RD Sharma Solutions Class 6 Maths Chapter 21 Data Handling I (Presentation of Data)
RD Sharma Solutions Class 6 Maths Chapter 21: Data Handling I (Presentation of Data) in RD Sharma Class 6 Math Chapter 21 teaches students how to arrange numbers and information so they make sense. This chapter teaches how to collect data, arrange it in tables, and represent it using tally marks, pictographs, and bar graphs. It forms the base for advanced topics in statistics and is extremely useful for students preparing for higher classes and competitive exams, where data interpretation is a frequent topic.
Practicing questions from RD Sharma Solutions Class 6 Chapter 21 helps students understand patterns, make comparisons, and draw conclusions from data—all of which are crucial analytical skills. This chapter follows the newest CBSE syllabus and works alongside NCERT Class 6 Math solutions to help students learn better. Regular practice of these problems improves logical thinking, boosts confidence, and prepares students for various Olympiads and reasoning-based exams. This makes Data Handling a must-practice topic for every Class 6 student.
RD Sharma Solutions Class 6 Maths Chapter 21 Data Handling I (Presentation of Data)
Data Handling is the method of collecting, organizing, and presenting numerical information in a way that makes it easy to understand and analyze. It involves arranging raw data into readable formats like tables, tally charts, pictographs, and bar graphs. This skill helps students interpret facts, observe patterns, and make informed decisions based on numbers.
Topics Covered in RD Sharma Class 6 Chapter 21
In RD Sharma Solutions Class 6 Maths Chapter 21, students will learn:
- What is Data? – Understanding raw data and its importance
- How to Organize Data – Arranging numbers in tables and using tally marks
- Presentation of Data – Using pictographs and bar graphs to show data visually
- Reading Graphs – Interpreting information from given graphs
- Drawing Pictographs – Representing data with pictures or symbols
- Creating Bar Graphs – Drawing vertical and horizontal bar graphs using scale
Exercises in RD Sharma Chapter 21 (Data Handling I)
The chapter is divided into one main exercise:
Exercise 21.1 – This exercise includes various problems on organizing data, drawing pictographs, and interpreting bar graphs. Questions vary from basic data arrangement to slightly advanced level graphical representation problems.
Why Students Should Practice This Chapter
Data Handling is a key part of the Class 6 Maths syllabus and frequently appears in Olympiads and competitive exams.
It builds analytical and logical reasoning skills, which are important for higher studies in Maths, Science, and even real-world decision making.
Practicing from RD Sharma Solutions Class 6 Maths Chapter 21 ensures students learn how to handle data systematically, making it easy to solve word problems and graphical questions confidently.
RD Sharma Solutions Class 6 Maths Chapter 21 - PDF Download
You can now easily access the RD Sharma Solutions Class 6 Maths Chapter 21 Data Handling I – Download PDF to practice important concepts like organizing, representing, and interpreting data. This PDF includes well-explained solutions, pictographs, bar graphs, and data tables that follow the latest CBSE syllabus. With this PDF, students can study anytime, revise faster, and strengthen their understanding of data handling. It’s a handy resource for exam preparation and builds a strong base for competitive exams.
Start learning smart—download the Chapter 21 RD Sharma PDF and make your maths practice simple and productive.
Don't Miss: Download PDF for All Chapters
Access Answers to Class 6 Maths RD Sharma Textbook Solutions for Chapter 21
1- Explain the following statistical terms in your own words:
(i) What constitutes an observation in statistical analysis?
(ii) How would you define data in the context of mathematics?
(iii) What does the term "frequency of an observation" mean?
(iv) Describe what a frequency distribution represents in statistical analysis.
Solution:
(i) An observation refers to information deliberately gathered from a primary source during statistical investigation. It represents individual pieces of information recorded during data collection.
(ii) Data refers to a systematically collected set of facts, numbers, measurements, or characteristics that serves as the foundation for statistical analysis and interpretation.
(iii) The frequency of an observation indicates how many times that particular value or outcome appears within a collected dataset. It quantifies the occurrence rate of specific values.
(iv) A frequency distribution is an organized arrangement of data that displays how often each distinct value occurs. It transforms raw data into a structured format that facilitates better understanding and analysis of the underlying patterns.
2- In a mathematics assessment, 30 sixth-grade students received the following final scores:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90
75, 88, 77, 37, 84, 58, 60, 48, 62, 56
44, 58, 52, 64, 98, 59, 70, 39, 50, 60
Answer the following:
(i) Group these scores in ascending intervals (30-39, 40-49, etc.) and create a frequency distribution.
(ii) What was the maximum score achieved?
(iii) What was the minimum score achieved?
(iv) Calculate the range of the scores.
(v) If students need 40 points to pass, how many students did not achieve a passing grade?
(vi) How many students achieved scores of 75 or higher?
(vii) Which specific values between 50 and 60 are missing from the dataset?
(viii) How many students scored below 50 points?
Solution: (i) Frequency distribution of mathematics assessment scores:
| Score Range | Frequency (Number of Students) |
| 30-39 | 2 |
| 40-49 | 4 |
| 50-59 | 3 |
| 60-69 | 8 |
| 70-79 | 3 |
| 80-89 | 2 |
| 90-99 | 2 |
| 100-109 | 1 |
| Total | 30 |
(ii) The maximum score achieved was 100 points.
(iii) The minimum score achieved was 37 points.
(iv) Range calculation:
Range = Maximum score - Minimum score
Range = 100 - 37 = 63 points
(v) Students who didn't achieve a passing grade (scores < 40):
The scores 37 and 39 are below 40.
Therefore, 2 students did not achieve a passing grade.
(vi) Students who scored 75 or higher:
The scores 75, 77, 78, 84, 88, 90, 98, and 100 are all 75 or higher.
Therefore, 8 students achieved scores of 75 or higher.
(vii) Missing values between 50 and 60:
The dataset includes 50, 52, 53, 55, 56, 58, 59, and 60.
The values 51, 54, and 57 are missing from the 50-60 range.
(viii) Students scoring below 50 points:
The scores 37, 39, 44, 48, and 48 are all below 50.
Therefore, 5 students scored below 50 points.
3. At a hospital's maternity ward, the weights (in kg) of 15 newborn babies recorded on a particular day were:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
Analyze this data to answer:
(i) Arrange these weights in descending order.
(ii) Determine the highest recorded weight.
(iii) Determine the lowest recorded weight.
(iv) Calculate the weight range.
(v) How many births occurred on this day?
(vi) How many babies weighed less than 2.5 kg?
(vii) How many babies weighed more than 2.8 kg?
(viii) How many babies weighed exactly 2.8 kg?
Solution:
(i) Weights arranged in descending order:
3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1
(ii) The highest recorded weight was 3.1 kg.
(iii) The lowest recorded weight was 2.1 kg.
(iv) Weight range calculation:
Range = Highest weight - Lowest weight
Range = 3.1 - 2.1 = 1.0 kg
(v) By counting the total number of weight entries in the dataset, we determine that 15 births occurred on this day.
(vi) Babies weighing less than 2.5 kg:
The weights 2.1, 2.2, 2.3, and 2.4 are all below 2.5 kg.
Therefore, 4 babies weighed less than 2.5 kg.
(vii) Babies weighing more than 2.8 kg:
The weights 2.9, 2.9, 3.0, and 3.1 are all above 2.8 kg.
Therefore, 4 babies weighed more than 2.8 kg.
(viii) Babies weighing exactly 2.8 kg:
Looking at the data, exactly 2 babies weighed 2.8 kg.
4. A survey recorded the number of children in 40 different households, resulting in the following dataset:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2
2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2
Create a comprehensive frequency distribution for this data.
Solution:
Frequency distribution of children per household:
| Number of Children | Frequency (Number of Households) |
| 0 | 5 |
| 1 | 7 |
| 2 | 12 |
| 3 | 5 |
| 4 | 5 |
| 5 | 3 |
| 6 | 3 |
| Total | 40 |
5- A standard six-sided die was rolled 25 times during a probability experiment. The following outcomes were recorded:
1, 5, 2, 4, 3
6, 1, 4, 2, 5
1, 6, 2, 6, 3
5, 4, 1, 3, 2
3, 6, 1, 5, 2
Construct a frequency table for the recorded outcomes.
Solution:
Frequency table of die roll outcomes:
| Outcome | Frequency |
| 1 | 5 |
| 2 | 5 |
| 3 | 4 |
| 4 | 3 |
| 5 | 4 |
| 6 | 4 |
| Total | 25 |
6- A traffic safety study monitored the number of accidents per day at a busy intersection over 30 days. The following data was collected:
6, 3, 5, 6, 4, 3, 2, 5, 4, 2
4, 2, 1, 2, 2, 0, 5, 4, 6, 1
6, 0, 5, 3, 6, 1, 5, 5, 2, 6
Create a frequency distribution table for this traffic accident data.
Solution:
Frequency distribution of daily traffic accidents:
| Number of Accidents | Frequency (Number of Days) |
| 0 | 2 |
| 1 | 3 |
| 2 | 6 |
| 3 | 3 |
| 4 | 4 |
| 5 | 6 |
| 6 | 6 |
| Total | 30 |
7- The ages (in years) of 30 eighth-grade students at a middle school were recorded as follows:
13, 14, 13, 12, 14, 13, 14, 15, 13, 14, 13, 14, 16, 12, 14
13, 14, 15, 16, 13, 14, 13, 12, 17, 13, 12, 13, 13, 13, 14
Develop a frequency table to organize this age data.
Solution:
Frequency table of eighth-grade student ages:
| Age (years) | Frequency (Number of Students) |
| 12 | 4 |
| 13 | 12 |
| 14 | 9 |
| 15 | 2 |
| 16 | 2 |
| 17 | 1 |
| Total | 30 |
8- The weekly wages (in Rs.) of 15 factory workers were documented as follows:
300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250
Generate a frequency table and answer:
(i) What is the range in weekly wages?
(ii) How many workers earn Rs. 350 per week?
(iii) How many workers receive the minimum wage?
Solution:
Frequency table of weekly wages:
| Weekly Wage (Rs.) | Frequency (Number of Workers) |
| 150 | 3 |
| 200 | 5 |
| 250 | 4 |
| 300 | 2 |
| 350 | 1 |
| Total | 15 |
(i) Range calculation:
Range = Maximum wage - Minimum wage
Range = Rs. 350 - Rs. 150 = Rs. 200
(ii) From the frequency table, we can see that 1 worker earns Rs. 350 per week.
(iii) The minimum wage in this dataset is Rs. 150.
According to the frequency table, 3 workers receive the minimum wage of Rs. 150.
9- In a history assessment, 25 sixth-grade students achieved the following scores:
9, 17, 12, 20, 9, 18, 25, 17, 19, 9, 12, 9, 12, 18, 17, 19, 20, 25, 9, 12, 17, 19, 19, 20, 9
Develop a frequency distribution table and answer:
(i) What is the range of the assessment scores?
(ii) What is the highest score achieved?
(iii) Which score appears most frequently in the dataset?
Solution:
Frequency distribution of history assessment scores:
| Score | Frequency (Number of Students) |
| 9 | 6 |
| 12 | 4 |
| 17 | 4 |
| 18 | 2 |
| 19 | 5 |
| 20 | 3 |
| 25 | 2 |
| Total | 25 |
(i) Range calculation:
Range = Highest score - Lowest score
Range = 25 - 9 = 16
(ii) The highest score achieved was 25.
(iii) By examining the frequency table, we can determine that the score 9 appears most frequently with a count of 6 occurrences.
Problem Set 10
10- A mathematics test was administered to 40 sixth-grade students who achieved the following scores:
8, 1, 3, 7, 6, 5, 5, 4, 4, 2
4, 9, 5, 3, 7, 1, 6, 5, 2, 7
7, 3, 8, 4, 2, 8, 9, 5, 8, 6
7, 4, 5, 6, 9, 6, 4, 4, 6, 6
Create a frequency table using tally marks and answer:
(i) How many students scored 7 or higher?
(ii) How many students scored below 4?
Solution:
Frequency table of mathematics test scores using tally marks:
| Score | Tally Marks | Frequency |
| 1 | II | 2 |
| 2 | III | 3 |
| 3 | III | 3 |
| 4 | IIIII I | 6 |
| 5 | IIIII | 5 |
| 6 | IIIII II | 7 |
| 7 | IIIII | 5 |
| 8 | IIII | 4 |
| 9 | III | 3 |
| Total | 40 |
(i) Students who scored 7 or higher:
Number of students = Frequency of 7 + Frequency of 8 + Frequency of 9
Number of students = 5 + 4 + 3 = 12
(ii) Students who scored below 4:
Number of students = Frequency of 1 + Frequency of 2 + Frequency of 3
Number of students = 2 + 3 + 3 = 8
RD Sharma Solutions Class 6 Maths Chapter 21 Data Handling I FAQs
What is covered in RD Sharma Class 6 Chapter 20 Mensuration?
RD Sharma Solutions Class 6 Maths Chapter 20 Mensuration covers key concepts like the area and perimeter of simple geometrical shapes such as squares, rectangles, and triangles. Students learn how to use formulas to calculate boundaries and surfaces of flat figures, including units of measurement. The chapter also introduces real-life applications of Mensuration, helping students understand how measurements are used in fields like construction, design, and architecture
Why should I use RD Sharma Solutions for Class 6 Maths Chapter 20 preparation?
RD Sharma Solutions Class 6 Chapter 20 Mensuration simplify complex problems. These solutions are excellent for students who need extra help understanding the logic behind formulas for area and perimeter. They also align well with NCERT Solutions Class 6 Maths, making them a reliable supplementary resource.
Is RD Sharma Class 6 Chapter 20 helpful for Olympiads and competitive exams?
Yes, Mensuration is a common topic in Olympiads and competitive exams, and practicing with RD Sharma Solutions Class 6 Chapter 20 helps students prepare effectively. The chapter includes a variety of problems, from basic level to application-based questions, that enhance logical thinking. It improves the student’s ability to solve questions involving real-life measurements
Are RD Sharma Solutions Class 6 Maths Chapter 20 aligned with the CBSE syllabus?
Absolutely! RD Sharma Solutions Class 6 Chapter 20 Mensuration are fully aligned with the latest CBSE syllabus for the academic year. The content is structured in a way that complements NCERT Class 6 Maths, ensuring that all important topics—such as perimeter, area, and measurement units—are covered thoroughly.
What are the benefits of practicing extra questions in Chapter 20 Mensuration?
Practicing extra questions from RD Sharma Class 6 Maths Chapter 20 Mensuration helps deepen your understanding of the topic. It allows students to apply formulas in various ways and prepares them for tricky or unseen questions in exams. Extra questions also improve speed, accuracy, and logical thinking—skills vital for both school assessments and competitive exams.