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 collecting, organizing, and presenting data. The NCERT Solutions guide learners through representing raw data using tally marks and tables, making it easier to understand. Students will practice counting frequencies to answer questions about the data, such as identifying the most and least common items or determining how many individuals fall within specific ranges. This chapter lays the groundwork for future statistical learning by developing critical thinking and analytical abilities. The solutions offer clear explanations and practice exercises, ensuring students grasp the core concepts of data interpretation and preparation for their assessments.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 9

Chapter summary

Chapter 9, Data Handling, for Class 6 Mathematics focuses on organizing data using tally marks and presenting it in tables. The NCERT Solutions cover exercises that involve collecting data, creating frequency tables, and interpreting the information to answer questions about data distribution, preferences, and occurrences. Key skills include counting, grouping, and analyzing data sets to find specific values and patterns.

Learning outcomes

  • Understand the concept of data handling and its importance.
  • Learn to use tally marks for organizing data.
  • Create frequency tables from given data.
  • Interpret data presented in tables to answer questions.
  • Identify the most frequent and least frequent data points.
  • Solve problems related to data interpretation in real-world scenarios.

Topics covered

Paper topics

  • Data Handling
  • Tally Marks
  • Frequency Tables
  • Data Organization
  • Data Interpretation
  • Mathematics
  • Class 6
  • CBSE

Important topics

  • Using Tally Marks
  • Creating Frequency Tables
  • Interpreting Data from Tables
  • Finding Minimum/Maximum Occurrences
  • Identifying Most Preferred Options

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Questions and Solutions

Question 1

In a mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks. The marks obtained are: 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 solve this problem, we first need to organize the given marks of 40 students using tally marks. We will create a table showing each mark, its tally representation, and the total number of students who obtained that mark (frequency).

Here is the table:

Marks Tally Marks No. of students
1 || 2
2 ||| 3
3 ||| 3
4 ||||||| 7
5 MI || 6
6 MI |||| 6
7 MI |||| 5
8 |||| 4
9 ||| 3

Let's verify the total number of students by summing the 'No. of students' column: 2 + 3 + 3 + 7 + 6 + 6 + 5 + 4 + 3 = 40. This matches the given total number of students.

Now, let's answer the specific questions:

  1. Marks equal to or more than 7: We need to count the students who scored 7, 8, or 9. From the table, the number of students are 5 (for mark 7) + 4 (for mark 8) + 3 (for mark 9) = 12 students.
  2. Marks below 4: We need to count the students who scored 1, 2, or 3. From the table, the number of students are 2 (for mark 1) + 3 (for mark 2) + 3 (for mark 3) = 8 students.

Answers:

  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, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi, Jalebi, Rasgulla, 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 are given the choices of sweets for 30 students. To organize this data, we will create a table using tally marks to count the preference for each type of sweet.

First, let's list the types of sweets mentioned: Ladoo, Barfi, Jalebi, Rasgulla.

Now, we count the occurrences of each sweet using tally marks:

Sweets Tally Marks No. of students
Ladoo MI MI || 11
Barfi ||| 3
Jalebi MI || 7
Rasgulla MI MI || 9

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

Now we can answer the questions:

  1. The table above shows the arrangement of sweets using tally marks and the number of students who prefer each.
  2. To find the sweet preferred by most students, we look for the highest number in the 'No. of students' column. The highest number is 11, which corresponds to Ladoo.

Answers:

  1. The table is provided above.
  2. Ladoo is the sweet preferred by most of the students, as 11 students chose it.

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:

We need to organize the results of Catherine's 40 dice throws using tally marks in a table. The possible outcomes when rolling a standard die are numbers 1 through 6.

Let's count the occurrences of each number using tally marks:

Numbers Tally Marks How many times?
1 MI || 7
2 MI | 6
3 MI 5
4 |||| 4
5 MI MI || 11
6 MI || 7

Let's verify the total number of throws: 7 + 6 + 5 + 4 + 11 + 7 = 40. This matches the given total number of throws.

Now, let's answer the specific questions based on the table:

  1. The minimum number of times: We look 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: We look for the largest count in the 'How many times?' column. The largest count is 11, which corresponds to the number 5.
  3. Numbers that appear an equal number of times: We need to find numbers that have the same frequency. Observing the 'How many times?' column, we see that the number 1 appeared 7 times and the number 6 also appeared 7 times. Therefore, 1 and 6 appeared an equal number of times.

Answers:

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

Common mistakes

  • Incorrectly using tally marks (e.g., not grouping in fives).
  • Miscounting frequencies from tally marks.
  • Errors in interpreting the questions asked about the data.
  • Data entry errors when transferring raw data to tables.

Revision tips

  • Practice creating tally mark tables for different data sets.
  • Carefully read each question before answering to ensure you understand what is being asked.
  • Double-check your counts for each category after creating the table.
  • Try to explain the data trends in your own words after solving the problems.

Practice MCQs

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

Q2. In tally marks, how is the number 5 represented?

Q3. If 11 students prefer Ladoo, how would this be shown using tally marks?

Q4. In Exercise 9.1, Question 1, what is the total number of students?

Q5. Which sweet was preferred by the maximum number of students in Exercise 9.2?

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 organize raw data using tally marks and present it in a table to make it easier to understand and interpret.

How do tally marks help in data handling?

Tally marks provide a quick and systematic way to count the occurrences of each item in a data set, especially when dealing with large amounts of data.

What does 'frequency' mean in the context of data handling?

Frequency refers to the number of times a particular data item appears in a data set. It is usually represented by tally marks and then counted.

How can these NCERT solutions help students prepare for exams?

These solutions offer clear, step-by-step explanations for each problem, helping students understand the methods and practice applying them to similar questions, thus boosting their confidence.

What kind of questions are covered in Exercise 9.1?

Exercise 9.1 involves arranging given marks of students in a table using tally marks and then answering questions about how many students scored above or below a certain mark.

What is the purpose of the table in Exercise 9.2?

The table in Exercise 9.2 is used to organize the choices of sweets preferred by students, using tally marks to count how many students prefer each type of sweet.

Important links

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