NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Ex 14.3)

It is the most important time for all students in Class 10 who will take their first board exams to prepare for the challenge. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 can be of great help for the same. There are a few common questions, nonetheless, that students frequently have about board exams. Nevertheless, board exams are largely similar to the examinations that students have taken in their previous semesters. Students can prepare with ease with the help of the tools available on the Extramarks website, like the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and many more.

The only distinction between other examinations and Class 10 board examinations is that board exams are the first nationalised exams for students in Class 10. A student’s academic and career prospects may advance if the exams are passed with good grades. A student’s level of sincerity and sense of responsibility is also indicated by how well they perform on their board exams. Students can perform well with the help of resources like the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 that are available on the Extramarks website.

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The future employment alternatives available to students may ultimately be determined by the stream they choose to enrol in for Class 11. For instance, if a student wants to work in fields related to Medical Science, they will need to do well in their Class 10 Science examination since they will need to study Biology in Class 11. To help in Class 10 Mathematics, Extramarks has prepared resources such as the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3.

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NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Ex 14.3) Exercise 14.3 

Extramarks has many useful tools available for Class 10 students like the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3. These solutions are prepared by highly knowledgeable mentors of Mathematics. Reference materials, such as the NCERT Solutions for Class 10 Maths, Chapter 14, Exercise 14.3, are created to help students with their exam preparation.Students can easily access all of the tools prepared by the mentors on the Extramarks website, including the NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3.Access NCERT Solutions Maths Class 10 Chapter 14 – Statistics

Human logic and mind are significantly influenced by Mathematics. It provides a powerful method for developing mental discipline and improving logical thinking. In order to excel in Class 10 Mathematics, students can benefit from tools such as the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3. Additionally, understanding Mathematics is crucial to comprehending the concepts of other disciplines, like Science, Social Studies, and even Music and the Arts. Numerous disciplines and fields involve the application of themes of Mathematics. Problems related to Engineering, Science, and Economics are resolved using the principles and techniques of Mathematics. Students can benefit greatly by using the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and other similar tools when preparing for the Mathematics board examination.

Many students find Mathematics to be extremely difficult. The reason could be their inability to relate to the subject. When students connect their subject to actual events, learning can be improved. However, because of the complex and difficult concepts, students are unable to connect math to real-world instances. Due to this, students are uncertain of the precise importance of Mathematics for them. The practise of different types of questions can help students understand the connection between real life and Mathematics. Students can also take help from the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 for the same purpose.

The saying “practice makes perfect” does not just apply to Mathematics. Every subject requires practice. However, it might be challenging for students to practise arithmetic problems if they do not enjoy solving Mathematics problems. However, if students do not exercise arithmetic ideas, their acquisition of conceptual knowledge will be hindered. Students are advised to make use of the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and other similar materials to practise efficiently. Students are advised to practise using the NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 to avoid making careless mistakes.

Many students may think and ask why should students pursue Mathematics as a subject. The answer to that could be:

  • It has been established that Mathematics fosters the growth of analytical and critical thinking.
  • Students are given the ability to effectively assess, describe, and alter situations.
  • Mathematics is sometimes regarded as the language of science.
  • Every part of life can benefit from the use of Mathematics. It is regarded as a crucial form of knowledge because of this.

Students are encouraged to make full use of the helpful tools available on the Extramarks website, which have been prepared by skilled mathematics mentors.These include the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 but are not limited to just solutions. Students can find revision notes, extra questions, past years’ papers, and also the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3.

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 Free PDF 

The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 available on the Extramarks website, can be of great help to the students preparing for their Class 10 board examinations. The Chapter 14 Maths Class 10 Exercise 14.3 solutions are specifically for the Class 10 Chapter 14 Exercise 14.3. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 are easy to access, and the students can depend on them for their examination preparation as these are prepared by subject matter specialists of Extramarks.

Class 10 Maths Chapter 14 Exercise 14.3 is part of Chapter 14 of Class 10 Mathematics which covers the topic of Statistics. The chapter is divided into different exercises, and  Statistics Class 10 Exercise 14.3 is just one of the multiple exercises from this chapter.

Students can find the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 on the Extramarks website with ease. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and other such tools are all created in a user-friendly manner. Students can easily access them and also understand them. This can enable the students to make use of the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and similar tools for their self-study sessions.

Class 10 Maths Chapter 14 Exercise 14.3 

The study of data gathering, analysis, interpretation, presentation, and organisation is known as statistics. In other words, it is a mathematical discipline for gathering and summarising data. Additionally, statistics might be considered a subfield of applied Mathematics. However, uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can determine the uncertainty and variation in many sectors. Probability, which is a key concept in statistics, essentially determines these uncertainties. To understand the concepts of this chapter better, students can make use of the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and many similar reference materials available on the Extramarks website. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 can help the student greatly in performing well in their examinations.

The chapter teaches some basics of Statistics. The measures of central tendency and dispersion are among the fundamental concepts in statistics. Mean, median, and mode are the core trends, whereas the variance and standard deviation are the dispersions. The mean represents the mean of the observations. When observations are sorted in order, the median value is in the middle. The most common observations in a data set are identified by their mode. The mean represents the mean of the observations. When observations are sorted in order, the median value is in the middle. The most common observations in a data set are identified by the mode. The degree of spread among the data collections is measured by variation. Data dispersion from the mean is measured by the standard deviation. The variance is equal to the square of the standard deviation. To understand all these concepts in-depth and practise the questions based on these, students can make use of the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and all the other solutions for this chapter, which are all available on the Extramarks website.

The application of Mathematics in the form of Statistics was once envisioned as the science of the state. The gathering and analysis of data regarding a nation’s economy, military, population, and other factors — is known as mathematical statistics. Mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory are some of the mathematical methods utilised in various analytics. There are essentially two categories of Statistics which are referred to as Descriptive Statistics and Deductive Statistics. Students can take help from tools like the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and revision notes for the same chapter to understand the topics in-depth.

Descriptive Statistics are used to summarise and interpret given data. The summary is created using a population sample and numerous variables, including mean and standard deviation. A set of data can be organised, represented, and explained using Descriptive Statistics by employing graphs, charts, and summary measures. To summarise data and present it in tables or graphs, common methods include histograms, pie charts, bars, and scatter plots. Simply put, descriptive statistics are that. To understand this better, students can take help from the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and other helpful reference materials.

After the data has been gathered, assessed, and summarised, Inferential Statistics is used to explain what the data indicate. Inferential Statistics uses the probability principle to examine if patterns observed in a study sample can be extrapolated to the larger population from which the sample was taken. Inferential Statistics can be used to forecast population sizes in addition to testing hypotheses and examining connections between variables. Inferential statistics are used to draw conclusions and inferences from samples, or to make precise generalisations.Class 10 Maths 14.3 Solutions Question 1

The NCERT books for Mathematics are organised in such a way that the chapters include a wide variety of exercises. This makes it easier for students to focus on one sub-topic at a time and prepare for all the sub-topics separately. This can help the students not get confused between different formulas, equations, etc. The NCERT solutions and other similar tools available on the Extramarks website have also been designed in accordance with this pattern. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 for example, are the solutions only for exercise 14.3. The rest of the exercises from Chapter 14 are also available in a similar format. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and the solutions to all the other exercises can be accessed by students on the Extramarks website.

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Class 10 Maths 14.3 Solutions Question 2 

Mathematics has a much greater impact on society than is generally recognised. The study of Statistics is concerned with the gathering and examination of data. It primarily serves to convey knowledge, compute probabilities, and store records. In essence, it improves humans’ understanding of the world through the use of numbers and other quantitative data. Thus, it is clear that Statistics has prevalent relevance in daily life. With the use of helpful resources created by the mentors of Extramarks, students can better understand all of these applications of Statistics. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 is just one instance of these helpful resources available on the Extramarks website.

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Class 10 Chapter 14 Exercise 14.3 Question 3 

The CBSE is responsible for creating test requirements, organising tests at the end of Class 10, and offering. The Class 10 board examinations are among the most significant tests a student will ever take in their academic career. Students get to choose the subject they want to pursue further study in based on how well they perform on the Class 10 board exams. Students in Class 10 are advised to take their board exams seriously as a result. Students may benefit from using the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 to help them study for their board exams. The school requires Class 10 students to take pre-board tests before the boards in order to get them ready for their board exams. The purpose of the pre-board exams is to familiarise students with the format of the board exam and aid in their preparation. Students can use resources like the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and others to get ready for their pre-boards and boards.

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Class 10th Exercise 14.3 Question Number 4 

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Ex 14.3 Class 10 Maths NCERT Solutions Question 5 

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Class 10 Maths Chapter 14 Exercise 14.3 Solutions Question 6 

The importance of mathematics in human life cannot be overstated. Several lucrative career opportunities, as well as research opportunities, are closely associated with this academic field. There is no doubt that Mathematics is one of the most organised and vital scientific disciplines. India has a long history of brilliant mathematicians who captivated the world with their ingenuity and exceptional abilities. Mathematics is taught as a prominent scientific discipline in the early stages of school education, and students are encouraged to continually strive to improve their understanding of it. Mathematics holds great significance as an academic discipline. A significant amount of human life is influenced by mathematics. In addition to being an academic field, it is also closely associated with a wide range of lucrative career opportunities, as well as research opportunities.

NCERT Solutions of Class 10 Maths Chapter 14 Question 7 

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Key Takeaways of NCERT Solutions Class 10 Maths Chapter 14 Exercise 14.3 free PDF 

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Q.1 The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption (in units) Number of consumers
65 – 85

85– 105

105– 125

125–145

145–165

165–185

185–205

4

5

13

20

14

8

4

 

 

 

 

 

 

 

 

 

Ans
xmlns=”http://www.w3.org/1998/Math/MathML”>We find class mark for each interval by using thefollowing relation.xi=Upper class limit+Lower class limit2Assumed mean(a)=135We proceed as below to find di, ui,  fiui.

Monthly consumption (in units) Number of consumers (fi) xi di = xi – 135 xmlns=”http://www.w3.org/1998/Math/MathML”>ui=xi135h fiui
65 – 85 4 75 -60 -3 -12
85 – 105 5 95 -40 -2 -10
105 – 125 13 115 -20 -1 -13
125 – 145 20 135 0 0 0
145 – 165 14 155 20 1 14
165 – 185 8 175 40 2 16
185 – 205 4 195 60 3 12
Total 68 7

 

 

 

 

 

 

 

xmlns=”http://www.w3.org/1998/Math/MathML”>

Mean=x¯=a+fiuifi×h                     

=135+768×20                   

=137.058Modal class

=125145From the given data, we havel=125, f1=20, f0=13,   f2=14, h=20

Mode=l+(f1f02f1f0f2)×h            

=125+(20132×201314)×20           

=135.76We know that 3 Median

=Mode+ 2 Meanor Median

=135.76+2×137.0583

=136.625

We observe all these three measures are approximately same.

Q.2 If the median of the distribution given below is 28.5, find the values of x and y.

Class interval Frequency
0 – 10

10– 20

20– 30

30–40

40–50

50–60

5

x

20

15

y

5

Total 60

 

 

 

 

 

 

 

 

 

Ans
We find cumulative frequency of the given data as below.

Class interval Frequency Cumulative frequency
0 – 10 10– 20 20– 30 30–40 40–50 50–60 5 x 20 15 y 5 5 5 + x 25 + x 40 + x 40 + x + y 45 + x + y
Total 60

 

 

 

 

Here,
n = 60
or 45 + x + y = 60
or x + y = 15 …(1)
Median of data is given as 28.5 that lies in the interval 20 – 30.
So, median class = 20 – 30 xmlns=”http://www.w3.org/1998/Math/MathML”>From the given data, we havel=20,Cumulative frequency (cf) of the class preceding the median class=5+x,Frequency of median class (f)=20,  Class size (h)=10     Median=l+(n2cff)×hor     28.5=20+(6025x20)×10or     x=8On putting this value of x in equation (1), we get        x+y=15or 8+y=15or        y=158=7Hence, values of x and y are 8 and 7 respectively.

Q.3 A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.

Class interval Frequency
Below 20

Below 25

Below 30

Below 35

Below 40

Below 45

Below 50

Below 55

Below 60

2

6

24

45

78

89

92

98

100

 

 

 

 

 

 

 

 

 

 

 

Ans
xmlns=”http://www.w3.org/1998/Math/MathML”>We write the class interval, number of policy holders (fi),and cumulative frequency (cf) as below in the following tableon the basis of the given information.

Class interval Number of policy holders (fi) Cumulative frequency (cf)
18 – 20 2 2
20 – 25 6 – 2 = 4 6
25 – 30 24 – 6 = 18 24
30 – 35 45 – 24 = 21 45
35 – 40 78 – 45 = 33 78
40 – 45 89 – 78 = 11 89
45 – 50 92 – 89 = 3 92
50 – 55 98 – 92 = 6 98
55 – 60 100 – 98 = 2 100
Total (n) 100

 

 

 

 

 

 

 

 

 

xmlns=”http://www.w3.org/1998/Math/MathML”>We have, n=100.n2=1002=50Cumulative frequency (cf) just greater than  n2=50 is 78 which belongs to interval 3540. Median class=3540Now, we havel=35,Cumulative frequency (cf) of the class preceding themedian class=45,Frequency of median class (f)=33,  

xmlns=”http://www.w3.org/1998/Math/MathML”>Class size (h)=5We know that     Median=l+(n2cff)×h    Median =35+(10024533)×5or     x=35.76

Hence, median age is 35.76 years.

Q.4 The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:

Length (in mm) Number of leaves
118 – 126

127– 135

136– 144

145–153

154–162

163–171

172–180

3

5

9

12

5

4

2

 

 

 

 

 

 

 

 

 

Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 – 126.5, 126.5 – 135.5, . . ., 171.5 – 180)

Ans

The given class intervals are not continuous. We convert it to continuous class intervals by subtracting 0.5 from eachof lower boundary and adding 0.5 in each of upper boundary.We write the class interval, number of leaves (fi),and cumulative frequency (cf) as below in the following tableon the basis of the given information.

Class interval Number of leaves (fi) Cumulative frequency (cf)
117.5 – 126.5 3 3
126.5 – 135.5 5 8
13.5 – 144.5 9 17
144.5 – 153.5 12 29
153.5 – 162.5 5 34
162.5 – 171.5 4 38
171.5 – 180.5 2 40
Total 40

 

 

 

 

 

 

 

We have, n=40.n2=402=20Cumulative frequency (cf) just greater than  n2=20 is 29 which belongs to interval 144.5153.5. Median class=144.5153.5Now, we havel=144.5,Cumulative frequency (cf) of the class preceding themedian class=17,Frequency of median class (f)=12,  Class size (h)=9We know that     Median=l+(n2cff)×h       Median =144.5+(4021712)×9or     Median =146.75Hence, median length of leaves is 146.75 mm.

Q.5 The following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours) Number of lamps
1500– 2000
2000– 2500
2500–3000
3000–3500
3500–4000
4000–4500
4500–5000
14
56
60
86
74
62
48

 

 

 

 

 

 

Find the median life time of a lamp.

Ans
xmlns=”http://www.w3.org/1998/Math/MathML”>We write the cumulative frequency (cf) as below in thefollowing table on the basis of the given information.

Life time (in hours) Number of lamps (fi) Cumulative frequency (cf)
1500 – 2000 14 14
2000 – 2500 56 70
2500 – 3000 60 130
3000 – 3500 86 216
3500 – 4000 74 290
4000 – 4500 62 352
4500 – 5000 48 400
Total (n) 400

 

 

 

 

 

 

 

xmlns=”http://www.w3.org/1998/Math/MathML”>

We have, n=400.n2=4002=200Cumulative frequency (cf) just greater than  n2=200 is 216 which belongs to interval 30003500. Median class=30003500

Now, we havel=3000,Cumulative frequency (cf) of the class preceding themedian class=130,Frequency of median class (f)=86,  Class size (h)=500

We know that     Median=l+(n2cff)×h       Median =3000+(400213086)×500or     Median =3406.98Hence, median life time of a lamp is 3406.98 hours.

Q.6 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters 1-4 4-7 7-10 10-13 13-16 16-19
Number of surnames 6 30 40 16 4 4

 

 

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Ans
xmlns=”http://www.w3.org/1998/Math/MathML”>We find the cumulative frequency (cf) as below in thefollowing table on the basis of the given information.

Number of letters Number of surnames (fi) Cumulative frequency (cf)
1 – 4 6 6
4 – 7 30 36
7 – 10 40 76
10 – 13 16 92
13 – 16 4 96
16 – 19 4 100

 

 

 

 

 

 

xmlns=”http://www.w3.org/1998/Math/MathML”>Total(n)=100We have, n=100.n2=1002=50Cumulative frequency (cf) just greater than  n2=50 is 76 which belongs to interval 710. Median class=710

xmlns=”http://www.w3.org/1998/Math/MathML”>Now, we havel=7,Cumulative frequency (cf) of the class preceding the median class=36,Frequency of median class (f)=40,  Class size (h)=3We know that     Median=l+(n2cff)×h       Median =7+(10023640)×3or     Median =8.05Median number of letters in the surnames is 8.05.Now, we find class mark for each interval by using the following relation.xi=Upper class limit+Lower class limit2Assumed mean(a)=11.5

We proceed as below to find di, ui, fiui .

Number of letters Number of surnames (fi) xi di = xi – a xmlns=”http://www.w3.org/1998/Math/MathML”>ui=xiah fiui
1 – 4 6 2.5 -9 -3 -18
4 – 7 30 5.5 -6 -2 -60
7 – 10 40 8.5 -3 -1 -40
10 – 13 16 11.5 0 0 0
13 – 16 4 14.5 3 1 4
16 – 19 4 17.5 6 2 8
Total (n) 100 -106

 

 

 

 

 

 

 

xmlns=”http://www.w3.org/1998/Math/MathML”>

Mean=x¯=a+fiuifi×h                    

=11.5+106100×3                   

=8.32We know that 3 Median=Mode+2 Mean       

3×8.05=Mode+2×8.32or Mode

=7.51

Hence, mean number of letters in the surnames is 8.32and modal size of the surnames is 7.51.

Q.7 The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight
(in kg)
40-45 45-50 50-55 55-60 60-65 65-70 70-75
Number of students 2 3 8 6 6 3 2

 

 

 

Ans
xmlns=”http://www.w3.org/1998/Math/MathML”>We find the cumulative frequency (cf) as below in the

following table on the basis of the given information.

Weight (in kg) Number of students (fi) Cumulative frequency (cf )
40 – 45 2 2
45 – 50 3 5
50 – 55 8 13
55 – 60 6 19
60 – 65 6 25
65 – 70 3 28
70 – 75 2 30
Total (n) 30

 

 

 

 

 

 

 

xmlns=”http://www.w3.org/1998/Math/MathML”>

We have, n=30.n2=302=15Cumulative frequency (cf) just greater than  n2=15 is 19 which belongs to interval 5560. Median class=5560

Now, we havel=55,Cumulative frequency (cf) of the class preceding themedian class=13,Frequency of median class (f)=6,  Class size (h)=5

We know that     

Median=l+(n2cff)×h       

Median =55+(302136)×5or    

 Median =56.67

Hence, median weight of students is 56.67 kg.

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FAQs (Frequently Asked Questions)

1. What national level competitive examinations can Class 10 students appear for apart from the mandatory board examinations?

There are various competitive examinations that the students of Class 10 can appear for. Here is a list of few of the Olympiads Class 10 students can appear in for various subjects:

  • Class 10 International Science Olympiad (ISO)
  • Class 10 International Maths Olympiad (IMO)
  • Class 10 English International Olympiad (EIO)
  • Class 10 General Knowledge International Olympiad (GKIO)
  • Class 10 International Computer Olympiad (ICO)

The helpful resources available at the Extramarks website like the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 can be of great help in these examinations. To prepare for these Olympiads, students should take advantage of the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.3 and other related resources.