NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.2

In compliance with the Societies Registration Act, the National Council of Educational Research and Training, or NCERT, was established as a separate body in 1961. It was established by the Indian government as a body that would focus on the promotion of the country’s culture, intellect, and humanitarianism. Thanks to NCERT, all candidates will obtain a common education. The NCERT Textbooks were written and published by all students in Classes 1 through 12. NCERT texts are thus required reading for all students.Students can utilise Mathematical ideas to resolve problems in the real world. Mathematics is used in every sector in some way. A Mathematical background may be helpful for many different types of jobs. Students can pursue professions in Astronomy, Astrophysics, Statistics, weather forecasting, and other related subjects by using the principles they learn in this course. Mathematics, one of a program’s foundational subjects, is covered in school beginning in the first grade.

The development of a learner as a whole depends on understanding the fundamentals of Mathematics. Statistics is the area of Mathematics that studies the extraction of valuable information. It may also be described as the gathering of information that is helpful to the state about many facets of people’s lives. The chapter provides information on various data presentations, including frequency distribution. The chapter also teaches students how to visualise data using a variety of graphs, including bar graphs, histograms, frequency polygons, etc. The chapter also teaches students how to calculate the Mean, Median, and Mode of the raw data to determine the central tendency. In-depth analyses of issues based on data collection and presentation for analytical purposes, a graphical depiction of data using various types of graphs, and measurements of central tendency are provided in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2. Students can improve their visualisation and Mathematics abilities after solving the Class 9 Chapter 14 Maths Exercise 14.2 with the help of these solutions.

Once the information has been obtained, students need to know how to display it in a way that is both helpful and understandable. The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2  in Class 9 Mathematics emphasises the various methods of presenting the data.

The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 includes several new terminologies, which the students should take note of as they will arise in the exercise questions, including class interval, upper-class limit, lower-class limit, class size, class breadth, and frequency distribution table. It is advised that students put the examples from the chapter into practise  to clear up any misunderstandings and memorise these concepts correctly.

The learner will strengthen their statistical foundation by regularly practising all the examples and becoming familiar with the keywords and their definitions.

The notion of “grouping” or “class intervals” is used to break up enormous amounts of data into smaller intervals or ranges so that it is easier to read. This is useful when the provided data is relatively extensive. These groups’ dimensions are referred to as “class size” or “class width.” The lower-class limit is the lowest number in these categories, while the upper-class limit is the highest number.

After practising Exercise 14.2 in Class 9 Maths, students will have a solid understanding of the three measures of central tendency for ungrouped data, such as mean, median, and mode.After learning this topic, students can use these formulas to solve problems at all levels efficiently. When studying for exams, students should become very familiar with the NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.2.All ideas and themes are fully explained in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2, along with the examples. Students can practise the problems after each chapter in an easy-to-understand manner in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2. They will be able to answer problems quickly and accurately if they use the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2. While students have access to a wide range of study materials, the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 are a practical option that can be found on the Extramarks website or mobile application.

NCERT Solutions For Class 9 Maths Chapter 14 Statistics (Ex 14.2) Exercise 14.2

Students’ theoretical and practical understanding can be improved by using the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2. All of the problems from Maths Class 9 Chapter 14 Exercise 14.2 have been covered in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 which is available as a PDF file to download. Along with the solutions, there are hints and techniques that will be useful while solving problems.

The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 are available in PDF format on Extramarks. Students can use the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 for a better knowledge of the topics and to understand the concepts and problems in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2.

Access NCERT Solutions For Class 9 Maths Chapter 14 – Statistics

The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 and solutions for other exercises are available for download. These solutions are created by knowledgeable teachers following the NCERT textbook criteria. The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 helps students to review the entire syllabus and fetch higher grades.

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.2

For students studying for the CBSE exams, the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 is the finest resource. It includes all the necessary study materials that will enable students to perform well on their board exams. The Class 9 Maths Chapter 14 Exercise 14.2:Statistics is an important chapter for both upper-division courses and exams.. Students will find it simple to understand the complex concepts in the upper levels if they thoroughly understand the chapter’s fundamental notions.

All of the problems in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2  are answered. The subject-matter experts can offer clear, step-by-step answers to all of the student’s inquiries. While preparing for the CBSE exams, the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 offer beneficial practice. The most effective technique to improve one’s knowledge is to use the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2. Each chapter should be finished with the students reading the solutions. They might analyse their deficiencies as a result and work to strengthen them.

Key features of the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 are the following:-

  • Students who use the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2  will do better in examinations.
  • The questions and answers given are correct.
  • One can find all of the answers to the questions from the textbook here.
  • The analysis and explanation of each issue from the Class 9 NCERT textbook are included in the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2. To ensure that students can comprehend topics as they go through them, the solutions are given thoroughly. Some of the most talented subject experts have developed the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2.
  • Students studying for Olympiads, state or national competitive examinations, and CBSE exams would find the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 to be of great use. The NCERT textbooks serve as the basis for the CBSE exams. Furthermore, The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 assists students in preparing for Class 10 and the associated board exams.

NCERT Solutions For Class 9

Each chapter must be thoroughly studied by students, who are also required to understand the definitions of all the themes and subtopics. Understanding the principles of each chapter is crucial for successfully preparing the chapters. Solving problems is the best way to understand the foundational concepts of Mathematics. Students should tackle the easy questions before moving on to the challenging ones. All students must adequately prepare for the board exams.

Students must become familiar with the syllabus before beginning their preparation for the Mathematics test. The syllabus is necessary to design a strategy for learning the Mathematics chapters. A crucial study aid for exams is the NCERT Solutions for Class 9. Writing has such an impact on the mind that when a student writes about a subject, they completely understand it. In addition to reviewing, students should set  aside  time for self-study. Students in Class 9 are required to take classes in subjects like Mathematics, which involves learning and proving a lot of formulae. Science, which involves learning and proving a lot of concepts from all three subsections, Physics, Chemistry, and Biology. The foundation for Class 10 boards is laid in Class 9. To prepare for the exam, students should start with the NCERT textbooks before moving on to other texts. For Class 9 students, Extramarks provides CBSE Study Materials to help with their academics. The NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 are one of the best study materials that are available on the Extramarks’ website for thorough preparation.

A team of subject-matter specialists created the CBSE Study Materials for Class 9, and the format is well-structured according to NCERT requirements. Each solution is broken down piece by piece so that students can easily understand it. Students will become more cognizant of their test response writing abilities as points are awarded at each level. The NCERT Class 9 book serves as the basis for the academic test question papers. Thus, addressing issues with CBSE Study Materials for Class 9 helps students become ready for exams.

CBSE Study Materials For Class 9

The  National Council of Educational Research and Training(NCERT) is an independent agency of the Indian government that develops educational and research resources for state and governments. The information in NCERT textbooks is adequate for students to grasp the foundational concepts of every subject that is being covered. There are activities and test questions at the end of each chapter or topic for students to practice. Students will find these exercises and questions to be of great assistance as they get ready for their class, board, and competitive examinations. To help students with their academics, Extramarks has provided the CBSE Study Materials for Class 9.

A team of experts create the CBSE Class 9 Study Materials, which follow NCERT standards and have a well-structured framework. Each solution is explained in detail so that students may understand it. As points are given for passing each level, students will become more aware of their capacity to create good exam-style responses. The NCERT Class 9 book serves as the basis for the academic test question papers. Students can prepare for the test by correcting the issues with the Class 9 CBSE Study Materials.

CBSE Study Materials

With the innovative, enjoyable, and simple-to-use CBSE study tools from Extramarks, students may learn more quickly and get ready for exams. The study resources are created by subject experts while keeping in mind the most recent CBSE syllabus. The information in these study materials is simple to remember, to the point, and helps students thoroughly understand. Students who take notes are more likely to easily memorise the material, which benefits them in their exam performance. In addition to managing their resources, students should plan their study time and strategy. It helps students finish the CBSE curriculum on time. Using CBSE Study Materials is often a wise exam preparation strategy. It increases the student’s knowledge of the subject and aids in their understanding.

The student’s capacity for learning is enhanced by the use of CBSE study materials. Students in grades 1 through 12 are advised to separate their study materials by subject. It is sufficient to study from the NCERT book for the particular subject; however, students may use the CBSE Study Materials after they have finished the NCERT textbooks for their courses. Students in grades 1 to 12 must give the concepts their full attention. To properly understand what they are learning, the principles of the concepts must be clear in their minds. All courses, including those in Mathematics, History, Science, and other subjects, should follow this procedure. The best way to remember any concept is to have CBSE Study Materials on pertinent themes. The resources can be used for revision as well.

Q.1 The blood groups of 30 students of Class VIII are recorded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,

A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O

Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?

Ans

The frequency distribution table is as given below:

Blood Group Number of students
A 9
B 6
AB 3
O 12
Total 30

The most common blood group is O because there are 12 students of this blood group.

The rarest blood group is AB because there are only three students of this blood group.

 

 

 

Q.2 The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?

Ans

The frequency table having intervals 0 – 5, 5 – 10, 10 – 15, … is given below:

Class Interval Tally mark Number of engineers
0-5 |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaaaaa@3D38@ 5
5-10 ||||   ||||  | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaGPaVpaaKqaabaGaaiiFaiaacYhacaGG8bGaaiiFaaaacaaMc8UaaiiFaaaa@457A@ 11
10-15 ||||   ||||  | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaGPaVpaaKqaabaGaaiiFaiaacYhacaGG8bGaaiiFaaaacaaMc8UaaiiFaaaa@457A@ 11
15-20 ||||  |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaGPaVlaacYhacaGG8bGaaiiFaiaacYhaaaa@42C3@ 9
20-25 | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8baaaa@3A0C@ 1
25-30 | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8baaaa@3A0C@ 1
30-35 || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaaaa@3B0C@ 2
Total 40

From the table, we observe that the residence of mostly engineers is 5 to 20 km away from their office. Few engineers have their homes more than 20 km away from their offices.

 

 

 

 

 

 

Q.3 he relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2
95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3
95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3
96.1 92.1 89

(i) Construct a grouped frequency distribution table with classes 84 – 86, 86 – 88, etc.

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data? The relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2
95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3
95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3
96.1 92.1 89

(i) Construct a grouped frequency distribution table with classes 84 – 86, 86 – 88, etc.

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data?

Ans

(i) The grouped frequency distribution table is given below:

Class interval Tally mark Frequency
84-86 | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8baaaa@3A0C@ 1
86-88 | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8baaaa@3A0C@ 1
88-90 || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaaaa@3B0C@ 2
90-92 || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaaaa@3B0C@ 2
92-94 |||| || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaiaacYhaaaa@3F38@ 7
94-96 |||| | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaaaa@3E38@ 6
96-98 |||| || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaiaacYhaaaa@3F38@ 7
98-100 |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaiaacYhacaGG8baaaa@3D0C@ 4
Total 30

(ii) These data are about rainy season.

(iii) Range of this data
= Maximum data – Minimum data
= 99.2 – 84.9 = 14.3

 

 

 

 

 

Q.4 The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:
161 150 154 165 168 161 154 162 150 151
162 164 171 165 158 154 156 172 160 170
153 159 161 170 162 165 166 168 165 164
154 152 153 156 158 162 160 161 173 166
161 159 162 167 168 159 158 153 154 159
(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 – 165, 165 – 170, etc.
(ii) What can you conclude about their heights from the table?

Ans

(i) The grouped frequency distribution table related to height of students is given below:

Class intervals Tally mark Number of students(f)
150 – 155 |||| |||| || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaWaaqcbaeaacaGG8bGaaiiFaiaacYhacaGG8baaaiaacYhacaGG8baaaa@4364@ 12
155 – 160 ||||  |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaGPaVlaacYhacaGG8bGaaiiFaiaacYhaaaa@42C3@ 9
160 – 165 |||| |||| |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaWaaqcbaeaacaGG8bGaaiiFaiaacYhacaGG8baaaiaacYhacaGG8bGaaiiFaiaacYhaaaa@4564@ 14
165- 170 |||| |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaWaaqcbaeaacaGG8bGaaiiFaiaacYhacaGG8baaaaaa@4164@ 10
170 – 175 |||| 5
Total 50

(ii) From the table it is clear that height of more than 50% students is less than 165 cm.

 

 

 

 

 

Q.5 A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
0.03 0.08 0.08 0.09 0.04 0.17
0.16 0.05 0.02 0.06 0.18 0.20
0.11 0.08 0.12 0.13 0.22 0.07
0.08 0.01 0.10 0.06 0.09 0.18
0.11 0.07 0.05 0.07 0.01 0.04
(i) Make a grouped frequency distribution table for this data with class intervals as 0.00 – 0.04, 0.04 – 0.08 and so on.
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?

Ans

(i) The grouped frequency distribution table for this data with class intervals as 0.00 – 0.04, 0.04 – 0.08 and so on is given below:

Class interval Tally mark Number of days
0.00 – 0.04 |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaiaacYhacaGG8baaaa@3D0C@ 4
0.04 – 0.08 |||| |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaiaacYhacaGG8bGaaiiFaaaa@4138@ 9
0.08 – 0.12 |||| |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaiaacYhacaGG8bGaaiiFaaaa@4138@ 9
0.12 – 0.16 || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaaaa@3B0C@ 2
0.16 – 0.20 |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaiaacYhacaGG8baaaa@3D0C@ 4
0.20 – 0.24 || MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaaaa@3B0C@ 2
Total 30

(ii) The concentration of sulphur dioxide is more than 0.11 parts per million for 8 (2+4+2) days.

 

 

 

 

 

 

Q.6 Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0
Prepare a frequency distribution table for the data given above.

Ans

The frequency distribution table for the data obtained by tossing the coin is given below:

Number of heads Tally mark Frequency
0 |||| | MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaaaa@3E38@ 6
1 |||| |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaWaaqcbaeaacaGG8bGaaiiFaiaacYhacaGG8baaaaaa@4164@ 10
2 |||| |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaadaajeaqaaiaacYhacaGG8bGaaiiFaiaacYhaaaGaaiiFaiaacYhacaGG8bGaaiiFaaaa@4138@ 9
3 |||| MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeqabaWaaqaafaaakeaacaGG8bGaaiiFaiaacYhacaGG8baaaa@3D0C@ 5
Total 30

 

 

 

 

 

Q.7 The value of π up to 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii) What are the most and the least frequently occurring digits?

Ans

(i) Frequency distribution of the digits from 0 to 9 is given below in the form of table:

Digits Frequency
0 2
1 5
2 5
3 8
4 4
5 5
6 4
7 4
8 5
9 8
Total 50

(ii) The most frequently occurring digits are 3 and 9. The least frequently occurring digit is 0.

 

 

 

 

 

 

 

 

 

Q.8 Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
1 6 2 3 5 12 5 8 4 8
10 3 4 12 2 8 15 1 17 6
3 2 8 5 9 6 8 7 14 12

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 – 10.

(ii) How many children watched television for 15 or more hours a week?

Ans

(i) The grouped frequency distribution table for given hours, taking class width 5 is given below:

Class interval Frequency
0 – 5 10
5 – 10 13
10 – 15 5
15 – 20 2
Total 30

(ii) 2 children watched television for 15 or more hours a week.

 

 

 

 

Q.9 A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5
3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7
2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8
3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4
4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.

Ans

A grouped frequency distribution table for the given data, using class intervals of size 0.5 starting from the interval 2 – 2.5 is given below:

Class interval Frequency
2 – 2.5 2
2.5 – 3.0 6
3.0 – 3.5 14
3.5 – 4.0 11
4.0 – 4.5 4
4.5 – 5.0 3
Total 40

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FAQs (Frequently Asked Questions)

1. Why are the NCERT Solutions For Class 9 Maths Chapter 14 Exercise 14.2 important?

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4. Is using the Class 9 Maths Chapter 14 Exercise 14.2 required for the Class 9 final exam?

Yes, the Class 9 final exam requires completion of the Class 9 Maths Chapter 14 Exercise 14.2. The exercises offer an exact and succinct version of questions that have been answered, students should utilise them as a reference. Brief key phrases or short points are used in Exercise 14.2 Class 9 Maths to aid in rapidly retaining the main idea. It can also be used to save time.