case study questions class 7 maths pdf chapter 3

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CBSE 7th Standard CBSE Mathematics question papers, important notes , study materials , Previuous Year questions, Syllabus and exam patterns. Free 7th Standard CBSE Mathematics books and syllabus online. Practice Online test for free in QB365 Study Material. Important keywords, Case Study Questions and Solutions. Updates about latest education news and Scholorships in one place.

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NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF Download

The NCERT Solutions for Class 7 Maths Chapter 3 Data Handling covers all the exercises included in the textbook. By referring to the Chapter 3 Data Handling Maths questions, students can easily understand each and every step so that they can build their problem-solving skills as well as comprehension skills which is a must to score good marks.

The NCERT Solutions for Class 7 Maths Chapter 3 Data Handling are well structured and systematic so that students can get an overall viewpoint of the important questions. By referring to the important questions of Chapter 3 Data Handling, students can improve their confidence level which can be implemented in the Maths final exam. 

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF

If students are looking for accurate and comprehensive answers then they can prefer utilising the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF. Students generally prefer utilising the NCERT Solutions after solving the Chapter 3 Data Handling Maths questions so that they can match their answers and accordingly they can work upon. Students can refer to the NCERT Solutions of Chapter 3 Data Handling from the Selfstudys from their comfort zone. 

How to Download the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling?

To download the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling, students need to follow the given steps, those steps are: 

• Visit the Selfstudys website. 

• Bring the arrow towards NCERT Books & Solutions. 

• A drop down menu will appear, select NCERT Solutions from the list. 

• A new page will appear, select Class 7 from the list of classes. 
• Click Maths from the list of classes. 
• Again a new page will appear, select Chapter 3 Data Handling from the list of classes. 

Features of NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF

It is advisable for students to know everything about the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF; those important features are discussed below: 

• Diagrams and Illustrations are Included: In the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling, diagrams and illustrations are included like wherever there is a need so that students can visualise the concepts well. 
• Answers are Included: Inside the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling revision, answers of all the NCERT questions are included so that students can understand the steps easily. 
• Provides Practise Questions: Students can easily practise questions from the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling theory as it is already available in it. By practising questions of Class 7 Maths, students can easily improve their problem solving skills. 
• Easy to Understand the Language: The Class 7 Maths language used in the NCERT Solutions are very easy to understand so that students can easily understand the questions and answers well. 
• All Topics are Covered: In the NCERT Class 7 Maths Solutions, all the topics of Chapter 3 Data Handling are covered so that students don’t miss out on any of the topics. 
• Step Wise Solutions are Given: All the questions of Chapter 3 Data Handling of Class 7 Maths are explained in a stepwise manner so that students can easily understand each and every step. 

What Are the Advantages of NCERT Solutions for Class 7 Maths Chapter 3 Data Handling?

The NCERT Solutions for Class 7 Maths Chapter 3 Data Handling provides several benefits to students; some of the benefits are discussed below: 

• Covered in a Comprehensive Way: Topics in the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling revision are covered in a comprehensive way so that students can understand all the chapters in a proper way. 
• Reduces Number of Mistakes: By practising more and more questions from the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling theory, students can learn to reduce the number of mistakes then and there. 
• Understands Concepts Better: By referring to the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF, students can understand the concepts in a better way.
• Make More Confidence: Solving maximum number of Class 7 Maths questions from the NCERT Solutions can help students to improve their problem solving skills and accordingly they can improve their confidence level. 
• Can Maintain Accuracy: Accuracy is considered to be closeness of the answers; students can easily maintain the accuracy by solving questions of Chapter 3 Data Handling from the NCERT Class 7 Maths Solutions. 
• Improves Problem Solving Skills: It is the ability to identify the problem and to analyse the answers so that students can score well; students can maintain their accuracy level by solving Chapter 3 Data Handling questions from the NCERT Class 7 Maths Solutions. 

How to Utilise NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF in an Effective Way? 

Here are some tips for students to follow so that they can utilise the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF in an effective way; those tips are discussed below: 

• Read the Chapter: Before attempting the questions from the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling, students need to read the chapter in a proper way so that they can understand the concepts and formulas in a better way. 
• Solve the Problems On Your Own: Students are advised to solve the problems of NCERT Solutions for Class 7 Maths Chapter 3 Data Handling theory so that they can know their strengths and weaknesses.  
• Check the Answers: After attempting questions from the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF, students need to check the answers. This will help students to understand the mistakes made while solving questions of Maths Chapter 3 Data Handling so that they can understand the correct method. 
• Understand the Logic Behind the Each Step: While referring to the NCERT Class 7 Maths Solutions, students should make sure that they have understood the logic behind each and every step. 
• Practise Questions on a Regular Basis: Students need to solve more questions of Chapter 3 Data Handling Maths from Class 7 NCERT Solutions on a regular basis so that they can retain it in their memory. 
• Revise Regularly: It is advisable for students to revise the Chapter 3 Data Handling topics and concepts on a regular basis so that students can solve questions from the NCERT Class 7 Maths Solutions. 

Who Can Benefit from NCERT Solutions for Class 7 Maths Chapter 3 Data Handling?

The NCERT Solutions for Class 7 Maths Chapter 3 Data Handling can benefit wide range of students; those are: 

• Class 7 Students: The NCERT Solutions for Class 7 Maths Chapter 3 Data Handling revision are designed in such a way that students can understand the topics in a better way and accordingly they can solve the problems on their own. 
• Competitive Exam Aspirants: Students who are preparing for competitive exam aspirants can go through the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling theory so that they can build a strong foundation. 
• Teachers and Tutors: Teachers and tutors can also utilise the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF so that they can easily understand the concepts without any complexity. The answers of Class 7 Maths questions are explained in a step by step approach so that students can understand it better. 
• Students Who Need Additional Practice: Students who want extra practice of Class 7 Maths Chapter 3 Data Handling as well as a strong foundation can use the NCERT Solutions so that they can build their own strategy. 
• Students Struggling With The Chapter: Students who find Chapter 3 Data Handling of Class 7 Maths difficult can utilise the NCERT Solutions so that they can eliminate the difficulty. 
• Students Who Need Self Study: The NCERT Class 7 Maths Solutions are considered to be the best study resources as it helps students in studying on their own. 

When Is the Best Time to Use NCERT Solutions for Class 7 Maths Chapter 3 Data Handling?

The best time to use the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling really depends on the student’s preferences and student’s way of learning; some of the scenarios are discussed below: 

• After Completing the Chapter: Once students have the basic understanding of the Chapter 3 Data Handling in the Class 7 Maths syllabus, they can start practising questions from the NCERT Solutions.  
• After Attempting the Questions: After attempting the Chapter 3 Data Handling questions on their own, students can refer to the NCERT Class 7 Maths Solutions on their own so that they can know the correct method of solving. 
• While Preparing: The NCERT Solutions for Class 7 Maths Chapter 3 Data Handling revision can be utilised while preparing so that students can strengthen their understanding level.
• To Revise: Students can prefer utilising the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling theory so that they can quickly revise the concepts. 
• To Complete Homework: If students want to complete the Maths Chapter 3 Data Handling from the Class 7, then they can prefer utilising the NCERT Solutions. 
• To Improve Problem Solving Skills: If in case, a student's problem solving skills is weak then he or she can prefer utilising the NCERT Solutions for Class 7 Maths Chapter 3 Data Handling PDF. 

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MCQ Questions for Class 7 Maths Chapter 3 Data Handling with Answers

We have compiled the NCERT MCQ Questions for Class 7 Maths Chapter 3 Data Handling with Answers Pdf free download covering the entire syllabus. Practice MCQ Questions for Class 7 Maths with Answers on a daily basis and score well in exams. Refer to the Data Handling Class 7 MCQs Questions with Answers here along with a detailed explanation.

Data Handling Class 7 MCQs Questions with Answers

Choose the correct option.

Question 1. Mean of the first six prime numbers is (a) 7.83 (b) 5.83 (c) 6.83 (d) 4.83

Answer: (c) 6.83

Question 2. What is the mode of the following set of numbers? 1, 2, 3, 2, 1, 5, 6, 1 (a) 3 (b) 1 (c) 2 (d) 5

Answer: (b) 1

Question 3. A die is rolled then the probability that the number of dot’s on its upper face is less than 5 is (a) 0 (b) \(\frac {1}{3}\) (c) \(\frac {2}{3}\) (d) 1

Answer: (c) \(\frac {2}{3}\)

Question 4. Which measure describes the centre of a set of data? (a) Mode (b) Mean (c) Median (d) All the these

Answer: (c) Median

Question 5. The data which is collected directly from the source is called (a) primary data (b) ungrouped data (c) grouped data (d) secondary data

Answer: (a) primary data

Question 6. The median of 1, 4, 1, 2, 0, 1, 5, 4, 2, 2 is (a) 0 (b) 1 (c) 2 (d) 4

Answer: (c) 2

Question 7. The range of 35, 40, 22, 17, 65, 31, 78, 33 is (a) 35 (b) 17 (c) 61 (d) 33

Answer: (c) 61

Question 8. A coin is tossed. What is the probability of getting tail? (a) 1 (b) \(\frac {1}{2}\) (c) 2 (d) 0

Answer: (b) \(\frac {1}{2}\)

Question 9. A die is thrown. What is the probability of getting 6? (a) 0 (b) \(\frac {1}{6}\) (c) \(\frac {1}{2}\) (d) 1

Answer: (a) 0

Question 10. The median of the data 20, 30, 40, 10,15, 25, 35 is (a) 20 (b) 25 (c) 30 (d) 40

Answer: (b) 25

Question 11. Range of data is equal to: (a) highest value + lowest value (b) highest value – lowest value (c) highest value × lowest value (d) highest value + lowest value

Answer: (b) highest value – lowest value

Question 12. Which of the following is the mean of the given data? (a) The middle value of the data arranged in ascending or descending order. (b) The value of the observation occurring most frequently. (c) The sum of all the values of the data divided by the total number of values. (d) None of these.

Answer: (c) The sum of all the values of the data divided by the total number of values.

Fill in the blanks

Question 1. The sum of all the observations when divided by the number of observations gives the ………………… of the data.

Answer: Mean

Question 2. The difference between the highest and the lowest observation is called the ………………… of the data.

Answer: Range

Question 3. The observation occurring the most in a set of given data is called the ………………… of the data.

Answer: Mode

Question 4. The mean of the first five natural numbers is …………………

Question 5. A die is thrown. The probability of getting a number less than 4 …………………

Answer: \(\frac {1}{2}\)

Question 6. The sum of all the observations, when divided by the number of observations gives the ………………. of the data. [median/mean]

Answer: mean

Question 7. The difference between the highest and the lowest observation is called the ………………. of the data. [mode/range]

Answer: range

Question 8. The mean of first ten whole ………………. numbers is [4.5/5.5]

Answer: 4.5

Question 9. The mean of first ten natural ………………. numbers is [5/5.5]

Answer: 5.5

Question 10. The mode is ………………. one of the given data, [always/not always]

Answer: always

Question 11. The mean is ………………. one of the given data, [always/not always]

Answer: not always

Q. 12 to 15 use the data. 5, 4, 0, 1, 6, 2, 4, 3, 7, 8

Question 12. Mean of the data is ……………….

Question 13. Range of the data is ……………….

Question 14. Median of the data is ……………….

Question 15. Mode of the data is ……………….

Question 16. A die is thrown. The probability of getting a prime number is ……………….

Question 17. For tossing a coin, the probability of getting ……………….

Hope the information shed above regarding NCERT MCQ Questions for Class 7 Maths Chapter 3 Data Handling with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 7 Maths Data Handling MCQs Multiple Choice Questions with Answers, feel free to reach us so that we can revert back to us at the earliest possible.

NCERT Solutions for Class 7 Maths Chapter 3 Free PDF Download

Ncert solutions for class 7 maths chapter 3 – data handling.

This chapter of Maths deals with data. Also, data is of various types, especially in Maths. The CBSE advise the utilization of NCERT books that contains all the study materials of the chapter. These NCERT Solutions for Class 7 Maths Chapter 3 is intended per the most recent course of study of the CBSE board. Also, it covers each topic mentioned in the NCERT book. Above all, it’s an answer to each question of the exercises mentioned in the chapter.

The NCERT Solutions for Class 7 Maths Chapter 3 designed while keeping in mind the flexibility of students who are about to use them.

These NCERT Solutions for Class 7 Maths Chapter 3 is ready by our team of specialist. Also, these specialists are in the field of education for years and have dedicated their lives to form straightforward guides. Above all, these solutions are obtainable on Toppr without charge in PDF format. So, download the Toppr iOS , Android app or Signup at no cost.

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Download NCERT Solutions for Class 7 here.

CBSE Class 7 Maths Chapter 3 – Data Handling NCERT Solutions

Data handling is one of the most common activities of Maths. Also, it helps in sorting, analyzing, and organizing things. Apart from that, presenting data is also an important part of data handling.

In simple words, data handling is a process of collecting, arranging, analyzing, and presenting data in an understandable form.

Sub-topics covered under NCERT Solutions for Class 7 Maths Chapter 3

3.1 introduction.

This topic discusses the various ways by which we can identify data with the help of given examples.

3.2 Collection of Data

This topic discusses the various ways by which we can collect data. Also, it tells that the collected data cannot give a proper result until it is properly processed.

3.3 Organisation of Data

A collected data look like a mess so to make it presentable we organize it. Also, organizing gives the data a rough layout which makes work easy for other steps.

3.4 Representative Values

The value which symbolizes a group of person or data is representative values. Also, they are the average of the whole group.

3.5 Arithmetic Mean

Arithmetic mean or mean is the average value of a group of unit. Arithmetic mean = \(\frac{sum of total value of unit}{total number of unit}\)

3.5.1 Range- It is the difference between the highest and lowest value.

Mode is the value that is obtainable after dividing the total of the unit with the total number. Mode = \(\frac{sum of all units}{total number of unit}\)

3.6.1 Mode of large data- For finding the mode of the large data, we tabulate it and then the frequency of it helps in finding the mean of the data.

Median refers to the mid-value that divides the entire unit into two equal halves.

3.8 Use of Bar Graphs with a Different Purpose

This topic discusses the different uses of bar graph which can help in presenting the data of frequency of mode for presentation on a graph.

3.8.1 Choosing a Scale- This helps you to choose the best measuring object (scale) for the graphs.

3.9 Chance and Probability

This topic discusses chances and probability

3.9.1 Chance- refers to the prediction of the outcome. And the probability is the chance of happening of an outcome.

You can download NCERT Solutions for Class 7 Maths Chapter 3 PDF by clicking on the download button below

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NCERT Solutions for Class 7

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• NCERT Solutions for Class 7 Maths Chapter 11 Free PDF Download
• NCERT Solutions for Class 7 Maths Chapter 1 Free PDF Download
• NCERT Solutions for Class 7 Maths Chapter 7 Free PDF Download
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RS Aggarwal Solutions Class 7 Chapter 3 Decimals

RS Aggarwal Solutions for Class 7 Maths Chapter 3 Decimals are available here. This chapter has a total of six exercises. Study path has prepared solutions to these exercises by our expert math teachers to help you to get good marks in exams. RS Aggarwal Solutions for Class 7  Chapter 3 has a ton of questions. We at Study Path solved each questions step by step with detailed explanations. Students must practice from practice these problems to score high marks in Maths.

Class 7 RS Aggarwal Solutions Chapter 3 Decimals

Class 7 rs aggarwal solutions chapter 3 ex 3a.

Class 7 RS Aggarwal Solutions Chapter 3 Ex 3B

Class 7 RS Aggarwal Solutions Chapter 3 Ex 3C

Class 7 RS Aggarwal Solutions Chapter 3 Ex 3D

Class 7 RS Aggarwal Solutions Chapter 3 Ex 3E

Class 7 RS Aggarwal Solutions Chapter 3 Test Paper

Chapter Brief of Chapter 3 Decimals Class 7 RS Aggarwal Solutions

Below we have summarised the topics that have been discussed in this chapter.

• Method of Converting a Decimal into a Fraction
• Converting a Fraction into Decimal
• Addition and Subtraction of Decimals
• Addition of Decimals
• Subtraction of Decimals
• Multiplication of Decimals
• Multiplication of a Decimal by 10, 100, 1000, etc.
• Multiplication of a Decimal by a Whole Number
• Multiplication of a Decimal by a Decimal
• Division of Decimals
• Dividing a Decimal By a Whole Number

We at Study Path work hard to provide you with the best solutions and study materials for free. We hope these solutions help you in your studies. Now, if have any doubts on RS Aggarwal Class 7 Solutions, please Comment below. We will definitely try to help you with this.

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Case Study Questions for Class 7 Maths

• Last modified on: 9 months ago
• Reading Time: 7 Minutes

Table of Contents

Here in this article, we are providing case study questions for class 7 maths.

Maths Class 7 Chapter List

Latest chapter list (2023-24).

There is total 13 chapters.

Chapter 1 Integers Case Study Questions Chapter 2 Fractions and Decimals Case Study Questions Chapter 3 Data Handling Case Study Questions Chapter 4 Simple Equations Case Study Questions Chapter 5 Lines and Angles Case Study Questions Chapter 6 The Triangles and its Properties Case Study Questions Chapter 7 Comparing Quantities Case Study Questions Chapter 8 Rational Numbers Case Study Questions Chapter 9 Perimeter and Area Case Study Questions Chapter 10 Algebraic Expressions Case Study Questions Chapter 11 Exponents and Powers Case Study Questions Chapter 12 Symmetry Case Study Questions Chapter 13 Visualising Solid Shapes Case Study Questions

Old Chapter List

Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangles and its Properties Chapter 7 Congruence of Triangles Chapter 8 Comparing Quantities Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry Chapter 15 Visualising Solid Shapes

Deleted Chapter:

• Chapter 7 Congruence of Triangles
• Chapter 10 Practical Geometry

Tips for Answering Case Study Questions for Class 7 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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NCERT Solutions for Class 7 Maths Chapter 3: Data Handling - Exercise 3.1

• NCERT Solutions
• Chapter 3 Data Handling Exercise 3.1

NCERT Solutions for Class 7 Maths Chapter 3 (EX 3.1)

NCERT Solutions For Class 7 Maths Chapter 3 - Exercise 3.1 by Vedantu are the best study material for your exam preparation. Vedantu’s Data Handling In Maths Class 7 NCERT Solutions are designed to help students get past the usual exam phobia with Maths. These solutions are prepared in accordance with CBSE guidelines to help students cover all the important questions for the exam. Download the Free PDFs for Class 7 Maths Chapter 3 Exercise 3.1 Solutions and start studying the smart way. Register Online for Class 7 Science tuition on Vedantu.com to score more marks in CBSE board examination.

Why Use Solved Class 11 Maths Exercises Solution NCERT

Exercise 3.1, 1.find the range of heights of any ten students in your class..

We will find the range of heights by getting the difference between the highest height and lowest height.

Range= Highest height – Lowest Height

 $ =5.3-4.2\dfrac{z}{3} $ 

$ =1.1 $ 

Hence, the range of height of ten students of the class is 1.1 feet.

2.Organize the following marks in a class statement, in a tabular form:

4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7.

(i) Which number is highest?

(ii) Which number is lowest?

(iii) What is the range of the lowest?

The highest number among the given data is 9.

The lowest number among the given data is 1.

We will find the range of marks by getting the difference between the highest value and lowest value.

Range= Highest value – Lowest value

$ =9-1 \\ $

Hence, the range of marks is 8.

We know that, arithmetic mean is the sum of all observations divided by the total number of observations.

$ \text{Mean=}\dfrac{\text{Sum of all observations}}{\text{Number of observations}} \\ $

$ \text{=}\dfrac{4+6+7+5+3+5+4+5+2+6+2+5+1+9+6+5+8+4+6+7}{20} \\ $

$ \text{=}\dfrac{100}{20} \\ $

$ \text{=5} \\ $

3.Find the mean of the first five whole numbers.

Ans: The first five whole numbers are 0, 1, 2, 3, 4.

Arithmetic mean is the sum of all observations divided by total number of observations.

$\text{Mean=}\dfrac{\text{Sum of all observations}}{\text{Number of observations}} \\ $

$ \text{=}\dfrac{0+1+2+3+4}{5} \\ $

$ \text{=}\dfrac{10}{5} \\ $

$ \text{=2} \\ $

Hence, the mean of the first five natural numbers is 2.

4. A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100. Find the mean score.

Ans: Arithmetic mean is sum of all observations divided by total number of observations.

Number of Observations= 8

$ \text{=}\dfrac{58+76+40+35+46+45+0+100}{8} \\ $

$ \text{=}\dfrac{400}{8} \\ $

$ \text{=50} \\ $

Hence, the mean score of the cricketer is 50.

5. Following table shows the points each player scored in four games.

Now answer the following questions.

(i) Find the mean to determine A’s average number of points scored per game.

(ii) To find the mean number of points per game for C, would you divide the total points by 3 or 47? Why? 

(iii) B played in all the four games. How would you find the meaning? 

(iv) Who is the best performer?

(i) The average of player A can be determined by dividing the sum of all scores of A by the number of games he played. 

 $ \text{Mean of player A=}\dfrac{\text{Sum of scored by A}}{\text{Number of games played by A}} \\ $

 $ \text{=}\dfrac{14+16+10+10}{4} \\ $

$ \text{ =}\dfrac{50}{4} \\ $

$ \text{ =12}\text{.5} \\ $

Hence, the average number of points scored by A is 12.5.

(ii)For finding average points scored, we divide the total scores by the total number of games played. In this case, C has played 3 games and therefore we will divide the total points by 3 and not by 4.

(iii)B played all 4 games. So, we will divide the total points scored by 4.

$ \text{Mean of player B=}\dfrac{\text{Sum of scored by B}}{\text{Number of games played by B}} \\ $

$ \text{=}\dfrac{0+8+6+4}{4} \\ $

$ \text{=}\dfrac{18}{4} \\ $

$ \text{=4}\text{.5} \\ $

(iv)Best performer is the one who has the highest average score among all the other players.

$ \text{Mean of player A=}\dfrac{\text{Sum of scored by A}}{\text{Number of games played by A}} \\ $

$ \text{=}\dfrac{14+16+10+10}{4} \\$ 

$ \text{=}\dfrac{50}{4} \\ $

$ \text{=12}\text{.5} \\ $

$  \text{Mean of player C=}\dfrac{\text{Sum of scored by C}}{\text{Number of games played by C}} \\ $

$ \text{=}\dfrac{8+11+13}{3} \\ $

$ \text{=}\dfrac{32}{3} \\ $

$ \text{=10}\text{.67} \\ $

On comparing means of all players, we can see that the average score of player A is the highest, i.e., 12.5.

Hence, player A is the best performer.

6. The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the: 

(i) The highest and the lowest marks obtained by the students. 

(ii) Range of the marks obtained. 

(iii) Mean marks obtained by the group.

(i) Highest marks obtained by the student = 95

Lowest marks obtained by the student = 39

(ii) We will find the range of marks by getting the difference between the highest value and lowest value.

$ =95-39 \\ $

Hence, the range of marks obtained is 56.

(iii) For finding average marks scored, we divide the total scores by the total number of observations.

 $ \text{Mean of obtained marks=}\dfrac{\text{Sum of marks}}{\text{Total number of marks}} \\ $

$ \text{=}\dfrac{85+76+90+85+39+48+56+95+81+75}{10} \\ $

$ \text{=}\dfrac{730}{10} \\$ 

$ \text{=73} \\ $

Hence, the mean marks obtained by the group of students is 73.

7.The enrolment in a school during six consecutive years was as follows: 1555, 1670, 1750, 2013, 2540, 2820. Find the mean enrolment of the school for this period.

Ans: To find the mean enrolment, we will divide the sum of numbers of enrolment by the number of years of enrolment period.

$ \text{Mean enrolment=}\dfrac{\text{Sum of number of enrolment}}{\text{Total number of years}} \\$ 

$ \text{=}\dfrac{1555+1670+1751+2013+2540+2820}{6} \\ $

$ \text{=}\dfrac{12348}{6} \\ $

$ \text{=2058} \\ $

Hence, the mean enrolment of school over 6 years is 2058.

9. The height of 10 girls were measured in cm and the results are as follows: 135, 150, 139, 128, 151, 132, 146, 149, 143, 141 

(i) What is the height of the tallest girl? 

(ii) What is the height of the shortest girl? 

(iii) What is the range of data? 

(iv) What is the mean height of the girls? 

(v) How many girls have heights more than the mean height?

(i)As seen from the above given data, the height of the tallest girl is 151cm.

(ii)As seen from the above given data, the height of the shortest girl is 128cm.

(iii)We will find the range of heights by getting the difference between the highest value and lowest value.

$ \text{Range= Highest Value}-\text{Lowest Value} \\ $

$ \text{=151-128} \\ $

$ \text{=23} \\ $

Hence, the range of heights is 23cm.

(iv)To find the mean height, we will divide the sum of heights of all girls by the number of girls.

$ \text{Mean of height=}\dfrac{\text{Sum of heights of all girls}}{\text{Total number of girls}} \\ $

$ \text{=}\dfrac{135+150+139+128+151+132+146+149+143+141}{10} \\$ 

$ \text{=}\dfrac{1414}{10} \\ $

$ \text{=141}\text{.4} \\ $

Hence, the mean height of girls is 141.4cm.

(v) Mean height is 141.4cm. From the above data, we can see that heights 150, 151, 146, 149 and 143 are more than the mean value. 

Hence, five girls have heights more than the mean height.

Exercise 3.2

1. The scores in mathematics test (out of 25) of students are as follows: 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 Find the mode and median of this data. Are they the same?

Ans; First, we shall arrange the given data in ascending order,

5, 9, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

Mode is the observation occurred the highest number of times.

Mode= observation with highest frequency

For Median,

Median is the middle observation.

Number of observations= 14 observations

$ \text{Median= Middle Observation} \\ $

$ \text{=}{{\left( \dfrac{14}{2} \right)}^{th}}\text{observation} \\ $

$ ={{7}^{th}}\text{observation} \\ $

$ \text{=20} \\ $

Yes, Mode and Median are the same for the given observations.

2. The runs scored in a cricket match by 11 players is as follows: 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15 Find the mean, mode and median of this data. Are the three the same?

Ans: Arranging the given data in ascending order,

6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

$ \text{Mean=}\dfrac{\text{Sum of observations}}{\text{Number of observations }} \\ $

$ \text{=}\dfrac{\text{6+8+10+10+15+15+15+80+100+120}}{11} \\ $

$ \text{=}\dfrac{429}{11} \\ $

$ \text{=39} \\ $

For Median, 

Total number of observations = n = 11 observations

$ \text{=}{{\left( \dfrac{n+1}{2} \right)}^{th}}\text{Observation} \\ $

$ \text{=}{{\left( \dfrac{11+1}{2} \right)}^{th}}\text{observation} \\$ 

$ \text{=}{{\left( \dfrac{12}{2} \right)}^{th}}\text{observation} \\ $

$ ={{6}^{th}}\text{observation} \\ $

$ \text{=15} \\ $

 Mode= observation with highest frequency

We can see from answers above that mean, median and mode are not the same.

3. The weight (in kg) of 15 students of a class are: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47 

(i) Find the mode and median of this data. 

(ii) Is there more than one mode? 

Ans; Arranging the given data in ascending order,

32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

(i) For Mode,

= 38kg and 43kg

Total number of observations = n = 15 observations

 $ \text{Median= Middle Observation} \\ $

 $ \text{=}{{\left( \dfrac{n+1}{2} \right)}^{th}}\text{Observation} \\ $

 $ \text{=}{{\left( \dfrac{15+1}{2} \right)}^{th}}\text{observation} \\ $

 $ \text{=}{{\left( \dfrac{16}{2} \right)}^{th}}\text{observation} \\ $

 $ ={{8}^{th}}\text{observation} \\ $

 $ \text{=40} \\ $

(ii)Yes, there are two modes, i.e., 38 and 43. This is because both 38 and 43 occur for the same highest number of times, 3.

4. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14 

Ans:  Arranging the given data in ascending order,

12, 12, 13, 13, 14, 14, 14, 16, 19

Mode= Observation with highest frequency

Total number of observations = n = 9 observations

  $  \text{Median= Middle Observation} \\ $

 $ \text{=}{{\left( \dfrac{9+1}{2} \right)}^{th}}\text{observation} \\ $

 $ \text{=}{{\left( \dfrac{10}{2} \right)}^{th}}\text{observation} \\ $

 $ ={{5}^{th}}\text{observation} \\ $

 $ \text{=14} \\ $

5. Tell whether the statement is true or false: 

(i) The mode is always one of the numbers in a data. 

(ii) The mean is one of the numbers in the data. 

(iii) The median is always one of the numbers in a data. 

(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 have mean 9.

Ans: (i) True, it is the number that occurs most frequently in the data

(ii) False, mean is the ratio of sum of all observations to the number of observations. Hence, it can or cannot be one of the observations.

(iii) True, median is the central value of data after the observations are placed in an ascending or descending order.

(iv) False, mean is the ratio of sum of all observations to the number of observations.

$ \text{=}\dfrac{6+4+3+8+9+12+13+9}{8} \\ $

$ \text{=}\dfrac{64}{8} \\ $

$ \text{=8} \\ $

The mean of given observations is 8.

Hence, the given statement is false.

Exercise 3.3

1. Use the bar graph to answer the following questions: 

(image will be uploaded soon)

(a) Which is the most popular pet? 

(b) How many students have dogs as pets? 

Ans:  

As seen from the graph, the bar of the cat is the tallest.

Hence, cats are the most popular pet.

As seen from the graph, the bar of the dog is till 8.

 Hence, 8 students have a dog as their pet.

2. Read the bar graph which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:

(i) About how many books were sold in 1989? 1990? 1992? 

(ii) In which year were about 475 books sold? About 225 books sold? 

(iii) In which years were fewer than 250 books sold? 

(iv) Can you explain how you would estimate the number of books sold in 1989?

Ans: (i) From the graph, we can see that

Number of books sold in 1989 = 180

Number of books sold in 1990 = 475

Number of books sold in 1992 = 225

(ii) On observing the graph, we can find that 475 books were sold in 1990 and 225 books were sold in 1992. 

(iii) From the graph, we find that in the years 1989 and 1992, books less than 250 were sold.

(iv) From the graph, we can calculate that 180 books were sold in 1989.

3. Number of children in six different classes are given below. Represent the data on a bar graph.

How would you choose a scale? 

Answer the following questions: 

(i)Which class has the maximum number of children? And the minimum? 

(ii)Find the ratio of students of class sixth to the students of class eighth.

(image will  be uploaded soon)

Scale = Difference between upper value and lower value of 1 unit on y-axis 

=25 children

(i) We can see from the graph that fifth class has the tallest bar and hence it has the maximum number of children.

We can see from the graph that the smallest bar corresponds to the tenth class and hence it has a minimum number of children.

(ii)Ratio of sixth class to eighth class

$ \text{Ratio=}\dfrac{\text{Number of students in class sixth}}{\text{Number of students in class eighth}} \\ $

$ \text{= }\dfrac{120}{100} \\ $

$ \text{=}\dfrac{6}{5} \\ $

$ \text{=6:5} \\$ 

4. The performance of a student in 1st term and 2nd term is given. Draw a double bar graph choosing appropriate scale and answer the following:

(i) In which subject has the child improved his performance the most? 

(ii) In which subject is the improvement the least? 

(iii) Has the performance gone down in any subject? 

Difference of marks of 1st term and 2nd term

English = 70 – 67 = 3 

Hindi = 65 – 72 = -7 

Maths = 95 – 88 = 7

Science = 85 – 81 = 4 

S. Science = 75 – 73 = 2

(i)We can see that Maths has a maximum difference.

Hence, the child has improved the most in maths.

(ii)We can see that S. Science has a minimum difference.

Hence, the child has improved the least in maths.

(ii)We can see that Hindi has a decrease in the size of bars.

Hence, children's performance has gone down in Hindi.

5. Consider this data collected from a survey of a colony.

(i) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph? 

(ii) Which sport is most popular? 

(iii) Which is more preferred, watching or participating in sports? 

 (image will be uploaded soon)

The double bar graph represents the number of people who like watching and participating in various sports.

(ii) We can observe from the graph that cricket has the tallest bar.

Hence, cricket is the most popular sport.

(iii) From the double bar graph graph, we can see that the watching (blue) bars are taller in comparison to participating (orange) bars.

Hence, watching sports is more preferred.

6. Take the data giving the minimum and the maximum temperature of various cities given in the beginning of this Chapter. Plot a double bat graph using the data and answer the following:

Temperature of cities as on 20.6.2006

(i) Which city has the largest difference in the minimum and maximum temperature on the given data? 

(ii) Which is the hottest city and which is the coldest city? 

(iii) Name two cities where the maximum temperature of one was less than the minimum temperature of the order. 

(iv) Name the city which has the least difference between its minimum and the maximum temperature.

(image will be uploaded soon) 

(i)Jammu has the largest difference in temperature i.e., 

Maximum temperature = 41℃ and 

Minimum temperature = 26℃.

Difference = 41℃ – 26℃ = 15℃

(ii)Jammu is the hottest city because the maximum temperature bar is the tallest and Bangalore is the coldest city because maximum temperature is shortest.

(iii)Maximum temperature of Bangalore - 28℃

Minimum temperature of two cities whose minimum temperature is higher than the maximum temperature of Bangalore are Ahmedabad and Jaipur = 29℃

(iv)Mumbai has the least difference in temperature i.e., 

Maximum temperature = 32℃ and

Minimum temperature = 27℃

Difference = 32℃ – 27℃ = 5℃

Exercise 3.4

1. Tell whether the following is certain to happen, impossible can happen but not certain. 

(i) You are older today than yesterday. 

(ii) A tossed coin will land heads up. 

(iii) A die when tossed shall land up with 8 on top. 

(iv) The next traffic light seen will be green. 

(v) Tomorrow will be a cloudy day. 

Ans: Let us first define the terms- 

Certain to happen means that the situation will definitely happen.

Impossible means that the situation can never happen.

Can happen but not certain means that the happening of the situation is not definite, i.e., it may or may not happen.

(i)We grow older every day. Hence, the statement is certain to happen.

(ii)A coin has two faces, heads and tails. The tossed coin can land on either heads or tails. Hence, the situation in the statement can happen but is not certain.

(iii)A die has six faces marked 1, 2, 3, 4, 5 and 6. The tossed die can land on either of the faces. The die does not have 8 on any of the faces. Hence, the situation in the statement is impossible.

(iv)A traffic light turns green after it has turned yellow. But we don’t know if the traffic light has turned yellow or red. Hence, the situation in the statement can happen but is not certain.

(v)We can never give the surety of the weather of an upcoming day. Hence, the situation in the statement is impossible.

2. There are 6 marbles in a box with numbers from 1 to 6 marked on each of them. 

(i) What is the probability of drawing a marble with number 2? 

(ii) What is the probability of drawing a marble with number 5? 

Ans: Total marbles from 1 to 6 marked in a box = 6

(i) $\text{Probability of drawing marble with number 2=}\dfrac{\text{Number of favourable outcome}}{\text{Number of possible outcomes}}$

Hence, $\text{P(appearance of 2)=}\dfrac{1}{6}$

(ii) $\text{Probability of drawing marble with number 5=}\dfrac{\text{Number of favourable outcome}}{\text{Number of possible outcomes}}$

Hence, $\text{P(appearance of 5)=}\dfrac{1}{6}$

3. A coin is flipped to decide which team starts the game. What is the probability that your team will start?

Ans: A coin has two possible outcomes: Head and Tail.

Probability of getting Head or Tail is equal.

$\text{Probability =}\dfrac{\text{Number of favourable outcome}}{\text{Number of possible outcomes}}$

Hence, $\text{P(starting game)=}\dfrac{1}{2}$

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Problems on Arithmetic Mean

Problems on the Median

Problems on Mode

Problems on Modal Class

Problems on Data Range

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FAQs on NCERT Solutions for Class 7 Maths Chapter 3: Data Handling - Exercise 3.1

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Q2. What are the topics in Chapter 3 of Class 7 Maths?

The topics are:

Introduction

Collecting Data

Organisation of Data

Representative Values

Arithmetic Mean

Mode of Large Data

Using Bar Graphs For Different Purpose

Choosing a Scale

Drawing Double Bar Graphs

Chance and Probability

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