NCERT Solutions Class 7 Maths Chapter 3

NCERT Solutions Class 7 Mathematics Chapter 3

NCERT Solutions for Class 7 Mathematics Chapter 3 Data Handling 

In this world, data is the fuel that allows us to explore and interpret a wide range of possibilities. The concept of data and its importance are introduced in the NCERT Class 7 Mathematics Chapter 3 data handling. This chapter covers everything from data collection to data storage and display, as well as how to determine the central tendency of the data collected. In Chapter 3, the relevance of the average, median, and mode to various data sets is also discussed, with examples. It also introduces the concept of probability and its theorem, which can be used to determine the likelihood of an event occurring. 

To understand the chapter in a better way, students should practise in-text and end-text exercises.They can solve these questions on their own or refer to NCERT Solutions for Class 7 Mathematics Chapter 3 to get answers to all the questions. Extramarks provides these solutions to help students to strengthen their preparation for the tests, exams or Olympiad .

NCERT Solutions for Class 7 Mathematics Chapter 3 Data Handling 

NCERT Solutions for Class 7 Mathematics Chapter 3  

Chapter 3 Data Handling 

Chapter 3 of Class 7 Mathematics Data handling is a chapter that describes  the procedures for working with data and storing it in various formats. According to the CBSE board, this is an important chapter because it teaches us how to analyse data from various fields. 

NCERT Solutions Class 7 Mathematics Chapter 3 

The answers given in NCERT Solutions for Class 7 Mathematics Chapter 3 cover a variety of important concepts that are necessary for understanding higher-level mathematics. The concept of calculating mean, median, and mode is thoroughly explained, and students will be able to recall it with ease. The average value is referred to as 'mean,' the midpoint value is referred to as 'median,' and the most common value is referred to as 'mode.' 

All the exercises from 3.1 to 3.9 are included in the NCERT Solutions for Class 7 Mathematics Chapter 3. In this article, you will find detailed solutions prepared by Extramarks experienced subject matter experts. These solutions are provided here in accordance with the NCERT textbook and CBSE guidelines. 

3.1 Introduction 

Students can learn what data is in the introduction to the data handling chapter. Data is simply well-organised information. Students will learn about the various steps in handling specific data, such as collecting the data, properly analysing it, evaluating it to obtain an average, and finally, how to represent the data. 

3.2 Collecting Data 

This section explains how students can learn about data collection from various sources. It also explains how to extract data from it and how to find answers by correlating with the situation. Consider some of the following scenarios: 

  • Gujarat  literacy rate-year?
  • Bangalore  current weather report
  • The number of females in a school  

3.3 Organisation of Data 

Students will learn how to properly organise data collected in this section. Students can learn how to organise and record data in a specific format. NCERT Solution for Class 7 Mathematics Chapter 3 explains all of the different types of data that are used to represent forms.  The tabular format is a widely used and basic format for accurately organising data.  Proper organisation of data is very important since it ensures that data is easy to understand and interpret.

3.4 Representative Values 

Students become aware of these values, which are referred to as representative values, in this lesson. These are used to explain how the data is organised. In the data handling chapter, students must remember the word 'average.' The term can be applied to a variety of situations, such as average temperature, average time, average distance, average number of boys, and so on. As a result, students should bear in mind  the approximate  value  rather than an exact value. In NCERT Solutions for Class 7 Mathematics Chapter 3, it is explained with examples and tables. 

3.5 Arithmetic Mean 

Students will learn about an important aspect of data management in this section. The average value of a group of units is known as the arithmetic mean or mean. It is computed using the formula: 

The sum of a unit's total values/The total number of units 

The NCERT Solutions contains examples with solutions applying the formula. If they ever get stuck on a question, they can always refer to the solutions prepared by subject matter experts. 

3.5.1 Range 

Students are taught the sub-topic of arithmetic mean. They must take an average for the mean, but must subtract the minimum from the maximum to obtain the range of complete data or observation. 

3.6 Mode 

Students can learn about another important topic known as a mode in this section. The mode, like the mean, is another type of symbolic value. Students must use various types of values depending on the type of data. The mode is a value that appears repeatedly in a set of observations. It means that the value that appears the most times can be considered the mode. 

3.6.1 Mode of Large Data 

We tabulate the large data to find the mode, and the frequency of the data helps us find the mean of the data. Students may be sceptical of the mode. How can the problem be solved if the data is too large? The problem is addressed in this part.

3.7 Median 

Students will learn about yet another type of representative value in this section. The ascending order should be remembered here. Find the exact middle value by writing all the observations in ascending order. It is capable of accurately classifying them into two groups. It's known as the median because it's located in the centre. In other words, the Median is the mid-value that divides a unit into two equal halves. 

3.8 Use of Bar Graphs with a Different Purpose 

The use of bar graphs  explores the various applications of the bar graph, including how it can be used to present data on frequency of mode on a graph. Students will learn about the concept of a bar graph and its variations in this lesson. It's a simple way to represent data in a structured way. 

3.8.1 Choosing a Scale 

After learning about bar graphs, students will be aware of using the scale to draw the bar graph. Students can choose a larger scale if the data is too large, and vice versa. Students can choose one unit that equals 1,10,100, and so on, depending on the values and size. The choosing scale may vary, but the plotting must be on point. 

Drawing Double Bar Graphs 

Students can learn more about bar graphs in this section. NCERT Mathematics Class 7 Chapter 3 clearly explains the concepts when data is given for two or more people to compare. Students must create bar Graphs for two groups, but must differentiate them by shading or colouring. 

3.9 Chance and Probability 

Students must estimate and expect chance and probability in the final section. Simply put, it is the possibility of something occurring. Probability is the term used when chance is defined mathematically. The ratio of favourable cases to the total number of possible cases determines the probability of an event occurring. Each topic is explained separately in NCERT Solutions for Class 7 Mathematics Chapter 3 so that the concept is clearly understood. 

3.9.1 Chance 

Chance is nothing more than a forecast. Students will be able to predict and express the data's outcome. It is necessary to predict the outcome, whether it is correct or incorrect. This concept is explained clearly with solved examples in these NCERT Solutions

3.9.2. Probability 

Probability is the final topic that students can learn in this chapter. Probability is the estimation of the chances of something happening, such as tossing a coin or rolling dice. 

Key Factors of NCERT Solutions for Class 7 Mathematics Chapter 3 

While solving these NCERT Solutions, students gain a variety of benefits, some of   them are listed below: 

  • The solutions were created and compiled by subject matter experts , hence their authenticity and accuracy is guaranteed. They are useful for both the teachers and the students, and they can be accessed anywhere without much hassle. 
  • The solutions are written in clear, simple language and include easily understandable charts and diagrams to ensure that students fully comprehend the subject. 
  • The solutions have been created with the goal of enhancing the students’ potential and achieving better results. 

NCERT Solutions for Class 7 Mathematics 

All textbook sums based on triangles, area, and perimeter of different shapes, data handling, integers, and other topics are covered in NCERT Solutions Class 7 Mathematics. As a result, CBSE students will be able to develop Mathematical knowledge and analytical skills. 

These solutions allow students of  grade 7 to develop  an in-depth understanding of Mathematics. Students from other boards refer to the NCERT Solutions for Class 7 Mathematics. They are reliable and accurate. You can access these chapter-wise solutions from the link given below.

Chapter 1 - Integers

Chapter 2 - Fractions and Decimals

Chapter 3 - Data Handling

Chapter 4 - Simple Equations

Chapter 5 - Lines and Angles

Chapter 6 - The Triangle 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

NCERT Solutions for Class 7 

Students who have a good grasp on the answers to all of the questions in the NCERT textbook can ace the exams easily. We have provided NCERT Solutions Class 7 to assist students in finding the most suitable solutions to their problems. Subject experts have written the answers based on the CBSE curriculum. Every question in the most recent NCERT books has 100% accurate step-by-step solutions. NCERT Solutions will help you imbibe your concepts to the core, ensuring that you retain them in the long run. It encourages students to practise daily without getting stressed and to improve their performance significantly. 

Q.1 Find the range of heights of any ten students of your class.

Ans.

Let the heights (in cm) of any ten students be124, 126, 133,135, 136, 139, 140, 142, 144, 147Highest value among these observations=147cmLowest value among these observations=124 cmRange=Highest value-Lowest value=(147124) cm=23 cm

Q.2 Organise the following marks in a class assessment, inat a bular 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 the greatest?(ii) Which number is the lowest?(iii) What is the range of the data?(iv) Find the arithmetic mean.

 

Ans.

(i)9 (ii)1 (iii)Range=9-1= 8 (iv)Arithmeticmean= Sum of all observations Total number of observations = 100 20 = 5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaaMe8Uaaeyo aaqaaiaabIcacaqGPbGaaeyAaiaabMcacaaMe8UaaGymaaqaaiaacI cacaWGPbGaamyAaiaadMgacaGGPaGaaGjbVlaabkfacaqGHbGaaeOB aiaabEgacaqGLbGaaeypaiaabMdacaqGTaGaaeymaiabg2da9maaL4 babaGaaeioaaaaaeaacaGGOaGaamyAaiaadAhacaGGPaGaaGjbVlaa bgeacaqGYbGaaeyAaiaabshacaqGObGaaeyBaiaabwgacaqG0bGaae yAaiaabogacaaMe8UaaeyBaiaabwgacaqGHbGaaeOBaiaab2dadaWc aaqaaiaabofacaqG1bGaaeyBaiaabccacaqGVbGaaeOzaiaabccaca qGHbGaaeiBaiaabYgacaqGGaGaae4BaiaabkgacaqGZbGaaeyzaiaa bkhacaqG2bGaaeyyaiaabshacaqGPbGaae4Baiaab6gacaqGZbaaba Gaaeivaiaab+gacaqG0bGaaeyyaiaabYgacaqGGaGaaeOBaiaabwha caqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+gacaqGMbGaaeiiai aab+gacaqGIbGaae4CaiaabwgacaqGYbGaaeODaiaabggacaqG0bGa aeyAaiaab+gacaqGUbGaae4CaaaaaeaacaaMe8UaaGjbVlaaysW7ca aMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaa ysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaG jbVlaaysW7caaMe8UaaGjbVlaaysW7cqGH9aqpdaWcaaqaaiaaigda caaIWaGaaGimaaqaaiaaikdacaaIWaaaaiabg2da9maaL4babaGaaG ynaaaaaaaa@C41C@

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

Ans.

First five whole numbers are 0, 1, 2, 3 and 4Since Mean=Sum of all observationsTotal number of observationsSo, Mean = 0+1+2+3+45=102=5Thus, mean of first five whole number is 5.

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

Ans.

Since Mean=Sum of all observationsTotal number of observations So,Mean=58+76+40+35+46+45+0+1008=4008=50Thus, the mean score is 50

Q.5 Following table shows the points of each player scored in four game.

Player Game Game Game Game
A 14 16 10 10
B 0 8 6 4
C 8 11 Did not Play 13

Now answer the following questions:
(i) find the mean to determine A’ save range number of points scored per game.
(ii) To find mean number of points per game of C,
would you divide the total points by 3 or by 4? Why?
(iii) B played in all four games. How would you find the mean?
(iv) Who is the best performer?

Ans.

(i) Since Mean= Sum of all observations Total number of observations So,Mean= 14+16+10+10 4 = 50 4 = 12.5 Thus, As average number of points scored per game is 12.5 (ii) Since C played only 3 games, so to find the mean number of points per game for C,divide the total points by 3. (iii) Mean of B = 0+8+6+4 4 = 18 4 =4.5 (iv) Since, the mean of Ais better and bigger than B and C, so A is the best performer. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcaaeaacaqGtbGa aeyAaiaab6gacaqGJbGaaeyzaiaabccacaqGnbGaaeyzaiaabggaca qGUbGaeyypa0ZaaSaaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4B aiaabAgacaqGGaGaaeyyaiaabYgacaqGSbGaaeiiaiaab+gacaqGIb Gaae4CaiaabwgacaqGYbGaaeODaiaabggacaqG0bGaaeyAaiaab+ga caqGUbGaae4CaaqaaiaabsfacaqGVbGaaeiDaiaabggacaqGSbGaae iiaiaab6gacaqG1bGaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqG VbGaaeOzaiaabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCaiaabA hacaqGHbGaaeiDaiaabMgacaqGVbGaaeOBaiaabohaaaGaaeiiaaqa aiaabofacaqGVbGaaeilaiaaysW7caqGnbGaaeyzaiaabggacaqGUb Gaeyypa0ZaaSaaaeaacaaIXaGaaGinaiabgUcaRiaaigdacaaI2aGa ey4kaSIaaGymaiaaicdacqGHRaWkcaaIXaGaaGimaaqaaiaaisdaaa aabaGaeyypa0ZaaSaaaeaacaaI1aGaaGimaaqaaiaaisdaaaGaeyyp a0ZaauIhaeaacaaIXaGaaGOmaiaac6cacaaI1aaaaaqaaiaabsfaca qGObGaaeyDaiaabohacaqGSaGaaeiiaiaabgeacaGGzaIaae4Caiaa bccacaqGHbGaaeODaiaabwgacaqGYbGaaeyyaiaabEgacaqGLbGaae iiaiaab6gacaqG1bGaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqG VbGaaeOzaiaabccacaqGWbGaae4BaiaabMgacaqGUbGaaeiDaiaabo hacaqGGaGaae4CaiaabogacaqGVbGaaeOCaiaabwgacaqGKbGaaeii aiaabchacaqGLbGaaeOCaiaabccacaqGNbGaaeyyaiaab2gacaqGLb GaaeiiaiaabMgacaqGZbGaaeiiaiaabgdacaqGYaGaaeOlaiaabwda aeaacaqGOaGaaeyAaiaabMgacaqGPaaabaGaae4uaiaabMgacaqGUb Gaae4yaiaabwgacaqGGaGaae4qaiaabccacaqGWbGaaeiBaiaabgga caqG5bGaaeyzaiaabsgacaqGGaGaae4Baiaab6gacaqGSbGaaeyEai aabccacaqGZaGaaeiiaiaabEgacaqGHbGaaeyBaiaabwgacaqGZbGa aeilaiaabccacaqGZbGaae4BaiaabccacaqG0bGaae4Baiaabccaca qGMbGaaeyAaiaab6gacaqGKbGaaeiiaiaabshacaqGObGaaeyzaiaa bccacaqGTbGaaeyzaiaabggacaqGUbGaaeiiaiaab6gacaqG1bGaae yBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzaaqaaiaabcha caqGVbGaaeyAaiaab6gacaqG0bGaae4CaiaabccacaqGWbGaaeyzai aabkhacaqGGaGaae4zaiaabggacaqGTbGaaeyzaiaabccacaqGMbGa ae4BaiaabkhacaqGGaGaae4qaiaacYcacaqGKbGaaeyAaiaabAhaca qGPbGaaeizaiaabwgacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaa bshacaqGVbGaaeiDaiaabggacaqGSbGaaeiiaiaabchacaqGVbGaae yAaiaab6gacaqG0bGaae4CaiaabccacaqGIbGaaeyEaiaabccacaqG ZaGaaeOlaaqaaiaabIcacaqGPbGaaeyAaiaabMgacaqGPaaabaGaae ytaiaabwgacaqGHbGaaeOBaiaabccacaqGVbGaaeOzaiaabccacaqG cbGaaeiiaiaab2dacaqGGaWaaSaaaeaacaaIWaGaey4kaSIaaGioai abgUcaRiaaiAdacqGHRaWkcaaI0aaabaGaaGinaaaacqGH9aqpdaWc aaqaaiaaigdacaaI4aaabaGaaGinaaaacqGH9aqpcaaI0aGaaiOlai aaiwdaaeaacaqGOaGaaeyAaiaabAhacaqGPaaabaGaae4uaiaabMga caqGUbGaae4yaiaabwgacaqGSaGaaeiiaiaabshacaqGObGaaeyzai aabccacaqGTbGaaeyzaiaabggacaqGUbGaaeiiaiaab+gacaqGMbGa aeiiaiaabgeacaaMb8UaaGjbVlaabMgacaqGZbGaaeiiaiaabkgaca qGLbGaaeiDaiaabshacaqGLbGaaeOCaiaabccacaqGHbGaaeOBaiaa bsgacaqGGaGaaeOyaiaabMgacaqGNbGaae4zaiaabwgacaqGYbGaae iiaiaabshacaqGObGaaeyyaiaab6gacaqGGaGaaeOqaiaabccacaqG HbGaaeOBaiaabsgacaqGGaGaae4qaiaabYcacaqGGaGaae4Caiaab+ gacaqGGaGaaeyqaiaabccacaqGPbGaae4CaaqaaiaabshacaqGObGa aeyzaiaabccacaqGIbGaaeyzaiaabohacaqG0bGaaeiiaiaabchaca qGLbGaaeOCaiaabAgacaqGVbGaaeOCaiaab2gacaqGLbGaaeOCaiaa b6caaaaa@8996@

Q.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) Highest and the lowest marks obtained by the students.
(ii) Range of the marks obtained.
(iii) Mean marks obtained by the group.

Ans.

(i) Clearly, the from the given data, the highest and the lowest marks are 95 and 39 respectively. (ii) Range=HighestLowest =9539=56 (iii)Mean= Sum of all observations Total number of observations = 85+76+90+58+39+48+56+95+81+75 10 = 70.3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaGaae4q aiaabYgacaqGLbGaaeyyaiaabkhacaqGSbGaaeyEaiaabYcacaqGGa GaaeiDaiaabIgacaqGLbGaaeiiaiaabAgacaqGYbGaae4Baiaab2ga caqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabEgacaqGPbGaaeODai aabwgacaqGUbGaaeiiaiaabsgacaqGHbGaaeiDaiaabggacaqGSaGa aeiiaiaabshacaqGObGaaeyzaiaabccacaqGObGaaeyAaiaabEgaca qGObGaaeyzaiaabohacaqG0bGaaeiiaiaabggacaqGUbGaaeizaiaa bccacaqG0bGaaeiAaiaabwgacaqGGaGaaeiBaiaab+gacaqG3bGaae yzaiaabohacaqG0baabaGaaeyBaiaabggacaqGYbGaae4Aaiaaboha caqGGaGaaeyyaiaabkhacaqGLbGaaeiiaiaabMdacaqG1aGaaeiiai aabggacaqGUbGaaeizaiaabccacaqGZaGaaeyoaiaabccacaqGYbGa aeyzaiaabohacaqGWbGaaeyzaiaabogacaqG0bGaaeyAaiaabAhaca qGLbGaaeiBaiaabMhacaqGUaaabaGaaeikaiaabMgacaqGPbGaaeyk aiaabccacaqGsbGaaeyyaiaab6gacaqGNbGaaeyzaiabg2da9iaabI eacaqGPbGaae4zaiaabIgacaqGLbGaae4CaiaabshacqGHsislcaqG mbGaae4BaiaabEhacaqGLbGaae4CaiaabshaaeaacqGH9aqpcaaI5a GaaGynaiabgkHiTiaaiodacaaI5aGaeyypa0JaaGynaiaaiAdaaeaa caqGOaGaaeyAaiaabMgacaqGPbGaaeykaiaaygW7caaMe8Uaaeytai aabwgacaqGHbGaaeOBaiabg2da9iaaysW7daWcaaqaaiaabofacaqG 1bGaaeyBaiaabccacaqGVbGaaeOzaiaabccacaqGHbGaaeiBaiaabY gacaqGGaGaae4BaiaabkgacaqGZbGaaeyzaiaabkhacaqG2bGaaeyy aiaabshacaqGPbGaae4Baiaab6gacaqGZbaabaGaaeivaiaab+gaca qG0bGaaeyyaiaabYgacaqGGaGaaeOBaiaabwhacaqGTbGaaeOyaiaa bwgacaqGYbGaaeiiaiaab+gacaqGMbGaaeiiaiaab+gacaqGIbGaae 4CaiaabwgacaqGYbGaaeODaiaabggacaqG0bGaaeyAaiaab+gacaqG UbGaae4CaaaacaqGGaaabaGaaGjbVlaaysW7caaMe8UaaGjbVlaays W7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Uaeyyp a0ZaaSaaaeaacaaI4aGaaGynaiabgUcaRiaaiEdacaaI2aGaey4kaS IaaGyoaiaaicdacqGHRaWkcaaI1aGaaGioaiabgUcaRiaaiodacaaI 5aGaey4kaSIaaGinaiaaiIdacqGHRaWkcaaI1aGaaGOnaiabgUcaRi aaiMdacaaI1aGaey4kaSIaaGioaiaaigdacqGHRaWkcaaI3aGaaGyn aaqaaiaaigdacaaIWaaaaaqaaiaaysW7caaMe8UaaGjbVlaaysW7ca aMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlab g2da9maaL4babaGaaG4naiaaicdacaGGUaGaaG4maaaaaaaa@2CFB@

Q.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.

Mean= Sum of all observations Total number of observations = 1555+1670+1750+2013+2540+2820 6 = 12348 6 = 2058 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaabbeaacaqGnbGaaeyzaiaabggacaqGUbGaeyyp a0ZaaSaaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgaca qGGaGaaeyyaiaabYgacaqGSbGaaeiiaiaab+gacaqGIbGaae4Caiaa bwgacaqGYbGaaeODaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaae 4CaaqaaiaabsfacaqGVbGaaeiDaiaabggacaqGSbGaaeiiaiaab6ga caqG1bGaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzai aabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCaiaabAhacaqGHbGa aeiDaiaabMgacaqGVbGaaeOBaiaabohaaaaabaGaeyypa0ZaaSaaae aacaaIXaGaaGynaiaaiwdacaaI1aGaey4kaSIaaGymaiaaiAdacaaI 3aGaaGimaiabgUcaRiaaigdacaaI3aGaaGynaiaaicdacqGHRaWkca aIYaGaaGimaiaaigdacaaIZaGaey4kaSIaaGOmaiaaiwdacaaI0aGa aGimaiabgUcaRiaaikdacaaI4aGaaGOmaiaaicdaaeaacaaI2aaaaa qaaiabg2da9maalaaabaGaaGymaiaaikdacaaIZaGaaGinaiaaiIda aeaacaaI2aaaaaqaaiabg2da9maaL4babaGaaGOmaiaaicdacaaI1a GaaGioaaaaaaaa@9170@

Q.8 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.

Mean= Sum of all observations Total number of observations = 1555+1670+1750+2013+2540+2820 6 = 12348 6 = 2058 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaabbeaacaqGnbGaaeyzaiaabggacaqGUbGaeyyp a0ZaaSaaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgaca qGGaGaaeyyaiaabYgacaqGSbGaaeiiaiaab+gacaqGIbGaae4Caiaa bwgacaqGYbGaaeODaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaae 4CaaqaaiaabsfacaqGVbGaaeiDaiaabggacaqGSbGaaeiiaiaab6ga caqG1bGaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzai aabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCaiaabAhacaqGHbGa aeiDaiaabMgacaqGVbGaaeOBaiaabohaaaaabaGaeyypa0ZaaSaaae aacaaIXaGaaGynaiaaiwdacaaI1aGaey4kaSIaaGymaiaaiAdacaaI 3aGaaGimaiabgUcaRiaaigdacaaI3aGaaGynaiaaicdacqGHRaWkca aIYaGaaGimaiaaigdacaaIZaGaey4kaSIaaGOmaiaaiwdacaaI0aGa aGimaiabgUcaRiaaikdacaaI4aGaaGOmaiaaicdaaeaacaaI2aaaaa qaaiabg2da9maalaaabaGaaGymaiaaikdacaaIZaGaaGinaiaaiIda aeaacaaI2aaaaaqaaiabg2da9maaL4babaGaaGOmaiaaicdacaaI1a GaaGioaaaaaaaa@9170@

Q.9 The rain fall (in mm) in a city on 7 days of a certain week was recorded as follows:

Day Mon Tue Wed Thu Fri Sat Sun
Rainfall

(in mm)

0.0 12.2 2.1 0.0 20.5 5.5 1.0

(i) Find the range of the rainfall in the above data.
(
ii)
Find the mean rainfall for the week.

(iii) On how many days was the rainfall less than the mean rainfall.

Ans.

(i) Range=Highest-Lowest =20.5 mm0.0 mm= 20.5 mm (ii)Mean rainfall = 0.0+12.2+2.1+0.0+20.5+5.5+1.0 7 = 41.3 7 =5.9mm (iii)For five days(Monday, Wednesday, Thursday, Saturday and Sunday), rainfall was less than the mean rainfall. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaGaaeOu aiaabggacaqGUbGaae4zaiaabwgacqGH9aqpcaqGibGaaeyAaiaabE gacaqGObGaaeyzaiaabohacaqG0bGaaeylaiaabYeacaqGVbGaae4D aiaabwgacaqGZbGaaeiDaaqaaiabg2da9iaaikdacaaIWaGaaiOlai aabwdacaqGGaGaaeyBaiaab2gacaGGTaGaaGimaiaac6cacaqGWaGa aeiiaiaab2gacaqGTbGaeyypa0ZaauIhaeaacaaIYaGaaGimaiaac6 cacaaI1aaaaiaaysW7caqGTbGaaeyBaaqaaiaabIcacaqGPbGaaeyA aiaabMcacaaMe8UaaeytaiaabwgacaqGHbGaaeOBaiaabccacaqGYb GaaeyyaiaabMgacaqGUbGaaeOzaiaabggacaqGSbGaaeiBaiaabcca cqGH9aqpcaqGGaWaaSaaaeaacaaIWaGaaiOlaiaaicdacqGHRaWkca aIXaGaaGOmaiaac6cacaaIYaGaey4kaSIaaGOmaiaac6cacaaIXaGa ey4kaSIaaGimaiaac6cacaaIWaGaey4kaSIaaGOmaiaaicdacaGGUa GaaGynaiabgUcaRiaaiwdacaGGUaGaaGynaiabgUcaRiaaigdacaGG UaGaaGimaaqaaiaaiEdaaaaabaGaaGjbVlaaysW7caaMe8UaaGjbVl aaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Ua aGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7ca aMe8Uaeyypa0ZaaSaaaeaacaaI0aGaaGymaiaac6cacaaIZaaabaGa aG4naaaacqGH9aqpcaaI1aGaaiOlaiaaiMdacaaMe8UaaeyBaiaab2 gaaeaacaqGOaGaaeyAaiaabMgacaqGPbGaaeykaiaaysW7caqGgbGa ae4BaiaabkhacaqGGaGaaeOzaiaabMgacaqG2bGaaeyzaiaabccaca qGKbGaaeyyaiaabMhacaqGZbGaaGjbVlaabIcacaqGnbGaae4Baiaa b6gacaqGKbGaaeyyaiaabMhacaqGSaGaaeiiaiaabEfacaqGLbGaae izaiaab6gacaqGLbGaae4CaiaabsgacaqGHbGaaeyEaiaabYcacaqG GaGaaeivaiaabIgacaqG1bGaaeOCaiaabohacaqGKbGaaeyyaiaabM hacaqGSaGaaeiiaiaabofacaqGHbGaaeiDaiaabwhacaqGYbGaaeiz aiaabggacaqG5baabaGaaGjbVlaaysW7caaMe8UaaGjbVlaabccaca qGHbGaaeOBaiaabsgacaqGGaGaae4uaiaabwhacaqGUbGaaeizaiaa bggacaqG5bGaaeykaiaabYcacaqGGaGaaeOCaiaabggacaqGPbGaae OBaiaabAgacaqGHbGaaeiBaiaabYgacaqGGaGaae4DaiaabggacaqG ZbGaaeiiaiaabYgacaqGLbGaae4CaiaabohacaqGGaGaaeiDaiaabI gacaqGHbGaaeOBaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeyB aiaabwgacaqGHbGaaeOBaiaabccacaqGYbGaaeyyaiaabMgacaqGUb GaaeOzaiaabggacaqGSbGaaeiBaiaab6caaaaa@2482@

Q.10 The heights of 10 girls were measured in cm and theresults are as follows:135,150,139,128,151,132,146,149,143,141iWhat is the height of the tallest girl?iiWhat is the height of the shortest girl?iiiWhat is the range of the data?ivWhat is the mean height of the girls?vHow many girls have heights more than the mean

Ans.

(i) The height of the tallest girl is 151 cm. (ii) The height of the shortest girl is 128. (iii) Range=HighestLowest=( 151128 )cm= 23cm (iv) Mean height = 135+150+139+128+151+132+146+149+143+141 10 = 1414 10 = 141.4cm Thus, five girls have more height than the mean height. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaGaaeiv aiaabIgacaqGLbGaaeiiaiaabIgacaqGLbGaaeyAaiaabEgacaqGOb GaaeiDaiaabccacaqGVbGaaeOzaiaabccacaqG0bGaaeiAaiaabwga caqGGaGaaeiDaiaabggacaqGSbGaaeiBaiaabwgacaqGZbGaaeiDai aabccacaqGNbGaaeyAaiaabkhacaqGSbGaaeiiaiaabMgacaqGZbGa aeiiaiaabgdacaqG1aGaaeymaiaabccacaqGJbGaaeyBaiaab6caae aacaqGOaGaaeyAaiaabMgacaqGPaGaaeiiaiaabsfacaqGObGaaeyz aiaabccacaqGObGaaeyzaiaabMgacaqGNbGaaeiAaiaabshacaqGGa Gaae4BaiaabAgacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaaboha caqGObGaae4BaiaabkhacaqG0bGaaeyzaiaabohacaqG0bGaaeiiai aabEgacaqGPbGaaeOCaiaabYgacaqGGaGaaeyAaiaabohacaqGGaGa aeymaiaabkdacaqG4aGaaeOlaaqaaiaabIcacaqGPbGaaeyAaiaabM gacaqGPaGaaeiiaiaabkfacaqGHbGaaeOBaiaabEgacaqGLbGaeyyp a0JaaeisaiaabMgacaqGNbGaaeiAaiaabwgacaqGZbGaaeiDaiabgk HiTiaabYeacaqGVbGaae4DaiaabwgacaqGZbGaaeiDaiabg2da9maa bmaabaGaaGymaiaaiwdacaaIXaGaeyOeI0IaaGymaiaaikdacaaI4a aacaGLOaGaayzkaaGaae4yaiaab2gacqGH9aqpdaqjEaqaaiaaikda caaIZaGaaGjbVlaabogacaqGTbaaaaqaaiaabIcacaqGPbGaaeODai aabMcacaqGGaGaaeytaiaabwgacaqGHbGaaeOBaiaabccacaqGObGa aeyzaiaabMgacaqGNbGaaeiAaiaabshaaeaacqGH9aqpdaWcaaqaai aaigdacaaIZaGaaGynaiabgUcaRiaaigdacaaI1aGaaGimaiabgUca RiaaigdacaaIZaGaaGyoaiabgUcaRiaaigdacaaIYaGaaGioaiabgU caRiaaigdacaaI1aGaaGymaiabgUcaRiaaigdacaaIZaGaaGOmaiab gUcaRiaaigdacaaI0aGaaGOnaiabgUcaRiaaigdacaaI0aGaaGyoai abgUcaRiaaigdacaaI0aGaaG4maiabgUcaRiaaigdacaaI0aGaaGym aaqaaiaaigdacaaIWaaaaaqaaiabg2da9maalaaabaGaaGymaiaais dacaaIXaGaaGinaaqaaiaaigdacaaIWaaaaaqaaiabg2da9maaL4ba baGaaGymaiaaisdacaaIXaGaaiOlaiaaisdacaaMe8Uaae4yaiaab2 gaaaaabaGaaeivaiaabIgacaqG1bGaae4CaiaabYcacaqGGaGaaeOz aiaabMgacaqG2bGaaeyzaiaabccacaqGNbGaaeyAaiaabkhacaqGSb Gaae4CaiaabccacaqGObGaaeyyaiaabAhacaqGLbGaaeiiaiaab2ga caqGVbGaaeOCaiaabwgacaqGGaGaaeiAaiaabwgacaqGPbGaae4zai aabIgacaqG0bGaaeiiaiaabshacaqGObGaaeyyaiaab6gacaqGGaGa aeiDaiaabIgacaqGLbGaaeiiaiaab2gacaqGLbGaaeyyaiaab6gaca qGGaGaaeiAaiaabwgacaqGPbGaae4zaiaabIgacaqG0bGaaeOlaaaa aa@1B15@

Q.11 The scores in mathmatics test (out of 25) of 15 students is 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 same?

Ans.

Arranging the score in ascending order.5,9,10,12,15,16,19,20,20,20,20,23,24,25,25Since, mode is that value of observation which occurs forthe most number of time and median is the middle observation.There are 15 values, so median would be the 8th observationand 20 occurs 4 times.So, Mode=20 and Median= 20Yes both are same.

Q.12 The runs scored in a cricket match by 11 players isas follows:6,15,120,50,100,80,10,15,8,10,15Find the mean, mode and median of this data.Are the three same?

Ans.

Arranging in ascending order to get 6,8,10,10,15,15,15,50,80,100,120 Mean= 6+8+10+10+15+15+15+50+80+100+120 11 = 429 11 = 39 Mode is that value of observation which occurs for the most number of time and median is the middle observation. There are 11 values, so median would be the 6th observation and 15 occurs 3 times. So, Mode=15and Median=15 No, these three are not same. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGbbGaaeOCaiaabkhacaqGHbGaaeOB aiaabEgacaqGPbGaaeOBaiaabEgacaqGGaGaaeyAaiaab6gacaqGGa GaaeyyaiaabohacaqGJbGaaeyzaiaab6gacaqGKbGaaeyAaiaab6ga caqGNbGaaeiiaiaab+gacaqGYbGaaeizaiaabwgacaqGYbGaaeiiai aabshacaqGVbGaaeiiaiaabEgacaqGLbGaaeiDaaqaaiaabAdacaqG SaGaaeioaiaabYcacaqGXaGaaeimaiaabYcacaqGXaGaaeimaiaabY cacaqGXaGaaeynaiaabYcacaqGXaGaaeynaiaabYcacaqGXaGaaeyn aiaabYcacaqG1aGaaeimaiaabYcacaqG4aGaaeimaiaabYcacaqGXa GaaeimaiaabcdacaqGSaGaaeymaiaabkdacaqGWaaabaGaaeytaiaa bwgacaqGHbGaaeOBaiabg2da9maalaaabaGaaGOnaiabgUcaRiaaiI dacqGHRaWkcaaIXaGaaGimaiabgUcaRiaaigdacaaIWaGaey4kaSIa aGymaiaaiwdacqGHRaWkcaaIXaGaaGynaiabgUcaRiaaigdacaaI1a Gaey4kaSIaaGynaiaaicdacqGHRaWkcaaI4aGaaGimaiabgUcaRiaa igdacaaIWaGaaGimaiabgUcaRiaaigdacaaIYaGaaGimaaqaaiaaig dacaaIXaaaaaqaaiaaxMaacaaMe8UaaGjbVlabg2da9maalaaabaGa aGinaiaaikdacaaI5aaabaGaaGymaiaaigdaaaGaeyypa0ZaauIhae aacaaIZaGaaGyoaaaaaeaacaqGnbGaae4BaiaabsgacaqGLbGaaeii aiaabMgacaqGZbGaaeiiaiaabshacaqGObGaaeyyaiaabshacaqGGa GaaeODaiaabggacaqGSbGaaeyDaiaabwgacaqGGaGaae4BaiaabAga caqGGaGaae4BaiaabkgacaqGZbGaaeyzaiaabkhacaqG2bGaaeyyai aabshacaqGPbGaae4Baiaab6gacaqGGaGaae4DaiaabIgacaqGPbGa ae4yaiaabIgacaqGGaGaae4BaiaabogacaqGJbGaaeyDaiaabkhaca qGZbGaaeiiaiaabAgacaqGVbGaaeOCaiaabccacaqG0bGaaeiAaiaa bwgacaqGGaGaaeyBaiaab+gacaqGZbGaaeiDaaqaaiaab6gacaqG1b GaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzaiaabcca caqG0bGaaeyAaiaab2gacaqGLbGaaeiiaiaabggacaqGUbGaaeizai aabccacaqGTbGaaeyzaiaabsgacaqGPbGaaeyyaiaab6gacaqGGaGa aeyAaiaabohacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaab2gaca qGPbGaaeizaiaabsgacaqGSbGaaeyzaiaabccacaqGVbGaaeOyaiaa bohacaqGLbGaaeOCaiaabAhacaqGHbGaaeiDaiaabMgacaqGVbGaae OBaiaab6caaeaacaqGubGaaeiAaiaabwgacaqGYbGaaeyzaiaabcca caqGHbGaaeOCaiaabwgacaqGGaGaaeymaiaabgdacaqGGaGaaeODai aabggacaqGSbGaaeyDaiaabwgacaqGZbGaaeilaiaabccacaqGZbGa ae4BaiaabccacaqGTbGaaeyzaiaabsgacaqGPbGaaeyyaiaab6gaca qGGaGaae4Daiaab+gacaqG1bGaaeiBaiaabsgacaqGGaGaaeOyaiaa bwgacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabAdacaqG0bGaae iAaiaabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCaiaabAhacaqG HbGaaeiDaiaabMgacaqGVbGaaeOBaaqaaiaabggacaqGUbGaaeizai aabccacaqGXaGaaeynaiaabccacaqGVbGaae4yaiaabogacaqG1bGa aeOCaiaabohacaqGGaGaae4maiaabccacaqG0bGaaeyAaiaab2gaca qGLbGaae4Caiaab6caaeaacaqGtbGaae4BaiaabYcacaqGGaWaauIh aeaacaqGnbGaae4BaiaabsgacaqGLbGaeyypa0Jaaeymaiaabwdaca aMe8Uaaeyyaiaab6gacaqGKbGaaeiiaiaab2eacaqGLbGaaeizaiaa bMgacaqGHbGaaeOBaiabg2da9iaabgdacaqG1aaaaaqaaiaab6eaca qGVbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGZbGaaeyzaiaa bccacaqG0bGaaeiAaiaabkhacaqGLbGaaeyzaiaabccacaqGHbGaae OCaiaabwgacaqGGaGaaeOBaiaab+gacaqG0bGaaeiiaiaabohacaqG HbGaaeyBaiaabwgacaqGUaaaaaa@7346@

Q.13 The weights inkg. of 15 students of a class are :38,42,35,37,45,50,32,43,43,40,36,38,43,38,47i Find the mode and median of this data.ii Is there more than one mode?

Ans.

Arranging the weight in ascending order. 32,35,36,37,38,38,38,40,42,43,43,43,45,47,50 Mode of given data is that value of observation which occurs for the most number of time and median is the middle observation. There are 15 values, so median would be the 8th observation So, Median= 40 Also 38 and 43 both occurs 3 times. So, Mode=38and 43 Yes there are two mode for given data. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGbbGaaeOCaiaabkhacaqGHbGaaeOB aiaabEgacaqGPbGaaeOBaiaabEgacaqGGaGaaeiDaiaabIgacaqGLb GaaeiiaiaabEhacaqGLbGaaeyAaiaabEgacaqGObGaaeiDaiaabcca caqGPbGaaeOBaiaabccacaqGHbGaae4CaiaabogacaqGLbGaaeOBai aabsgacaqGPbGaaeOBaiaabEgacaqGGaGaae4BaiaabkhacaqGKbGa aeyzaiaabkhacaqGUaaabaGaae4maiaabkdacaqGSaGaae4maiaabw dacaqGSaGaae4maiaabAdacaqGSaGaae4maiaabEdacaqGSaGaae4m aiaabIdacaqGSaGaae4maiaabIdacaqGSaGaae4maiaabIdacaqGSa GaaeinaiaabcdacaqGSaGaaeinaiaabkdacaqGSaGaaeinaiaaboda caqGSaGaaeinaiaabodacaqGSaGaaeinaiaabodacaqGSaGaaeinai aabwdacaqGSaGaaeinaiaabEdacaqGSaGaaeynaiaabcdaaeaacaqG nbGaae4BaiaabsgacaqGLbGaaeiiaiaab+gacaqGMbGaaeiiaiaabE gacaqGPbGaaeODaiaabwgacaqGUbGaaeiiaiaabsgacaqGHbGaaeiD aiaabggacaqGGaGaaeyAaiaabohacaqGGaGaaeiDaiaabIgacaqGHb GaaeiDaiaabccacaqG2bGaaeyyaiaabYgacaqG1bGaaeyzaiaabcca caqGVbGaaeOzaiaabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCai aabAhacaqGHbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaqG3bGa aeiAaiaabMgacaqGJbGaaeiAaiaabccacaqGVbGaae4yaiaabogaca qG1bGaaeOCaiaabohacaqGGaGaaeOzaiaab+gacaqGYbaabaGaaeiD aiaabIgacaqGLbGaaeiiaiaab2gacaqGVbGaae4CaiaabshacaqGGa GaaeOBaiaabwhacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+ga caqGMbGaaeiiaiaabshacaqGPbGaaeyBaiaabwgacaqGGaGaaeyyai aab6gacaqGKbGaaeiiaiaab2gacaqGLbGaaeizaiaabMgacaqGHbGa aeOBaiaabccacaqGPbGaae4CaiaabccacaqG0bGaaeiAaiaabwgaca qGGaGaaeyBaiaabMgacaqGKbGaaeizaiaabYgacaqGLbGaaeiiaiaa b+gacaqGIbGaae4CaiaabwgacaqGYbGaaeODaiaabggacaqG0bGaae yAaiaab+gacaqGUbGaaeOlaaqaaiaabsfacaqGObGaaeyzaiaabkha caqGLbGaaeiiaiaabggacaqGYbGaaeyzaiaabccacaqGXaGaaeynai aabccacaqG2bGaaeyyaiaabYgacaqG1bGaaeyzaiaabohacaqGSaGa aeiiaiaabohacaqGVbGaaeiiaiaab2gacaqGLbGaaeizaiaabMgaca qGHbGaaeOBaiaabccacaqG3bGaae4BaiaabwhacaqGSbGaaeizaiaa bccacaqGIbGaaeyzaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaae ioaiaabshacaqGObGaaeiiaiaab+gacaqGIbGaae4CaiaabwgacaqG YbGaaeODaiaabggacaqG0bGaaeyAaiaab+gacaqGUbaabaGaae4uai aab+gacaqGSaGaaeiiaiaab2eacaqGLbGaaeizaiaabMgacaqGHbGa aeOBaiabg2da9maaL4babaGaaeinaiaabcdaaaaabaGaaeyqaiaabY gacaqGZbGaae4BaiaabccacaqGZaGaaeioaiaabccacaqGHbGaaeOB aiaabsgacaqGGaGaaeinaiaabodacaqGGaGaaeOyaiaab+gacaqG0b GaaeiAaiaabccacaqGVbGaae4yaiaabogacaqG1bGaaeOCaiaaboha caqGGaGaae4maiaabccacaqG0bGaaeyAaiaab2gacaqGLbGaae4Cai aab6caaeaacaqGtbGaae4BaiaabYcacaqGGaWaauIhaeaacaqGnbGa ae4BaiaabsgacaqGLbGaeyypa0Jaae4maiaabIdacaaMe8Uaaeyyai aab6gacaqGKbGaaeiiaiaabsdacaqGZaaaaaqaaiaabMfacaqGLbGa ae4CaiaabccacaqG0bGaaeiAaiaabwgacaqGYbGaaeyzaiaabccaca qGHbGaaeOCaiaabwgacaqGGaGaaeiDaiaabEhacaqGVbGaaeiiaiaa b2gacaqGVbGaaeizaiaabwgacaqGGaGaaeOzaiaab+gacaqGYbGaae iiaiaabEgacaqGPbGaaeODaiaabwgacaqGUbGaaeiiaiaabsgacaqG HbGaaeiDaiaabggacaqGUaaaaaa@7978@

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

Ans.

Arrange in ascending order to get: 12,12,13,13,14,14,1416,19 Mode of given data is that value of observation which occurs for the most number of time and median is the middle observation. There are 9 values, so median would be the 5th observation So, Median= 14 Also 14 occurs 3 times. So, Mode=14 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGbbGaaeOCaiaabkhacaqGHbGaaeOB aiaabEgacaqGLbGaaeiiaiaabMgacaqGUbGaaeiiaiaabggacaqGZb Gaae4yaiaabwgacaqGUbGaaeizaiaabMgacaqGUbGaae4zaiaabcca caqGVbGaaeOCaiaabsgacaqGLbGaaeOCaiaabccacaqG0bGaae4Bai aabccacaqGNbGaaeyzaiaabshacaqG6aaabaGaaeymaiaabkdacaqG SaGaaeymaiaabkdacaqGSaGaaeymaiaabodacaqGSaGaaeymaiaabo dacaqGSaGaaeymaiaabsdacaqGSaGaaeymaiaabsdacaqGSaGaaeym aiaabsdacaqGXaGaaeOnaiaabYcacaqGXaGaaeyoaaqaaiaab2eaca qGVbGaaeizaiaabwgacaqGGaGaae4BaiaabAgacaqGGaGaae4zaiaa bMgacaqG2bGaaeyzaiaab6gacaqGGaGaaeizaiaabggacaqG0bGaae yyaiaabccacaqGPbGaae4CaiaabccacaqG0bGaaeiAaiaabggacaqG 0bGaaeiiaiaabAhacaqGHbGaaeiBaiaabwhacaqGLbGaaeiiaiaab+ gacaqGMbGaaeiiaiaab+gacaqGIbGaae4CaiaabwgacaqGYbGaaeOD aiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaaeiiaiaabEhacaqGOb GaaeyAaiaabogacaqGObGaaeiiaiaab+gacaqGJbGaae4yaiaabwha caqGYbGaae4CaiaabccacaqGMbGaae4BaiaabkhaaeaacaqG0bGaae iAaiaabwgacaqGGaGaaeyBaiaab+gacaqGZbGaaeiDaiaabccacaqG UbGaaeyDaiaab2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabA gacaqGGaGaaeiDaiaabMgacaqGTbGaaeyzaiaabccacaqGHbGaaeOB aiaabsgacaqGGaGaaeyBaiaabwgacaqGKbGaaeyAaiaabggacaqGUb GaaeiiaiaabMgacaqGZbGaaeiiaiaabshacaqGObGaaeyzaiaabcca caqGTbGaaeyAaiaabsgacaqGKbGaaeiBaiaabwgacaqGGaGaae4Bai aabkgacaqGZbGaaeyzaiaabkhacaqG2bGaaeyyaiaabshacaqGPbGa ae4Baiaab6gacaqGUaaabaGaaeivaiaabIgacaqGLbGaaeOCaiaabw gacaqGGaGaaeyyaiaabkhacaqGLbGaaeiiaiaabMdacaqGGaGaaeOD aiaabggacaqGSbGaaeyDaiaabwgacaqGZbGaaeilaiaabccacaqGZb Gaae4BaiaabccacaqGTbGaaeyzaiaabsgacaqGPbGaaeyyaiaab6ga caqGGaGaae4Daiaab+gacaqG1bGaaeiBaiaabsgacaqGGaGaaeOyai aabwgacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabwdacaqG0bGa aeiAaiaabccacaqGVbGaaeOyaiaabohacaqGLbGaaeOCaiaabAhaca qGHbGaaeiDaiaabMgacaqGVbGaaeOBaaqaaiaabofacaqGVbGaaeil aiaabccacaqGnbGaaeyzaiaabsgacaqGPbGaaeyyaiaab6gacqGH9a qpdaqjEaqaaiaabgdacaqG0aaaaaqaaiaabgeacaqGSbGaae4Caiaa b+gacaqGGaGaaeymaiaabsdacaqGGaGaae4BaiaabogacaqGJbGaae yDaiaabkhacaqGZbGaaeiiaiaabodacaqGGaGaaeiDaiaabMgacaqG TbGaaeyzaiaabohacaqGUaaabaGaae4uaiaab+gacaqGSaGaaeiiam aaL4babaGaaeytaiaab+gacaqGKbGaaeyzaiabg2da9iaabgdacaqG 0aaaaaaaaa@349E@

Q.15

Tell whether the statement is true or false: (i) The mode is always one of the numbers in a data. ( ii )The mean can be one of the numbers in a data. ( iii )The median is always one of the numbers in a data. ( iv ) A data always has a mode. ( v ) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaaieqacaWFubGaa8xzaiaa=XgacaWFSbGa a8hiaiaa=DhacaWFObGaa8xzaiaa=rhacaWFObGaa8xzaiaa=jhaca WFGaGaa8hDaiaa=HgacaWFLbGaa8hiaiaa=nhacaWF0bGaa8xyaiaa =rhacaWFLbGaa8xBaiaa=vgacaWFUbGaa8hDaiaa=bcacaWFPbGaa8 3Caiaa=bcacaWF0bGaa8NCaiaa=vhacaWFLbGaa8hiaiaa=9gacaWF YbGaa8hiaiaa=zgacaWFHbGaa8hBaiaa=nhacaWFLbGaa8Noaaqaai aa=HcacaWFPbGaa8xkaiaa=bcacaWFubGaa8hAaiaa=vgacaWFGaGa a8xBaiaa=9gacaWFKbGaa8xzaiaa=bcacaWFPbGaa83Caiaa=bcaca WFHbGaa8hBaiaa=DhacaWFHbGaa8xEaiaa=nhacaWFGaGaa83Baiaa =5gacaWFLbGaa8hiaiaa=9gacaWFMbGaa8hiaiaa=rhacaWFObGaa8 xzaiaa=bcacaWFUbGaa8xDaiaa=1gacaWFIbGaa8xzaiaa=jhacaWF ZbGaa8hiaiaa=LgacaWFUbGaa8hiaiaa=fgacaWFGaGaa8hzaiaa=f gacaWF0bGaa8xyaiaa=5caaeaadaqadaqaaiaa=LgacaWFPbaacaGL OaGaayzkaaGaa8hvaiaa=HgacaWFLbGaa8hiaiaa=1gacaWFLbGaa8 xyaiaa=5gacaWFGaGaa83yaiaa=fgacaWFUbGaa8hiaiaa=jgacaWF LbGaa8hiaiaa=9gacaWFUbGaa8xzaiaa=bcacaWFVbGaa8Nzaiaa=b cacaWF0bGaa8hAaiaa=vgacaWFGaGaa8NBaiaa=vhacaWFTbGaa8Ny aiaa=vgacaWFYbGaa83Caiaa=bcacaWFPbGaa8NBaiaa=bcacaWFHb Gaa8hiaiaa=rgacaWFHbGaa8hDaiaa=fgacaWFUaaabaWaaeWaaeaa caWFPbGaa8xAaiaa=LgaaiaawIcacaGLPaaacaWFubGaa8hAaiaa=v gacaWFGaGaa8xBaiaa=vgacaWFKbGaa8xAaiaa=fgacaWFUbGaa8hi aiaa=LgacaWFZbGaa8hiaiaa=fgacaWFSbGaa83Daiaa=fgacaWF5b Gaa83Caiaa=bcacaWFVbGaa8NBaiaa=vgacaWFGaGaa83Baiaa=zga caWFGaGaa8hDaiaa=HgacaWFLbGaa8hiaiaa=5gacaWF1bGaa8xBai aa=jgacaWFLbGaa8NCaiaa=nhacaWFGaGaa8xAaiaa=5gacaWFGaGa a8xyaiaa=bcacaWFKbGaa8xyaiaa=rhacaWFHbGaa8Nlaaqaamaabm aabaGaa8xAaiaa=zhaaiaawIcacaGLPaaacaWFGaGaa8xqaiaa=bca caWFKbGaa8xyaiaa=rhacaWFHbGaa8hiaiaa=fgacaWFSbGaa83Dai aa=fgacaWF5bGaa83Caiaa=bcacaWFObGaa8xyaiaa=nhacaWFGaGa a8xyaiaa=bcacaWFTbGaa83Baiaa=rgacaWFLbGaa8Nlaaqaamaabm aabaGaa8NDaaGaayjkaiaawMcaaiaa=bcacaWFubGaa8hAaiaa=vga caWFGaGaa8hzaiaa=fgacaWF0bGaa8xyaiaa=bcacaWF2aGaa8hlai aa=bcacaWF0aGaa8hlaiaa=bcacaWFZaGaa8hlaiaa=bcacaWF4aGa a8hlaiaa=bcacaWF5aGaa8hlaiaa=bcacaWFXaGaa8Nmaiaa=Xcaca WFGaGaa8xmaiaa=ndacaWFSaGaa8hiaiaa=LdacaWFGaGaa8hAaiaa =fgacaWFZbGaa8hiaiaa=1gacaWFLbGaa8xyaiaa=5gacaWFGaGaa8 xoaiaa=5caaaaa@25A6@

Ans.

(i) True , because mode is the value that occurs most of the time and it belongs to the given data. (ii) False , Mean may or may not belong to the data. (iii) True , because median is the middle observation of given data. (iv) False The given data is: 6,4,3,8,9,12,13,9. So, Mean= 6+4+3+8+9+12+13+9 8 = 64 8 =8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaWaauIh aeaacaqGubGaaeOCaiaabwhacaqGLbaaaiaabYcacaqGGaGaaeOyai aabwgacaqGJbGaaeyyaiaabwhacaqGZbGaaeyzaiaabccacaqGTbGa ae4BaiaabsgacaqGLbGaaeiiaiaabMgacaqGZbGaaeiiaiaabshaca qGObGaaeyzaiaabccacaqG2bGaaeyyaiaabYgacaqG1bGaaeyzaiaa bccacaqG0bGaaeiAaiaabggacaqG0bGaaeiiaiaab+gacaqGJbGaae 4yaiaabwhacaqGYbGaae4CaiaabccacaqGTbGaae4BaiaabohacaqG 0bGaaeiiaiaab+gacaqGMbaabaGaaGjbVlaaysW7caaMe8UaaGjbVl aabshacaqGObGaaeyzaiaabccacaqG0bGaaeyAaiaab2gacaqGLbGa aeiiaiaabggacaqGUbGaaeizaiaabccacaqGPbGaaeiDaiaabccaca qGIbGaaeyzaiaabYgacaqGVbGaaeOBaiaabEgacaqGZbGaaeiiaiaa bshacaqGVbGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGNbGaae yAaiaabAhacaqGLbGaaeOBaiaabccacaqGKbGaaeyyaiaabshacaqG HbGaaeOlaaqaaiaabIcacaqGPbGaaeyAaiaabMcacaqGGaWaauIhae aacaqGgbGaaeyyaiaabYgacaqGZbGaaeyzaaaacaqGSaGaaeiiaiaa b2eacaqGLbGaaeyyaiaab6gacaqGGaGaaeyBaiaabggacaqG5bGaae iiaiaab+gacaqGYbGaaeiiaiaab2gacaqGHbGaaeyEaiaabccacaqG UbGaae4BaiaabshacaqGGaGaaeOyaiaabwgacaqGSbGaae4Baiaab6 gacaqGNbGaaeiiaiaabshacaqGVbGaaeiiaiaabshacaqGObGaaeyz aiaabccacaqGKbGaaeyyaiaabshacaqGHbGaaeOlaaqaaiaabIcaca qGPbGaaeyAaiaabMgacaqGPaGaaeiiamaaL4babaGaaeivaiaabkha caqG1bGaaeyzaaaacaqGSaGaaeiiaiaabkgacaqGLbGaae4yaiaabg gacaqG1bGaae4CaiaabwgacaqGGaGaaeyBaiaabwgacaqGKbGaaeyA aiaabggacaqGUbGaaeiiaiaabMgacaqGZbGaaeiiaiaabshacaqGOb GaaeyzaiaabccacaqGTbGaaeyAaiaabsgacaqGKbGaaeiBaiaabwga caqGGaGaae4BaiaabkgacaqGZbGaaeyzaiaabkhacaqG2bGaaeyyai aabshacaqGPbGaae4Baiaab6gaaeaacaaMe8UaaGjbVlaaysW7caaM e8Uaae4BaiaabAgacaqGGaGaae4zaiaabMgacaqG2bGaaeyzaiaab6 gacaqGGaGaaeizaiaabggacaqG0bGaaeyyaiaab6caaeaacaqGOaGa aeyAaiaabAhacaqGPaGaaeiiamaaL4babaGaaeOraiaabggacaqGSb Gaae4CaiaabwgaaaaabaGaaeivaiaabIgacaqGLbGaaeiiaiaabEga caqGPbGaaeODaiaabwgacaqGUbGaaeiiaiaabsgacaqGHbGaaeiDai aabggacaqGGaGaaeyAaiaabohacaqG6aGaaeiiaiaabAdacaqGSaGa aeinaiaabYcacaqGZaGaaeilaiaabIdacaqGSaGaaeyoaiaabYcaca qGXaGaaeOmaiaabYcacaqGXaGaae4maiaabYcacaqG5aGaaeOlaaqa aiaabofacaqGVbGaaeilaiaabccacaqGnbGaaeyzaiaabggacaqGUb Gaeyypa0ZaaSaaaeaacaaI2aGaey4kaSIaaGinaiabgUcaRiaaioda cqGHRaWkcaaI4aGaey4kaSIaaGyoaiabgUcaRiaaigdacaaIYaGaey 4kaSIaaGymaiaaiodacqGHRaWkcaaI5aaabaGaaGioaaaaaeaacaaM e8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaays W7caaMe8UaaGjbVlabg2da9maalaaabaGaaGOnaiaaisdaaeaacaaI 4aaaaaqaaiaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaays W7caaMe8UaaGjbVlaaysW7caaMe8Uaeyypa0JaaGioaaaaaa@65DF@

Q.16 Use the bar graph (Fig below) to a answer the following question
(a) Which is the most popular pet?
(b) How many children have dog as a pet?

Ans.

(a) The bar showing cats is the tallest, so cat is the most popular pet.
(b) From the bar graph, the number of children having dog as a pet is 8.

Q.17

Read the bar graph Figbelow and answer the questionshat follow: Number of books sold by a book store during fiveconsecutive years.

( i ) About how many books were sold in 1989? 1990? 1992? ( ii ) Inwhich 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) In 1989, 175 books were sold in 1990, 475 books were sold. In 1992, 225 books were sold. (ii) From the graph, it can be concluded that 475 books were sold in the year 1990 and 225 books were sold in the year 1992. (iii) From the graph, it can be concluded that in the years 1989 and 1992, the number of books sold were less than 250. (iv) From the graph, it can be concluded that the number of books sold in the year 1989 is about 1 and 3 4 thpart of 1 cm The scale is taken as 1 cm = 100 books So, 100+ 3 4 ×100=100+75=175 Therefore, about 175 books were sold in the year 1989. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaGaaeys aiaab6gacaqGGaGaaeymaiaabMdacaqG4aGaaeyoaiaabYcacaqGGa GaaeymaiaabEdacaqG1aGaaeiiaiaabkgacaqGVbGaae4BaiaabUga caqGZbGaaeiiaiaabEhacaqGLbGaaeOCaiaabwgacaqGGaGaae4Cai aab+gacaqGSbGaaeizaiaabccacaqGPbGaaeOBaiaabccacaqGXaGa aeyoaiaabMdacaqGWaGaaeilaiaabccacaqG0aGaae4naiaabwdaca qGGaGaaeOyaiaab+gacaqGVbGaae4AaiaabohacaqGGaGaae4Daiaa bwgacaqGYbGaaeyzaiaabccacaqGZbGaae4BaiaabYgacaqGKbGaae OlaaqaaiaabMeacaqGUbGaaeiiaiaabgdacaqG5aGaaeyoaiaabkda caqGSaGaaeiiaiaabkdacaqGYaGaaeynaiaabccacaqGIbGaae4Bai aab+gacaqGRbGaae4CaiaabccacaqG3bGaaeyzaiaabkhacaqGLbGa aeiiaiaabohacaqGVbGaaeiBaiaabsgacaqGUaaabaGaaeikaiaabM gacaqGPbGaaeykaiaabccacaqGgbGaaeOCaiaab+gacaqGTbGaaeii aiaabshacaqGObGaaeyzaiaabccacaqGNbGaaeOCaiaabggacaqGWb GaaeiAaiaabYcacaqGGaGaaeyAaiaabshacaqGGaGaae4yaiaabgga caqGUbGaaeiiaiaabkgacaqGLbGaaeiiaiaabogacaqGVbGaaeOBai aabogacaqGSbGaaeyDaiaabsgacaqGLbGaaeizaiaabccacaqG0bGa aeiAaiaabggacaqG0bGaaeiiaiaabsdacaqG3aGaaeynaiaabccaca qGIbGaae4Baiaab+gacaqGRbGaae4CaiaabccacaqG3bGaaeyzaiaa bkhacaqGLbaabaGaae4Caiaab+gacaqGSbGaaeizaiaabccacaqGPb GaaeOBaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeyEaiaabwga caqGHbGaaeOCaiaabccacaqGXaGaaeyoaiaabMdacaqGWaGaaeiiai aabggacaqGUbGaaeizaiaabccacaqGYaGaaeOmaiaabwdacaqGGaGa aeOyaiaab+gacaqGVbGaae4AaiaabohacaqGGaGaae4Daiaabwgaca qGYbGaaeyzaiaabccacaqGZbGaae4BaiaabYgacaqGKbGaaeiiaiaa bMgacaqGUbGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqG5bGaae yzaiaabggacaqGYbGaaeiiaiaabgdacaqG5aGaaeyoaiaabkdacaqG UaaabaGaaeikaiaabMgacaqGPbGaaeyAaiaabMcacaqGGaGaaeOrai aabkhacaqGVbGaaeyBaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGa ae4zaiaabkhacaqGHbGaaeiCaiaabIgacaqGSaGaaeiiaiaabMgaca qG0bGaaeiiaiaabogacaqGHbGaaeOBaiaabccacaqGIbGaaeyzaiaa bccacaqGJbGaae4Baiaab6gacaqGJbGaaeiBaiaabwhacaqGKbGaae yzaiaabsgacaqGGaGaaeiDaiaabIgacaqGHbGaaeiDaiaabccacaqG PbGaaeOBaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeyEaiaabw gacaqGHbGaaeOCaiaabohaaeaacaqGXaGaaeyoaiaabIdacaqG5aGa aeiiaiaabggacaqGUbGaaeizaiaabccacaqGXaGaaeyoaiaabMdaca qGYaGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeOBaiaa bwhacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+gacaqGMbGaae iiaiaabkgacaqGVbGaae4BaiaabUgacaqGZbGaaeiiaiaabohacaqG VbGaaeiBaiaabsgacaqGGaGaae4DaiaabwgacaqGYbGaaeyzaiaabc cacaqGSbGaaeyzaiaabohacaqGZbGaaeiiaiaabshacaqGObGaaeyy aiaab6gacaqGGaGaaeOmaiaabwdacaqGWaGaaeOlaaqaaiaabIcaca qGPbGaaeODaiaabMcacaqGGaGaaeOraiaabkhacaqGVbGaaeyBaiaa bccacaqG0bGaaeiAaiaabwgacaqGGaGaae4zaiaabkhacaqGHbGaae iCaiaabIgacaqGSaGaaeiiaiaabMgacaqG0bGaaeiiaiaabogacaqG HbGaaeOBaiaabccacaqGIbGaaeyzaiaabccacaqGJbGaae4Baiaab6 gacaqGJbGaaeiBaiaabwhacaqGKbGaaeyzaiaabsgacaqGGaGaaeiD aiaabIgacaqGHbGaaeiDaiaabccacaqG0bGaaeiAaiaabwgacaqGGa GaaeOBaiaabwhacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+ga caqGMbaabaGaaeOyaiaab+gacaqGVbGaae4AaiaabohacaqGGaGaae 4Caiaab+gacaqGSbGaaeizaiaabccacaqGPbGaaeOBaiaabccacaqG 0bGaaeiAaiaabwgacaqGGaGaaeyEaiaabwgacaqGHbGaaeOCaiaabc cacaqGXaGaaeyoaiaabIdacaqG5aGaaeiiaiaabMgacaqGZbGaaeii aiaabggacaqGIbGaae4BaiaabwhacaqG0bGaaeiiaiaabgdacaqGGa Gaaeyyaiaab6gacaqGKbGaaeiiamaalaaabaGaaG4maaqaaiaaisda aaGaaeiDaiaabIgacaaMe8UaaeiCaiaabggacaqGYbGaaeiDaiaabc cacaqGVbGaaeOzaiaabccacaqGXaGaaeiiaiaabogacaqGTbaabaGa aeivaiaabIgacaqGLbGaaeiiaiaabohacaqGJbGaaeyyaiaabYgaca qGLbGaaeiiaiaabMgacaqGZbGaaeiiaiaabshacaqGHbGaae4Aaiaa bwgacaqGUbGaaeiiaiaabggacaqGZbGaaeiiaiaabgdacaqGGaGaae 4yaiaab2gacaqGGaGaaeypaiaabccacaqGXaGaaeimaiaabcdacaqG GaGaaeOyaiaab+gacaqGVbGaae4AaiaabohaaeaacaqGtbGaae4Bai aabYcacaqGGaGaaeymaiaabcdacaqGWaGaae4kamaalaaabaGaaG4m aaqaaiaaisdaaaGaey41aqRaaGymaiaaicdacaaIWaGaeyypa0JaaG ymaiaaicdacaaIWaGaey4kaSIaaG4naiaaiwdacqGH9aqpcaaIXaGa aG4naiaaiwdaaeaacaqGubGaaeiAaiaabwgacaqGYbGaaeyzaiaabA gacaqGVbGaaeOCaiaabwgacaqGSaGaaeiiaiaabggacaqGIbGaae4B aiaabwhacaqG0bGaaeiiaiaabgdacaqG3aGaaeynaiaabccacaqGIb Gaae4Baiaab+gacaqGRbGaae4CaiaabccacaqG3bGaaeyzaiaabkha caqGLbGaaeiiaiaabohacaqGVbGaaeiBaiaabsgacaqGGaGaaeyAai aab6gacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabMhacaqGLbGa aeyyaiaabkhacaqGGaGaaeymaiaabMdacaqG4aGaaeyoaiaab6caaa aa@18E2@

Q.18 Number of children in six different classes are given below.
Represent the data on a bar graph.

Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of Children 135 120 95 100 90 80

(a) How would you choose a scale?
(
b)
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 eight.

Ans.

(a)Choose a scale as 1 unit = 10 children, because we can show a clear difference between the number of students of class 7th and class 9th. (b) (i) The bar representing the number of children of class fifth is tallest, there are maximum number of children in class fifth and the bar representing the number of children of class tenth is smallest, there are minimum number of children in class tenth. (ii) The number of student in class sixth is 120 and the number of student in class eight is 100. So, the ratio ratio is = 120 100 = 20×6 20×5 = 6 5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyyaiaabMcacaaMe8Uaae4q aiaabIgacaqGVbGaae4BaiaabohacaqGLbGaaeiiaiaabggacaqGGa Gaae4CaiaabogacaqGHbGaaeiBaiaabwgacaqGGaGaaeyyaiaaboha caqGGaGaaeymaiaabccacaqG1bGaaeOBaiaabMgacaqG0bGaaeiiai aab2dacaqGGaGaaeymaiaabcdacaqGGaGaae4yaiaabIgacaqGPbGa aeiBaiaabsgacaqGYbGaaeyzaiaab6gacaqGSaGaaeiiaiaabkgaca qGLbGaae4yaiaabggacaqG1bGaae4CaiaabwgacaqGGaGaae4Daiaa bwgacaqGGaGaae4yaiaabggacaqGUbaabaGaae4CaiaabIgacaqGVb Gaae4DaiaabccacaqGHbGaaeiiaiaabogacaqGSbGaaeyzaiaabgga caqGYbGaaeiiaiaabsgacaqGPbGaaeOzaiaabAgacaqGLbGaaeOCai aabwgacaqGUbGaae4yaiaabwgacaqGGaGaaeOyaiaabwgacaqG0bGa ae4DaiaabwgacaqGLbGaaeOBaiaabccacaqG0bGaaeiAaiaabwgaca qGGaGaaeOBaiaabwhacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaa b+gacaqGMbGaaeiiaiaabohacaqG0bGaaeyDaiaabsgacaqGLbGaae OBaiaabshacaqGZbGaaeiiaiaab+gacaqGMbGaaeiiaaqaaiaaboga caqGSbGaaeyyaiaabohacaqGZbGaaeiiaiaabEdacaqG0bGaaeiAai aabccacaqGHbGaaeOBaiaabsgacaqGGaGaae4yaiaabYgacaqGHbGa ae4CaiaabohacaqGGaGaaeyoaiaabshacaqGObGaaeOlaaqaaiaabI cacaqGIbGaaeykaaqaaiaabIcacaqGPbGaaeykaaqaaiaabsfacaqG ObGaaeyzaiaabccacaqGIbGaaeyyaiaabkhacaqGGaGaaeOCaiaabw gacaqGWbGaaeOCaiaabwgacaqGZbGaaeyzaiaab6gacaqG0bGaaeyA aiaab6gacaqGNbGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGUb GaaeyDaiaab2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabAga caqGGaGaae4yaiaabIgacaqGPbGaaeiBaiaabsgacaqGYbGaaeyzai aab6gacaqGGaGaae4BaiaabAgacaqGGaGaae4yaiaabYgacaqGHbGa ae4CaiaabohacaqGGaGaaeOzaiaabMgacaqGMbGaaeiDaiaabIgaca qGGaGaaeyAaiaabohaaeaacaqG0bGaaeyyaiaabYgacaqGSbGaaeyz aiaabohacaqG0bGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGYb GaaeyzaiaabccacaqGHbGaaeOCaiaabwgacaqGGaGaaeyBaiaabgga caqG4bGaaeyAaiaab2gacaqG1bGaaeyBaiaabccacaqGUbGaaeyDai aab2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabAgacaqGGaGa ae4yaiaabIgacaqGPbGaaeiBaiaabsgacaqGYbGaaeyzaiaab6gaca qGGaGaaeyAaiaab6gacaqGGaGaae4yaiaabYgacaqGHbGaae4Caiaa bohacaqGGaGaaeOzaiaabMgacaqGMbGaaeiDaiaabIgaaeaacaqGHb GaaeOBaiaabsgacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabkga caqGHbGaaeOCaiaabccacaqGYbGaaeyzaiaabchacaqGYbGaaeyzai aabohacaqGLbGaaeOBaiaabshacaqGPbGaaeOBaiaabEgacaqGGaGa aeiDaiaabIgacaqGLbGaaeiiaiaab6gacaqG1bGaaeyBaiaabkgaca qGLbGaaeOCaiaabccacaqGVbGaaeOzaiaabccacaqGJbGaaeiAaiaa bMgacaqGSbGaaeizaiaabkhacaqGLbGaaeOBaiaabccacaqGVbGaae OzaiaabccacaqGJbGaaeiBaiaabggacaqGZbGaae4CaiaabccacaqG 0bGaaeyzaiaab6gacaqG0bGaaeiAaiaabccacaqGPbGaae4Caaqaai aabohacaqGTbGaaeyyaiaabYgacaqGSbGaaeyzaiaabohacaqG0bGa aeilaiaabccacaqG0bGaaeiAaiaabwgacaqGYbGaaeyzaiaabccaca qGHbGaaeOCaiaabwgacaqGGaGaaeyBaiaabMgacaqGUbGaaeyAaiaa b2gacaqG1bGaaeyBaiaabccacaqGUbGaaeyDaiaab2gacaqGIbGaae yzaiaabkhacaqGGaGaae4BaiaabAgacaqGGaGaae4yaiaabIgacaqG PbGaaeiBaiaabsgacaqGYbGaaeyzaiaab6gacaqGGaGaaeyAaiaab6 gacaqGGaGaae4yaiaabYgacaqGHbGaae4CaiaabohacaqGGaGaaeiD aiaabwgacaqGUbGaaeiDaiaabIgacaqGUaaabaGaaeikaiaabMgaca qGPbGaaeykaaqaaiaabsfacaqGObGaaeyzaiaabccacaqGUbGaaeyD aiaab2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabAgacaqGGa Gaae4CaiaabshacaqG1bGaaeizaiaabwgacaqGUbGaaeiDaiaabcca caqGPbGaaeOBaiaabccacaqGJbGaaeiBaiaabggacaqGZbGaae4Cai aabccacaqGZbGaaeyAaiaabIhacaqG0bGaaeiAaiaabccacaqGPbGa ae4CaiaabccacaqGXaGaaeOmaiaabcdacaqGGaGaaeyyaiaab6gaca qGKbGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGUbGaaeyDaiaa b2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabAgacaqGGaaaba Gaae4CaiaabshacaqG1bGaaeizaiaabwgacaqGUbGaaeiDaiaabcca caqGPbGaaeOBaiaabccacaqGJbGaaeiBaiaabggacaqGZbGaae4Cai aabccacaqGLbGaaeyAaiaabEgacaqGObGaaeiDaiaabccacaqGPbGa ae4CaiaabccacaqGXaGaaeimaiaabcdacaqGUaaabaGaae4uaiaab+ gacaqGSaGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGYbGaaeyy aiaabshacaqGPbGaae4BaiaabccacaqGYbGaaeyyaiaabshacaqGPb Gaae4BaiaabccacaqGPbGaae4CaiaabccacaqG9aGaaeiiamaalaaa baGaaGymaiaaikdacaaIWaaabaGaaGymaiaaicdacaaIWaaaaiabg2 da9maalaaabaGaaGOmaiaaicdacqGHxdaTcaaI2aaabaGaaGOmaiaa icdacqGHxdaTcaaI1aaaaiabg2da9maaL4babaWaaSaaaeaacaaI2a aabaGaaGynaaaaaaaaaaa@0D0B@

Q.19 The performance of student sin 1st Term and 2nd Term is given.
Draw a double bar graph choosing appropriate
s
cale and answer the following:

Subject English Hindi Maths Science S.Science
1st Term

(M.M. 100)

67 72 88 81 73
2nd Term

(M. M. 100)

70 65 95 85 75

(i) In which subject, has the child improved h is performance the most?
(ii) in which subject is the improvement the least?
(iii) Has the performance gone down in any subject?

Ans.

(i) There was a maximum increase in the marks obtained in Maths. Thus, the child improved his performance the most in Maths. (ii) From the graph, we observe that the improvment was least in S. Science. (iii) From the graph, we observe that the performance in Hindi has grown down. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaGaaeiv aiaabIgacaqGLbGaaeOCaiaabwgacaqGGaGaae4DaiaabggacaqGZb GaaeiiaiaabggacaqGGaGaaeyBaiaabggacaqG4bGaaeyAaiaab2ga caqG1bGaaeyBaiaabccacaqGPbGaaeOBaiaabogacaqGYbGaaeyzai aabggacaqGZbGaaeyzaiaabccacaqGPbGaaeOBaiaabccacaqG0bGa aeiAaiaabwgacaqGGaGaaeyBaiaabggacaqGYbGaae4Aaiaabohaca qGGaGaae4BaiaabkgacaqG0bGaaeyyaiaabMgacaqGUbGaaeyzaiaa bsgacaqGGaGaaeyAaiaab6gaaeaacaqGnbGaaeyyaiaabshacaqGOb Gaae4Caiaab6cacaqGGaGaaeivaiaabIgacaqG1bGaae4CaiaabYca caqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabogacaqGObGaaeyAai aabYgacaqGKbGaaeiiaiaabMgacaqGTbGaaeiCaiaabkhacaqGVbGa aeODaiaabwgacaqGKbGaaeiiaiaabIgacaqGPbGaae4Caiaabccaca qGWbGaaeyzaiaabkhacaqGMbGaae4BaiaabkhacaqGTbGaaeyyaiaa b6gacaqGJbGaaeyzaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaae yBaiaab+gacaqGZbGaaeiDaaqaaiaabMgacaqGUbGaaeiiaiaab2ea caqGHbGaaeiDaiaabIgacaqGZbGaaeOlaaqaaiaabIcacaqGPbGaae yAaiaabMcacaqGGaGaiaiMbAeacGaGygOCaiacaIzGVbGaiaiMb2ga cGaGygiiaiacaIzG0bGaiaiMbIgacGaGygyzaiacaIzGGaGaiaiMbE gacGaGygOCaiacaIzGHbGaiaiMbchacGaGygiAaiacaIzGSaGaiaiM bccacGaGyg4DaiacaIzGLbGaiaiMbccacGaGyg4BaiacaIzGIbGaia iMbohacGaGygyzaiacaIzGYbGaiaiMbAhacGaGygyzaiacaIzGGaGa iaiMbshacGaGygiAaiacaIzGHbGaiaiMbshacaqGGaGaaeiDaiaabI gacaqGLbGaaeiiaiaabMgacaqGTbGaaeiCaiaabkhacaqGVbGaaeOD aiaab2gacaqGLbGaaeOBaiaabshacaqGGaGaae4DaiaabggacaqGZb GaaeiiaiaabYgacaqGLbGaaeyyaiaabohacaqG0baabaGaaeyAaiaa b6gacaqGGaGaae4uaiaab6cacaqGGaGaae4uaiaabogacaqGPbGaae yzaiaab6gacaqGJbGaaeyzaiaab6caaeaacaqGOaGaaeyAaiaabMga caqGPbGaaeykaiaabccacaqGgbGaaeOCaiaab+gacaqGTbGaaeiiai aabshacaqGObGaaeyzaiaabccacaqGNbGaaeOCaiaabggacaqGWbGa aeiAaiaabYcacaqGGaGaae4DaiaabwgacaqGGaGaae4Baiaabkgaca qGZbGaaeyzaiaabkhacaqG2bGaaeyzaiaabccacaqG0bGaaeiAaiaa bggacaqG0bGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGWbGaae yzaiaabkhacaqGMbGaae4BaiaabkhacaqGTbGaaeyyaiaab6gacaqG JbGaaeyzaiaabccacaqGPbGaaeOBaiaabccacaqGibGaaeyAaiaab6 gacaqGKbGaaeyAaaqaaiaabIgacaqGHbGaae4CaiaabccacaqGNbGa aeOCaiaab+gacaqG3bGaaeOBaiaabccacaqGKbGaae4BaiaabEhaca qGUbGaaeOlaaaaaa@4E32@

Q.20 Consider this data collected from a survey of a colony.

Favorite Sport Cricket Basket Ball Swimming Hockey Athletics
Watching 1240 470 510 423 250
Participating 620 320 320 250 105

(i) Draw a double bar graph choosing an appropriate scale. What do you infer from the graph?
(
ii) Which sport is most popular?
(
iii) Which is more preferred watching or participating sport?

Ans.

(i)

(ii) From the bar graph, the bar representing the number of people who like watching and participating in cricket is the tallest among all the bars.Thus, cricket is the most popular sport. (iii) The bars showing watchig spot are longer than the bars showing participating in spot. Thus, watching different types of sports is more preffered than participating in the sports. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMgacaqGPaGaaeii aiaabAeacaqGYbGaae4Baiaab2gacaqGGaGaaeiDaiaabIgacaqGLb GaaeiiaiaabkgacaqGHbGaaeOCaiaabccacaqGNbGaaeOCaiaabgga caqGWbGaaeiAaiaabYcacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiai aabkgacaqGHbGaaeOCaiaabccacaqGYbGaaeyzaiaabchacaqGYbGa aeyzaiaabohacaqGLbGaaeOBaiaabshacaqGPbGaaeOBaiaabEgaca qGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaab6gacaqG1bGaaeyBaiaa bkgacaqGLbGaaeOCaaqaaiaab+gacaqGMbGaaeiiaiaabchacaqGLb Gaae4BaiaabchacaqGSbGaaeyzaiaabccacaqGGaGaae4DaiaabIga caqGVbGaaeiiaiaabYgacaqGPbGaae4AaiaabwgacaqGGaGaae4Dai aabggacaqG0bGaae4yaiaabIgacaqGPbGaaeOBaiaabEgacaqGGaGa aeyyaiaab6gacaqGKbGaaeiiaiaabchacaqGHbGaaeOCaiaabshaca qGPbGaae4yaiaabMgacaqGWbGaaeyyaiaabshacaqGPbGaaeOBaiaa bEgacaqGGaGaaeyAaiaab6gacaqGGaGaae4yaiaabkhacaqGPbGaae 4yaiaabUgacaqGLbGaaeiDaaqaaiaabMgacaqGZbGaaeiiaiaabsha caqGObGaaeyzaiaabccacaqG0bGaaeyyaiaabYgacaqGSbGaaeyzai aabohacaqG0bGaaeiiaiaabggacaqGTbGaae4Baiaab6gacaqGNbGa aeiiaiaabggacaqGSbGaaeiBaiaabccacaqG0bGaaeiAaiaabwgaca qGGaGaaeOyaiaabggacaqGYbGaae4Caiaab6cacaqGubGaaeiAaiaa bwhacaqGZbGaaeilaiaabccacaqGJbGaaeOCaiaabMgacaqGJbGaae 4AaiaabwgacaqG0bGaaeiiaiaabMgacaqGZbGaaeiiaiaabshacaqG ObGaaeyzaiaabccacaqGTbGaae4BaiaabohacaqG0baabaGaaeiCai aab+gacaqGWbGaaeyDaiaabYgacaqGHbGaaeOCaiaabccacaqGZbGa aeiCaiaab+gacaqGYbGaaeiDaiaab6caaeaacaqGOaGaaeyAaiaabM gacaqGPbGaaeykaiaabccacaqGubGaaeiAaiaabwgacaqGGaGaaeOy aiaabggacaqGYbGaae4CaiaabccacaqGZbGaaeiAaiaab+gacaqG3b GaaeyAaiaab6gacaqGNbGaaeiiaiaabEhacaqGHbGaaeiDaiaaboga caqGObGaaeyAaiaabEgacaqGGaGaae4CaiaabchacaqGVbGaaeiDai aabccacaqGHbGaaeOCaiaabwgacaqGGaGaaeiBaiaab+gacaqGUbGa ae4zaiaabwgacaqGYbGaaeiiaiaabshacaqGObGaaeyyaiaab6gaca qGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabkgacaqGHbGaaeOCaiaa bohaaeaacaqGZbGaaeiAaiaab+gacaqG3bGaaeyAaiaab6gacaqGNb GaaeiiaiaabchacaqGHbGaaeOCaiaabshacaqGPbGaae4yaiaabMga caqGWbGaaeyyaiaabshacaqGPbGaaeOBaiaabEgacaqGGaGaaeyAai aab6gacaqGGaGaae4CaiaabchacaqGVbGaaeiDaiaab6cacaqGGaGa aeivaiaabIgacaqG1bGaae4CaiaabYcacaqGGaGaae4Daiaabggaca qG0bGaae4yaiaabIgacaqGPbGaaeOBaiaabEgacaqGGaGaaeizaiaa bMgacaqGMbGaaeOzaiaabwgacaqGYbGaaeyzaiaab6gacaqG0bGaae iiaiaabshacaqG5bGaaeiCaiaabwgacaqGZbaabaGaae4BaiaabAga caqGGaGaae4CaiaabchacaqGVbGaaeOCaiaabshacaqGZbGaaeiiai aabMgacaqGZbGaaeiiaiaab2gacaqGVbGaaeOCaiaabwgacaqGGaGa aeiCaiaabkhacaqGLbGaaeOzaiaabAgacaqGLbGaaeOCaiaabwgaca qGKbGaaeiiaiaabshacaqGObGaaeyyaiaab6gacaqGGaGaaeiCaiaa bggacaqGYbGaaeiDaiaabMgacaqGJbGaaeyAaiaabchacaqGHbGaae iDaiaabMgacaqGUbGaae4zaiaabccacaqGPbGaaeOBaiaabccacaqG 0bGaaeiAaiaabwgacaqGGaGaae4CaiaabchacaqGVbGaaeOCaiaabs hacaqGZbGaaeOlaaaaaa@811D@

Q.21 Take the data giving the mininum and the maximum temperature of various cities given in the beginning of this chapter.

City Max. Min
Ahemdabad 38°C 29°C
Amritsar 37°C 26°C
Banglore 28°C 21°C
Chennai 36°C 27°C
Delhi 38°C 28°C
Jaipur 39°C 29°C
Jammu 41°C 26°C
Mumbai 32°C 27°C

Plot a double bar graph using thedata and answer the following:
(i)
Which city has the largest difference in the minimum
and maximum temperature on the given date?
(
ii)
Which is the hottest city and which is the coldest city?
(
iii)
Name two cities where maximum temperature of one
was less than the minimum temperature of the other.
(
iv) Name the city which has the least difference between
its minimum and the maximum temperature.

Ans.

A double bar graph for given data is shown as below:

(i) From the graph, we observe that Jammu has the largest difference in its minimum and maximum temprature on the given date. (ii) From graph, we observe that Jammu is the hottest city and Banglore is the coldest city. (iii) Banglore and Jaipur, Banglore and Ahemdabad. For Banglore, the maximum temprature was 28°C, while temprature of both cities was 29°C. (iv) From graph, we observe that the city which has the least difference between its minimum and maximum temprature is Mumbai. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaqGGaGaaeOr aiaabkhacaqGVbGaaeyBaiaabccacaqG0bGaaeiAaiaabwgacaqGGa Gaae4zaiaabkhacaqGHbGaaeiCaiaabIgacaqGSaGaaeiiaiaabEha caqGLbGaaeiiaiaab+gacaqGIbGaae4CaiaabwgacaqGYbGaaeODai aabwgacaqGGaGaaeiDaiaabIgacaqGHbGaaeiDaiaabccacaqGkbGa aeyyaiaab2gacaqGTbGaaeyDaiaabccacaqGObGaaeyyaiaabohaca qGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabYgacaqGHbGaaeOCaiaa bEgacaqGLbGaae4CaiaabshaaeaacaaMe8UaaGjbVlaaysW7caaMe8 UaaeizaiaabMgacaqGMbGaaeOzaiaabwgacaqGYbGaaeyzaiaab6ga caqGJbGaaeyzaiaabccacaqGPbGaaeOBaiaabccacaqGPbGaaeiDai aabohacaqGGaGaaeyBaiaabMgacaqGUbGaaeyAaiaab2gacaqG1bGa aeyBaiaabccacaqGHbGaaeOBaiaabsgacaqGGaGaaeyBaiaabggaca qG4bGaaeyAaiaab2gacaqG1bGaaeyBaiaabccacaqG0bGaaeyzaiaa b2gacaqGWbGaaeOCaiaabggacaqG0bGaaeyDaiaabkhacaqGLbGaae iiaiaab+gacaqGUbGaaeiiaiaabshacaqGObGaaeyzaiaabccaaeaa caaMe8UaaGjbVlaaysW7caaMe8Uaae4zaiaabMgacaqG2bGaaeyzai aab6gacaqGGaGaaeizaiaabggacaqG0bGaaeyzaiaab6caaeaacaqG OaGaaeyAaiaabMgacaqGPaGaaeiiaiaabAeacaqGYbGaae4Baiaab2 gacaqGGaGaae4zaiaabkhacaqGHbGaaeiCaiaabIgacaqGSaGaaeii aiaabEhacaqGLbGaaeiiaiaab+gacaqGIbGaae4CaiaabwgacaqGYb GaaeODaiaabwgacaqGGaGaaeiDaiaabIgacaqGHbGaaeiDaiaabcca caqGkbGaaeyyaiaab2gacaqGTbGaaeyDaiaabccacaqGPbGaae4Cai aabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeiAaiaab+gacaqG0bGa aeiDaiaabwgacaqGZbGaaeiDaiaabccacaqGJbGaaeyAaiaabshaca qG5baabaGaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caqGHbGaaeOB aiaabsgacaqGGaGaaeOqaiaabggacaqGUbGaae4zaiaabYgacaqGVb GaaeOCaiaabwgacaqGGaGaaeyAaiaabohacaqGGaGaaeiDaiaabIga caqGLbGaaeiiaiaabogacaqGVbGaaeiBaiaabsgacaqGLbGaae4Cai aabshacaqGGaGaae4yaiaabMgacaqG0bGaaeyEaiaab6caaeaacaqG OaGaaeyAaiaabMgacaqGPbGaaeykaiaabccacaqGcbGaaeyyaiaab6 gacaqGNbGaaeiBaiaab+gacaqGYbGaaeyzaiaabccacaqGHbGaaeOB aiaabsgacaqGGaGaaeOsaiaabggacaqGPbGaaeiCaiaabwhacaqGYb GaaeilaiaabccacaqGcbGaaeyyaiaab6gacaqGNbGaaeiBaiaab+ga caqGYbGaaeyzaiaabccacaqGHbGaaeOBaiaabsgacaqGGaGaaeyqai aabIgacaqGLbGaaeyBaiaabsgacaqGHbGaaeOyaiaabggacaqGKbGa aeOlaaqaaiaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaeOraiaab+ gacaqGYbGaaeiiaiaabkeacaqGHbGaaeOBaiaabEgacaqGSbGaae4B aiaabkhacaqGLbGaaeilaiaabccacaqG0bGaaeiAaiaabwgacaqGGa GaaeyBaiaabggacaqG4bGaaeyAaiaab2gacaqG1bGaaeyBaiaabcca caqG0bGaaeyzaiaab2gacaqGWbGaaeOCaiaabggacaqG0bGaaeyDai aabkhacaqGLbGaaeiiaiaabEhacaqGHbGaae4CaiaabccacaqGYaGa aeioaiabgclaWkaadoeacaqGSaGaaeiiaiaabEhacaqGObGaaeyAai aabYgacaqGLbaabaGaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caqG 0bGaaeyzaiaab2gacaqGWbGaaeOCaiaabggacaqG0bGaaeyDaiaabk hacaqGLbGaaeiiaiaab+gacaqGMbGaaeiiaiaabkgacaqGVbGaaeiD aiaabIgacaqGGaGaae4yaiaabMgacaqG0bGaaeyAaiaabwgacaqGZb GaaeiiaiaabEhacaqGHbGaae4CaiaabccacaqGYaGaaeyoaiabgcla WkaadoeacaGGUaaabaGaaeikaiaabMgacaqG2bGaaeykaiaabccaca qGgbGaaeOCaiaab+gacaqGTbGaaeiiaiaabEgacaqGYbGaaeyyaiaa bchacaqGObGaaeilaiaabccacaqG3bGaaeyzaiaabccacaqGVbGaae OyaiaabohacaqGLbGaaeOCaiaabAhacaqGLbGaaeiiaiaabshacaqG ObGaaeyyaiaabshacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabo gacaqGPbGaaeiDaiaabMhacaqGGaGaae4DaiaabIgacaqGPbGaae4y aiaabIgacaqGGaGaaeiAaiaabggacaqGZbGaaeiiaiaabshacaqGOb GaaeyzaaqaaiaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaeiBaiaa bwgacaqGHbGaae4CaiaabshacaqGGaGaaeizaiaabMgacaqGMbGaae OzaiaabwgacaqGYbGaaeyzaiaab6gacaqGJbGaaeyzaiaabccacaqG IbGaaeyzaiaabshacaqG3bGaaeyzaiaabwgacaqGUbGaaeiiaiaabM gacaqG0bGaae4CaiaabccacaqGTbGaaeyAaiaab6gacaqGPbGaaeyB aiaabwhacaqGTbGaaeiiaiaabggacaqGUbGaaeizaiaabccacaqGTb GaaeyyaiaabIhacaqGPbGaaeyBaiaabwhacaqGTbaabaGaaGjbVlaa ysW7caaMe8UaaGjbVlaaysW7caqG0bGaaeyzaiaab2gacaqGWbGaae OCaiaabggacaqG0bGaaeyDaiaabkhacaqGLbGaaeiiaiaabMgacaqG ZbGaaeiiaiaab2eacaqG1bGaaeyBaiaabkgacaqGHbGaaeyAaiaab6 caaaaa@113C@

Q.22 Tell whether the following is cretain to happen, impossible, can happed but not certain.
(i) You are older today than yesterday.
(ii) Atossed 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) Tomorrowl will be a coludy day.

Ans.

(i) Certain
(ii) Can happen but not certain
(iii) Impossible
(iv) Can happen but not certain
(v) Can happen but not certain

Q.23 There are 6 marbles in a box with numbers from 1 to 6 marked on each o0f them.
(i) What is the probability of drawing a marble with number 2?
(ii) What is the probability of drawing a marble with umber 5?

Ans.

(i)Since, Probability = Number of favourable outcomes Number of possible outcomes So,P(apperance of 2) = 1 6 (ii) P(apperance of 2) = 1 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGOaGaaeyAaiaabMcacaaMe8Uaae4u aiaabMgacaqGUbGaae4yaiaabwgacaqGSaGaaGjbVpaaL4babaGaae iuaiaabkhacaqGVbGaaeOyaiaabggacaqGIbGaaeyAaiaabYgacaqG PbGaaeiDaiaabMhacaqGGaGaeyypa0JaaeiiamaalaaabaGaaeOtai aabwhacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+gacaqGMbGa aeiiaiaabAgacaqGHbGaaeODaiaab+gacaqG1bGaaeOCaiaabggaca qGIbGaaeiBaiaabwgacaqGGaGaae4BaiaabwhacaqG0bGaae4yaiaa b+gacaqGTbGaaeyzaiaabohaaeaacaqGobGaaeyDaiaab2gacaqGIb GaaeyzaiaabkhacaqGGaGaae4BaiaabAgacaqGGaGaaeiCaiaab+ga caqGZbGaae4CaiaabMgacaqGIbGaaeiBaiaabwgacaqGGaGaae4Bai aabwhacaqG0bGaae4yaiaab+gacaqGTbGaaeyzaiaabohaaaaaaaqa aiaaysW7caaMe8UaaGjbVlaaysW7caqGtbGaae4BaiaabYcacaqGqb GaaeikaiaabggacaqGWbGaaeiCaiaabwgacaqGYbGaaeyyaiaab6ga caqGJbGaaeyzaiaabccacaqGVbGaaeOzaiaabccacaqGYaGaaeykai aabccacqGH9aqpdaqjEaqaamaalaaabaGaaGymaaqaaiaaiAdaaaaa aaqaaiaabIcacaqGPbGaaeyAaiaabMcacaqGGaGaaeiuaiaabIcaca qGHbGaaeiCaiaabchacaqGLbGaaeOCaiaabggacaqGUbGaae4yaiaa bwgacaqGGaGaae4BaiaabAgacaqGGaGaaeOmaiaabMcacaqGGaGaey ypa0ZaauIhaeaadaWcaaqaaiaaigdaaeaacaaI2aaaaaaaaaaa@B6EA@

Q.24 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 faces namelyHead and Tail. One team can opt either Head or Tail. Since, Probability= Number of favourable outcomes Number of favourable outcomes So, Probability(our team start first) = 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGbbGaaeiiaiaabogacaqGVbGaaeyA aiaab6gacaqGGaGaaeiAaiaabggacaqGZbGaaeiiaiaabshacaqG3b Gaae4BaiaabccacaqGMbGaaeyyaiaabogacaqGLbGaae4Caiaabcca caqGUbGaaeyyaiaab2gacaqGLbGaaeiBaiaabMhacqGHsislcaqGib GaaeyzaiaabggacaqGKbGaaeiiaiaabggacaqGUbGaaeizaiaabcca caqGubGaaeyyaiaabMgacaqGSbGaaeOlaaqaaiaab+eacaqGUbGaae yzaiaabccacaqG0bGaaeyzaiaabggacaqGTbGaaeiiaiaabogacaqG HbGaaeOBaiaabccacaqGVbGaaeiCaiaabshacaqGGaGaaeyzaiaabM gacaqG0bGaaeiAaiaabwgacaqGYbGaaeiiaiaabIeacaqGLbGaaeyy aiaabsgacaqGGaGaae4BaiaabkhacaqGGaGaaeivaiaabggacaqGPb GaaeiBaiaab6caaeaacaqGtbGaaeyAaiaab6gacaqGJbGaaeyzaiaa bYcacaqGGaWaauIhaeaacaqGqbGaaeOCaiaab+gacaqGIbGaaeyyai aabkgacaqGPbGaaeiBaiaabMgacaqG0bGaaeyEaiabg2da9maalaaa baGaaeOtaiaabwhacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+ gacaqGMbGaaeiiaiaabAgacaqGHbGaaeODaiaab+gacaqG1bGaaeOC aiaabggacaqGIbGaaeiBaiaabwgacaqGGaGaae4BaiaabwhacaqG0b Gaae4yaiaab+gacaqGTbGaaeyzaiaabohaaeaacaqGobGaaeyDaiaa b2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabAgacaqGGaGaae OzaiaabggacaqG2bGaae4BaiaabwhacaqGYbGaaeyyaiaabkgacaqG SbGaaeyzaiaabccacaqGVbGaaeyDaiaabshacaqGJbGaae4Baiaab2 gacaqGLbGaae4CaaaaaaaabaGaae4uaiaab+gacaqGSaGaaeiiaiaa bcfacaqGYbGaae4BaiaabkgacaqGHbGaaeOyaiaabMgacaqGSbGaae yAaiaabshacaqG5bGaaeikaiaab+gacaqG1bGaaeOCaiaabccacaqG 0bGaaeyzaiaabggacaqGTbGaaeiiaiaabohacaqG0bGaaeyyaiaabk hacaqG0bGaaeiiaiaabAgacaqGPbGaaeOCaiaabohacaqG0bGaaeyk aiaabccacqGH9aqpdaqjEaqaaiaabccadaWcaaqaaiaaigdaaeaaca aIYaaaaaaaaaaa@EB22@

Q.25 A box contains pairs of socks of two colours (black and white) I have picked out a white sock.
I pick out one more with my eyes closed. What is the probability that it will make a pair?

Ans.

While closing the eyes, one can draw either a black sock or a white sock. Therefore, there are two possible cases. Since, Probability= Number of favourable outcomes Number of favourable outcomes So, P(a pair of white socks will be formed) = 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVz0xg9vqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe qaamaaeaqbaaGceaqabeaacaqGxbGaaeiAaiaabMgacaqGSbGaaeyz aiaabccacaqGJbGaaeiBaiaab+gacaqGZbGaaeyAaiaab6gacaqGNb GaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGLbGaaeyEaiaabwga caqGZbGaaeilaiaabccacaqGVbGaaeOBaiaabwgacaqGGaGaae4yai aabggacaqGUbGaaeiiaiaabsgacaqGYbGaaeyyaiaabEhacaqGGaGa aeyzaiaabMgacaqG0bGaaeiAaiaabwgacaqGYbGaaeiiaiaabggaca qGGaGaaeOyaiaabYgacaqGHbGaae4yaiaabUgacaqGGaGaae4Caiaa b+gacaqGJbGaae4Aaaqaaiaab+gacaqGYbGaaeiiaiaabggacaqGGa Gaae4DaiaabIgacaqGPbGaaeiDaiaabwgacaqGGaGaae4Caiaab+ga caqGJbGaae4Aaiaab6caaeaacaqGubGaaeiAaiaabwgacaqGYbGaae yzaiaabAgacaqGVbGaaeOCaiaabwgacaqGSaGaaeiiaiaabshacaqG ObGaaeyzaiaabkhacaqGLbGaaeiiaiaabggacaqGYbGaaeyzaiaabc cacaqG0bGaae4Daiaab+gacaqGGaGaaeiCaiaab+gacaqGZbGaae4C aiaabMgacaqGIbGaaeiBaiaabwgacaqGGaGaae4yaiaabggacaqGZb GaaeyzaiaabohacaqGUaaabaGaae4uaiaabMgacaqGUbGaae4yaiaa bwgacaqGSaGaaeiiamaaL4babaGaaeiuaiaabkhacaqGVbGaaeOyai aabggacaqGIbGaaeyAaiaabYgacaqGPbGaaeiDaiaabMhacaqG9aWa aSaaaeaacaqGobGaaeyDaiaab2gacaqGIbGaaeyzaiaabkhacaqGGa Gaae4BaiaabAgacaqGGaGaaeOzaiaabggacaqG2bGaae4Baiaabwha caqGYbGaaeyyaiaabkgacaqGSbGaaeyzaiaabccacaqGVbGaaeyDai aabshacaqGJbGaae4Baiaab2gacaqGLbGaae4Caaqaaiaab6eacaqG 1bGaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzaiaabc cacaqGMbGaaeyyaiaabAhacaqGVbGaaeyDaiaabkhacaqGHbGaaeOy aiaabYgacaqGLbGaaeiiaiaab+gacaqG1bGaaeiDaiaabogacaqGVb GaaeyBaiaabwgacaqGZbaaaaaaaeaacaqGtbGaae4BaiaabYcacaqG GaGaaeiuaiaabIcacaqGHbGaaeiiaiaabchacaqGHbGaaeyAaiaabk hacaqGGaGaae4BaiaabAgacaqGGaGaae4DaiaabIgacaqGPbGaaeiD aiaabwgacaqGGaGaae4Caiaab+gacaqGJbGaae4AaiaabohacaqGGa Gaae4DaiaabMgacaqGSbGaaeiBaiaabccacaqGIbGaaeyzaiaabcca caqGMbGaae4BaiaabkhacaqGTbGaaeyzaiaabsgacaqGPaGaaeiiai aab2dadaqjEaqaamaalaaabaGaaGymaaqaaiaaikdaaaaaaaaaaa@0BF3@

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FAQs (Frequently Asked Questions)
1. How many exercises are there in Chapter 3 data handling of the NCERT Solutions for Class 7 Mathematics?

This chapter has four exercises. Exercise 3.1 has five short and four long answer questions. Exercise 3.2 has two short and three long answer questions. Exercise 3.3 has three short and three long answer questions and Exercise 3.4 has two short and two long answer questions.

2. What are the key formulas in Chapter 3 of the NCERT textbook for Class 7 Mathematics?

Calculation of arithmetic mean, mean, median, and mode, probability, and other formulas are described in these solutions. These are the foundations for learning data handling techniques. These formulas, as well as the key definitions, can be found at the end of the chapter for a quick review.

3. Why is Chapter 3 of the NCERT Solutions for Class 7 Mathematics so important?

The concepts covered in NCERT Solutions for Class 7 Mathematics Chapter 3 are excellent for honing  study skills because the examples and exercises in the chapter are based on experiential learning. Students can access hundreds of practise problems on mean, median, mode, bar graphs, and probability, questions. Besides this they can use the problem-solving techniques explained in the examples to stay ahead in the competition.

4. Is it mandatory for me to practise all of the questions in NCERT Solutions Class 7 Mathematics Data Handling?

To improve their data handling skills, students should complete all of the examples and practise questions. The sample examples and exercise questions will ensure that students have a strong foundation to deal with higher mathematical concepts and even Mathematics for competitive exams in the future.