IIII IIII 9

Let's check the total number of students: 11 (Ladoo) + 3 (Barfi) + 7 (Jalebi) + 9 (Rasgulla) = 30 students. This matches the given total.

  1. The table above shows the arrangement of sweets using tally marks and the count of students for each.
  2. To find which sweet is preferred by most students, we look for the sweet with the highest number of tally marks or the largest count. In this case, Ladoo is preferred by 11 students, which is the highest number.

Answer:

  1. The table is provided above.
  2. Ladoo is the sweet preferred by most of the students.

Question 3

Catherine threw a dice 40 times and noted the number appearing each time as shown below:

1 3 5 6 3 6 5 4 1 6

2 5 3 4 1 6 5 5 6 1

1 2 2 3 2 5 4 5 5 6

5 1 6 2 5 3 2 4 1 5

Make a table and enter the data using tally marks. Find the number that appeared:

  1. The minimum number of times.
  2. The maximum number of times.
  3. Find those numbers that appear an equal number of times.
Solution:

First, we will organize the data from the 40 dice throws into a table using tally marks to count how many times each number (1 through 6) appeared.

Numbers Tally Marks How many times?
1 IIII II 7
2 IIII I 6
3 IIII 5
4 IIII 4
5 IIII IIII 11
6 IIII II 7

Let's check the total number of throws: 7 + 6 + 5 + 4 + 11 + 7 = 40. This matches the total number of times the dice was thrown.

  1. The minimum number of times a number appeared is found by looking for the smallest count in the 'How many times?' column. The smallest count is 4, which corresponds to the number 4.
  2. The maximum number of times a number appeared is found by looking for the largest count in the 'How many times?' column. The largest count is 11, which corresponds to the number 5.
  3. To find numbers that appear an equal number of times, we look for identical counts in the 'How many times?' column. We see that the number 1 appeared 7 times and the number 6 also appeared 7 times.

Answer:

  1. The minimum number of times = 4 (for the number 4).
  2. The maximum number of times = 11 (for the number 5).
  3. The numbers 1 and 6 appear an equal number of times (7 times each).

Common mistakes

  • Incorrectly using tally marks (e.g., not grouping in fives).
  • Miscounting data points when creating tables.
  • Errors in interpreting the frequency from tally marks.
  • Confusing minimum and maximum values.
  • Overlooking data points that appear an equal number of times.

Revision tips

  • Practice creating tally marks accurately for each data set.
  • Double-check your frequency counts against the original data.
  • Pay close attention to the specific questions asked after creating the table.
  • Review the examples to understand different ways data can be presented and analyzed.
  • Try to create your own small data sets and practice organizing them.

Practice MCQs

Q1. What is the primary method used in this chapter to organize raw data?

Q2. In Exercise 9.1, Question 1, how many students scored 7 or more marks?

Q3. Which sweet was preferred by the least number of students in Exercise 9.2?

Q4. In Exercise 9.3, what is the maximum number of times any number appeared when the dice was thrown 40 times?

Q5. According to Exercise 9.3, which numbers appeared an equal number of times?

Frequently asked questions

What is the main goal of Chapter 9: Data Handling in Class 6 Maths?

The main goal is to teach students how to collect, organize, represent, and interpret data using methods like tally marks and frequency tables.

How do tally marks help in organizing data?

Tally marks provide a quick and systematic way to count the occurrences (frequency) of each data item, making it easier to create a summary table.

What does it mean to find the 'maximum number of times' a number appeared?

It means identifying which number occurred most frequently in the given data set, as shown by the highest count in the tally marks or frequency table.

Are these NCERT Solutions for Class 6 Maths Chapter 9 suitable for exam preparation?

Yes, these solutions offer clear explanations and step-by-step methods for all exercises, which are excellent for understanding concepts and practicing for exams.

What kind of data is typically handled in this chapter?

This chapter deals with both numerical data (like marks or dice rolls) and categorical data (like choices of sweets).

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