CBSE Class 6 Maths Chapter 5: Data Handling NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Maths, Chapter 5, Data Handling, introduces students to the essential skills of organizing and interpreting information. The NCERT Solutions for this chapter focus on practical applications, guiding learners through exercises involving tally marks for counting occurrences, understanding bar graphs for visual representation, and analyzing frequency distributions to identify patterns. Students will develop the ability to systematically collect, organize, and present data, enabling them to draw meaningful conclusions. These solutions offer clear, step-by-step explanations to solve a variety of problems, reinforcing the foundational concepts of data handling. Mastering these skills is crucial for building a strong base in statistics and preparing effectively for future academic challenges.

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Quick info

BoardCBSE
ClassClass 6
SubjectMaths Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 5

Chapter summary

Chapter 5, Data Handling, focuses on the basics of collecting, organizing, and presenting data. The NCERT Solutions for this chapter guide students through understanding tally marks for data representation, interpreting bar graphs, and analyzing frequency of data points. It covers identifying patterns and drawing simple conclusions from data sets, essential skills for early statistical understanding.

Learning outcomes

  • Understand the use of tally marks for data representation.
  • Interpret data presented in various formats.
  • Solve problems related to frequency and data analysis.
  • Identify patterns and trends in data sets.
  • Differentiate between true and false statements about bar graphs.

Topics covered

Paper topics

  • Data Handling
  • Tally Marks
  • Data Representation
  • Frequency
  • Bar Graphs
  • Data Interpretation
  • Data Analysis
  • Statistics Basics

Important topics

  • Tally Marks Representation
  • Interpreting Bar Graphs
  • Counting Frequencies
  • Comparing Data Sets

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Questions and Solutions

Question 1

Using tally marks, which one of the following represents the number eight?
Solution: Tally marks are used to count data. Each group of five is represented by four vertical lines and one diagonal line crossing them (\(\text{M/}\)). To represent the number eight, we need one group of five and three more. This is shown as \(\text{M/III}\). Therefore, option (D) is the correct representation.

Question 2

The marks (out of 10) obtained by 28 students in a Mathematics test are listed as below: 8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9, 2, 0. The number of students who obtained marks more than or equal to 5 is:
Solution: First, let's list the marks obtained by the 28 students: 8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9, 2, 0. We need to find the number of students who scored 5 or more marks. Let's count them: 8, 6, 5, 5, 5, 5, 8, 8, 10, 10, 8, 7, 8, 8, 9, 9, 10, 10. Counting these values, we find there are 17 students who scored marks greater than or equal to 5. Thus, the correct option is (D).

Question 3

In question 2 above, the number of students who scored marks less than 4 is:
Solution: The marks obtained by the 28 students are: 8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9, 2, 0. We need to find the number of students who scored marks less than 4. The marks less than 4 are 0, 1, 2, and 3. Let's count how many students obtained these marks: Marks 0: 4 students; Marks 1: 2 students; Marks 2: 2 students; Marks 3: 2 students. The total number of students who scored less than 4 is 4 + 2 + 2 + 2 = 10. Therefore, option (D) is correct.

Question 4

The choices of the fruits of 42 students in a class are as follows: A, O, B, M, A, G, B, G, A, G, B, M, A, G, M, A, B, G, M, B, A, O, M, M, O, G, B, O, M, G, A, A, B, M, O, M, O, M, O, M, O, M, O. where A, B, G, M and O stand for the fruits Apple, Banana, Grapes, Mango and Orange respectively. Which two fruits are liked by an equal number of students?
Solution: Let's count the number of students who liked each type of fruit based on the given data:

Apple (A): 9 students

Banana (B): 8 students

Grapes (G): 8 students

Mango (M): 10 students

Orange (O): 7 students

By comparing these counts, we can see that Banana and Grapes are each liked by 8 students. Therefore, Banana and Grapes are the two fruits liked by an equal number of students. Option (D) is correct.

Question 5

According to the data in question 4, which fruit is liked by most of the students?
Solution: From the counts calculated in the previous question:

Apple (A): 9 students

Banana (B): 8 students

Grapes (G): 8 students

Mango (M): 10 students

Orange (O): 7 students

Comparing these numbers, Mango is liked by 10 students, which is the highest number among all the fruits. Therefore, Mango is the fruit liked by most of the students. Option (C) is correct.

Question 6

In a bar graph, the width of bars may be unequal. State whether this statement is True (T) or False (F).
Solution: In a bar graph, it is essential that all bars have the same width to ensure a fair visual comparison of data. Unequal widths can distort the perception of the data. Therefore, the statement is False (F).

Question 7

In a bar graph, bars of uniform width are drawn vertically only. State whether this statement is True (T) or False (F).
Solution: Bar graphs can be drawn with bars oriented either vertically or horizontally. The key features are uniform width and appropriate spacing, not the direction of the bars. Therefore, the statement that bars are drawn vertically only is False (F).

Question 8

In a bar graph, the gap between two consecutive bars may not be the same. State whether this statement is True (T) or False (F).
Solution: For a bar graph to be clear and easy to interpret, the gap between any two consecutive bars must be consistent. This uniformity in spacing helps in distinguishing between different categories of data. Therefore, the statement that the gap may not be the same is False (F).

Common mistakes

  • Incorrectly counting tally marks.
  • Misinterpreting data from bar graphs.
  • Confusing 'more than' and 'less than' conditions in data analysis.
  • Assuming bar graphs can only be vertical.

Revision tips

  • Practice drawing tally marks for different numbers.
  • Visualize data presented in bar graphs and extract information.
  • Review the properties of bar graphs (width, gap).
  • Work through each example and exercise to reinforce understanding.

Practice MCQs

Q1. Which of the following correctly represents the number eight using tally marks?

Q2. In a test, if 28 students scored marks, how many students scored 5 or more marks, given the data?

Q3. From the same test data, how many students scored less than 4?

Q4. In a survey of fruit preferences, if Banana and Grapes were liked by an equal number of students, which option would be correct?

Q5. Which fruit was liked by the most students according to the survey data?

Frequently asked questions

What is the main focus of Chapter 5: Data Handling for Class 6 Maths?

Chapter 5 focuses on the fundamental concepts of collecting, organizing, representing, and interpreting data using tools like tally marks and bar graphs.

How do tally marks help in data handling?

Tally marks provide a quick and efficient way to count the frequency of data items by grouping them in sets of five, making data easier to manage and read.

What are the key properties of a bar graph mentioned in the solutions?

Bar graphs use bars of uniform width, and the gap between consecutive bars should also be uniform. Bars can be drawn vertically or horizontally.

How can these NCERT Solutions help students prepare for exams?

These solutions offer detailed, step-by-step explanations for each question, helping students understand the methods, practice problem-solving, and identify common errors for better exam preparation.

What does it mean to interpret data?

Interpreting data means analyzing the organized information to draw conclusions, identify trends, and answer specific questions, such as which item is most frequent or least frequent.

Important links

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