NCERT Solutions for Class 11 Maths Chapter 15 Statistics (Ex 15.3) Exercise 15.3

Throughout a student’s academic career, Mathematics serves as one of the most important subjects. Mathematics is one of the subjects for Class 11 students studying in the Science and Commerce stream under the Central Board of Secondary Education (CBSE). Also, it is frequently regarded as the most difficult subject by Class 11 students. Not only do students need to fully grasp the theories in Mathematics, but they also need to practise answering the questions. Many times, despite studying and comprehending every topic in the curriculum, students do not complete enough exercises. They are therefore at a disadvantage when taking the annual exam. They must address this issue in order to secure better marks in the exams. To help solve this problem, Extramarks provides NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3.

The most crucial resource for practising questions for the annual exams is NCERT exercises. Therefore, it is usually recommended for students to answer the questions from the NCERT textbook. They also require accurate solutions to the questions, so they can examine their answers. Therefore, the NCERT solutions give students the assistance they require while  getting ready for the annual exams. Using the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 will help students apply the concepts from the chapter in a more straightforward and accurate manner. Highly skilled teachers have produced detailed and error-free NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. They develop these solutions while taking into account the comprehension skills of students in Class 11. The problems in this exercise have been divided into smaller, more manageable parts to make writing answers easier. Teachers frequently emphasise the requirement for detailed, step-by-step answers. In order to achieve optimal exam results, students should follow the step-by-step instructions in the NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3.Numerous formulas presented in the NCERT textbook are difficult for many students to understand and remember, which hinders them from using them to answer the questions in the exercises. However, if they practise the stepwise solutions in the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3, it will be easier for them to remember the formulas and execute them correctly.

Solving the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 helps students get the necessary practise they need to successfully solve the Mathematics question paper in the annual examinations. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 can help students get acquainted with the types of questions asked in the annual exams. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 are available on Extramarks so that students can assess their own answers. With the assistance of these solutions, students can evaluate their strong and weak areas. Experts with years of expertise have created the solutions to the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. Since these solutions are prepared step-by-step in accordance with the marking scheme, students can use them to hone their answering abilities. For additional practice, students should work through multiple test questions. Several lengthy and challenging problems are frequently included in the Mathematics question paper in exams. Attempting to answer these questions takes a lot of time from students. As a result, they find themselves in a dilemma where they are unable to attempt some questions while knowing the answers due to time constraints. However, they can get out of this dilemma by working on  NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. As they work through more questions from the NCERT exercises, they will develop a solid plan for answering the questions. Ultimately, they can speed up their writing and improve their time management skills. This puts the students at an advantage in their exams because they know how to approach these problems correctly.

The Extramarks Learning App offers chapter-by-chapter worksheets, engaging activities, an infinite amount of practise questions, and much more to ensure a thorough understanding of all the topics in the syllabus for Class 11 students. Students can create an upward learning curve and analyse their knowledge using MCQs, mock tests, and adaptive tests with increasing levels of difficulty. Additionally, for help with Class 11 Maths Chapter 15 Exercise 15.3, students can obtain the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 described in detail.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics (Ex 15.3) Exercise 15.3

It might not always be possible for students to access the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. Although it may not always be possible, having an internet connection is essential. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 in PDF format, should be available to students who desire to keep learning. For a student’s educational needs, Extramarks provides a complete solution. Despite the fact that NCERT textbooks are an excellent source of study material, students frequently struggle to find reliable NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3.The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 from Extramarks are precise and thorough. Additionally, it gives students access to a holistic learning solution that blends the advantages of real-world classrooms with  study materials like the NCERT solutions.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Exercise 15.3

The Central Board of Secondary Education (CBSE) is one of India’s major school education boards. It is the board with the largest enrollment of students. Moreover, thousands of schools are associated with it. The CBSE is responsible for formulating the syllabus for Class 11. The board prescribes the NCERT textbooks for students to follow in Class 11. The NCERT textbook contains numerous questions that are very important for the exams. These questions help students become thorough with the topics that not only help them in the examinations but also in their higher studies. To succeed in their higher education, students need to have a solid grasp of the concepts of Mathematics. However, Class 11 students find it challenging to study for their exams. The Class 11 Mathematics curriculum includes a lot of fresh concepts. Students need to have access to all the required study materials in order to perform well on the annual exams. One of the most important study tools for preparing for the exams is the NCERT textbook. The exercises include different types of questions. Students are required to correctly answer these questions prior to taking the annual exams. As they try to solve these questions and find answers, they come across a number of challenges. Students can get help in this area from the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3, which are available on Extramarks.

Class 11 Maths Exercise 15.3 deals with the topic Analysis of Frequency Distributions. This exercise deals with the important concept of coefficient of variation(C.V.). The exercise contains 5 questions. These types of questions often appear in examinations. The proper examples and visuals are used in the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. It boosts students’ confidence as a result, which helps them perform well in the final exam. Offering sufficient examples for practice helps students develop a conceptual understanding of each topic. The CBSE curriculum is completely followed by NCERT textbooks. The NCERT textbook is the source of most of the exam questions. To perform well on their exams, students must practise the exercises diligently. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 are also accessible on Extramarks. The in-house subject specialists have put up the solutions and study materials on the platform. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 given to the students, have been verified as accurate and factual. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 will help them to solidify their fundamentals and play a significant role during their whole study period, whether it be for the Class 11 examination or any competitive examination.

In order to quickly and efficiently answer the questions in this exercise, students should follow several easy steps. Writing step-by-step answers is a requirement in Mathematics.  If they want to receive the highest possible marks, they must be aware of the steps to take when writing answers.The textbook’s explanations of the topic should be properly read and understood by the students. In addition, if they are having trouble grasping the topics, they can rely on the study materials offered by Extramarks. They should read through the examples in the NCERT book once they have a firm grasp of the concepts. They will gain insight on how to approach the questions as a result. After then, students should try to answer each question in sequence. Prior to checking the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3, they should attempt to solve the problems on their own. They should make an effort to remember every method that might be employed in order to answer the questions. After answering each question, they should verify their answers by referring to the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. They should use the solutions to correct the incorrect answers they have written. Until they can appropriately solve such problems, they should attempt to solve them repeatedly. To obtain answers to the questions they are unable to answer, they should also check the solutions. They should try to answer the questions from the exercise until they have mastered the correct approach. They can become more familiar with the questions and write more quickly as a result. They should try to finish the exercise as quickly as they can. This would enable them to finish the examination paper on time by enabling them to solve such questions more quickly and efficiently.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Exercise 15.3

There are many ways in which students can benefit from using the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 on Extramarks. Using the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3, students can evaluate their own learning and determine their strong and weak areas. Additionally, the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 give evaluated and analysed learning while assisting students in the development of a wide range of skills, including logical and reasoning skills. The NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3 also assist students in successfully preparing for the annual exams.It is regarded as a vital stage in test preparation. Conceptual understanding and application are essential when practising mathematical problems. The detailed, step-by-step solutions provided in the NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.3 allow students to solve difficult questions.

Class 12 students can fully comprehend the problems even if they are tackling them for the first time thanks to Extramarks’ detailed NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. Alternative, simpler solutions to some problems are also provided in Extramarks’ NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3. Along with the Class 11 annual exams, the chapter on Statistics is a crucial component of competitive exams like JEE Mains and JEE Advanced. Since college admissions are based on these exams, a student’s performance on them determines their career. This results in them feeling extremely under pressure, which can occasionally demotivate them. The NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 and other study materials provided by Extramarks, however, aid students in fully grasping the concepts and helping them stick in their minds for a long time. As students prepare for various exams, this gives them more confidence.

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Q.1 From the data given below state which group is more variable, A or B?

Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group A 9 17 32 33 40 10 9
Group B 10 20 30 25 43 15 7

 

 

 

Ans.
For group A:

Marks(A)fixiui=xi−A10ui2fiuifiui210−20915−39−278120−301725−24−346830−403235−11−323240−503345=A000050−60405511404060−70106524204070−80975392781150−6342  Mean(x¯)=A+∑i=1nfiuin×h  =45+−6150×10 =45−0.4 =44.6Variance(σ2)=h2n2[n∑in(fiui2)−(∑infiui)2]

Variance(σ2)=(10)2(150)2[150×342−(−6)2]          =1225(51300−36)      =1225×51264          =227.84Standard deviation(σ)          =227.84          =15.09 Marks(A)fixiui=xi−A10ui2fiuifiui210−201015−39−309020−302025−24− 408030−403035−11−303040−502545=A000050−60435511434360−70156524306070−80775392163150−6366    

Mean(x¯)=A+∑i=1nfiuin×h =45+−6150×10 =45−0.4 =44.6

Variance(σ2)=h2n2 [n∑in(fiui2)−(∑infiui)2]Variance(σ2)=(10)2(150)2 [150×366−(−6)2]         =1225(54900−36)         =1225×54864         =243.84Standard deviation(σ)         =243.84         =15.61

Since, both groups have equal mean. Group B has greater standard deviation. So, group B is more variable than group A.

Q.2 From the prices of shares X and Y below, find out which is more stable in value:

X 35 54 52 53 56 58 52 50 51 49
Y 108 107 105 105 106 107 104 103 104 101

 

 

Ans.
For prices of share X:

Mean(x¯)=35+54+52+53+56+58+52+50+51+4910         =51010         =51

xi(xi−x¯)(xi−x¯)23535−51=−162565454−51=395252−51=115353−51=245656−51=5255858−51=7495252−51=115050−51=−115151−51=004949−51=−24350Variance(σ2)=∑i=1n(xi−x¯)2N=35010=35∴Standard deviation(σ)=35=5.91C.V.(share X)=σx¯×100=5.9151×100=11.59(Appox.)

For prices of share Y:

Mean(y¯)=108+107+105+105+106+107+104+103+104+10110         =105010         =105yi(yi−y¯)(yi−y¯)2108108−105=39107107−105=24105105−105=00105105−105=00106106−105=11107107−105=24104104−105=−11103103−105=−24104104−105=−11101101−105=−41640Variance(σ2)=∑i=1n(xi−x¯)2N=4010=4∴Standard deviation(σ)=4 =2

C.V.(share Y)=σy¯×100=2105×100=1.9<11.59C.V. of prices of share Y is lesser than that of share X.Thus, the prices of share Y are more stable than that of share X.

Q.3 An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

Firm A Firm B
No. of wage earners 586 648
Mean of monthly wages Rs. 5253 Rs. 5253
Variance of distribution of wages 100 121

1. Which firm A or B pays larger amount as monthly wages?
2. Which firm, A or B, shows greater variability in individual wages?

Ans.

i.         Monthly wage of firm A = Rs. 5253     Number of workers in firm A = 586     Total paid amount in wages = Rs. 5253 × 586                                       = Rs. 3078258           Monthly wage of firm B = Rs. 5253     Number of workers in firm A = 648      Total paid amount in wages = Rs. 5253 x 648                                        = Rs.3403944Thus, firm B pays the larger amount as monthly wages.ii. Variance of distribution of wages in firm A = 100               Standard deviation of wages in firm A = 100                                                      = 10       Variance of distribution of wages in firm B = 121                 Standard deviation of wages in firm B = 121                                                        = 11Since the average monthly wages in both the firms is same,i.e., Rs. 5253, therefore, the firm with greater standard deviationwill have more variability.Thus, the firm B has greater variability in the individual wages.

Q.4 The following is the record of goals scored by team A in a football session:

No. of goals scored 0 1 2 3 4
No. of matched 1 9 7 5 3

 

 

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Ans.

No. of goals x i No. of matches f i

x i − x ¯ x i − x ¯ 2 f i x i − x ¯ 2 0 1 0−2=−2 4 4 1 9 1−2=−1 1 9 2 7 2−2=0 0 0 3 5 3−2=1 1 5 4 3 4−2=2 4 12 25 30

Mean = ∑i=1nfixin       = 5025       = 2Variationσ2= ∑i=1nfixi–x¯2n= 3025= 1.2Standard deviation= 1.2= 1.09Standard deviation of team B= 1.25 goalsMean of team B= 2The team with lower standard deviation is more consistent.Therefore, team A is more consistent.

Q.5 The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:

∑i=150xi=212,  ∑i=150xi2=902.8,   ∑i=150yi=261,  ∑i=150yi2=1457.6Which is more varying, the length or weight?

Ans.

∑i=150xi=212,  ∑i=150xi2=902.8,Mean=∑i=150xi50            =21250            =4.24Variance(σ2)=∑i=150xi250−(∑i=150xi50)2                    =902.850−(21250)2                    =18.056−17.978                    =0.078Standandard deviation(σ)                   =0.078                   =0.28C.V. of length=σx¯×100                     =6.6 

∑i=150yi=261,  ∑i=150yi2=1457.6Mean(y¯)=∑i=150yi50                  =26150  =5.22Variance(σ2)=∑i=150yi250−(∑i=150yi50)2                    =1457.650−(26150)2                    =29.15−27.25                    =1.89Standandard deviation (σ)                    =1.89                    =1.37C.V. of weight=σy¯×100                    =1.375.22×100                    =26.24

Since, C.V. of weights is greater than the C.V. of lengths.Therefore, weights are more varing than lengths.

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1. Are the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3 available to access offline?

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Extramarks provides NCERT solutions for Class 12 Mathematics, including the NCERT Solutions For Class 11 Maths Chapter 15 Exercise 15.3.