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NCERT Solutions for Class 9 Maths Chapter 14: Statistics - Exercise 14.4

Last updated date: 15th Jul 2024
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NCERT Solutions for Class 9 Maths Chapter 14 (Ex 14.4)

Free PDF download of NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.4 and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 9 Maths Chapter 14 Statistics Exercise 14.4 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register and get all exercise solutions in your emails. Download NCERT Maths Class 9 created by master teachers at Vedantu. Students can also avail of NCERT Solutions Class 9 Science from our website. Besides, find NCERT Book Solutions to get more understanding of various subjects.

 Class: NCERT Solutions for Class 9 Subject: Class 9 Maths Chapter Name: Chapter 14 - Statistics Exercise: Exercise - 14.4 Content-Type: Text, Videos, Images and PDF Format Academic Year: 2024-25 Medium: English and Hindi Available Materials: Chapter WiseExercise Wise Other Materials Important QuestionsRevision Notes

List of Topics Covered Under NCERT Solutions for Class 9 Maths Chapter 14- Statistics

 Introduction Collection of Data Presentation of Data Graphical representation of Data Measures of central tendency

A Glance About The Topic Measures of Central Tendency

The mean can be calculated by the sum of all the observations by the total number of observations. The formula for calculating mean value is given below.

Mean =  $\frac{Sum \,of \,all \,the \,observations}{Total \,number \,of \,observations}$

$\overline{x} = \frac{ \sum_{i=1}^{n} x_{i}}{n}$

The value which occurred frequently in the list of observations is known as a mode of the observation.

The mid-value of the series of observations is known as the median. If the number of observations is odd, then the mid-value is a median. If the number of observations is even, then the average of two observations is a median. The formula for calculating the median is given below.

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NCERT Solutions for Class 9 Maths Chapter 14: Statistics - Exercise 14.4
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Access NCERT Solutions for Class 9 Maths Chapter 14 – Statistics

Exercise 14.4

1. The following number of goals was scored by a team in a series of $10$ matches:

$\text{2, 3, 4, 5, 0, 1, 3, 3, 4, 3}$

Find the mean, median and mode of these scores.

Ans: It is given that the number of goals scored by the team is

$\text{2, 3, 4, 5, 0, 1, 3, 3, 4, 3}$.

The formula for calculating the Mean of any data is given by:

$\text{Mean of data=}\frac{\text{Sum of all observations}}{\text{Total number of observations}}$

Therefore, $\text{Mean score=}\frac{\text{2+3+4+5+0+1+3+3+4+3}}{\text{10}}$

$\text{=}\frac{\text{28}}{\text{10}}=2.8$

$2.8goals$

Now arranging the number of goals in ascending order to calculate the median of the given data,

$\text{0, 1, 2, 3, 3, 3, 3, 4, 4, 5}$

Since the number of observations is an even number, that is, $\text{10}$. Hence, the mean of $\frac{10}{2}$ i.e., ${{5}^{th}}$  and $\frac{\text{10}}{\text{2}}\text{+1}$ i.e., ${{6}^{th}}$ observation, while arranged in ascending or descending, will give us the median.

Therefore, $\text{Median score=}\frac{{{\text{5}}^{\text{th}}}\text{observation+}{{\text{6}}^{\text{th}}}\text{observation}}{\text{2}}$

$\text{=}\frac{\text{3+3}}{\text{2}}=3$.

The observation with maximum frequency is the Mode of the data.

Since the frequency of $3$ is maximum, therefore the mode score of data is $3$.

2. In a mathematics test given to $\text{15}$ students, the following marks (out of $\text{100}$) are recorded:

$\text{41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60}$

Find the mean, median and mode of this data.

Ans:

The formula for calculating the Mean of any data is given by:

$\text{Mean of data=}\frac{\text{Sum of all observations}}{\text{Total number of observations}}$

$\text{=}\frac{\text{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}}{15}$

$\text{=}\frac{\text{822}}{\text{15}}\text{=54}\text{.8}$.

Now arranging the scores obtained by $\text{15}$ students in an ascending order,

$\text{39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98}$

Since the number of observations is an odd number, that is, $\text{15}$. Hence, the median of data will be $\frac{\text{15+1}}{\text{2}}\text{=}{{\text{8}}^{\text{th}}}\text{observation}$, while arranged in ascending or descending.

Therefore, median score of data $\text{=52}$.

The observation with maximum frequency is the Mode of the data.

Since the frequency of $\text{52}$ is maximum, therefore the mode score of the data is $\text{52}$.

3. The following observations have been arranged in ascending order. If the median of the data is $\text{63}$, find the value of $\text{x}$.

$\text{29, 32, 48, 50, x, x + 2, 72, 78, 84, 95}$

Ans: Since the number of observations is an even number, that is, $\text{10}$. Hence, the mean of $\frac{10}{2}$ i.e., ${{5}^{th}}$  and $\frac{\text{10}}{\text{2}}\text{+1}$ i.e., ${{6}^{th}}$ observation, while arranged in ascending or descending, will give us the median.

Therefore, $\text{Median of }data\text{=}\frac{{{\text{5}}^{\text{th}}}\text{observation+}{{\text{6}}^{\text{th}}}\text{observation}}{\text{2}}$

$\Rightarrow \text{63=}\frac{\text{x+x+2}}{\text{2}}$

$\Rightarrow \text{63=}\frac{\text{2x+2}}{\text{2}}$

$\Rightarrow \text{63=x+1}$

$\Rightarrow \text{x=62}$

4. Find the mode of $\text{14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18}$.

Ans:

Firstly, arranging the data in an ascending order,

$\text{14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28}$

The observation with maximum frequency is the Mode of the data.

Since the frequency of $\text{14}$ is maximum, therefore the mode of the given data is $\text{14}$.

5. Find the mean salary of $\text{60}$ workers of a factory from the following table:

 Salary (in Rs.) Number of workers $\text{3000}$ $\text{16}$ $\text{4000}$ $\text{12}$ $\text{5000}$ $\text{10}$ $\text{6000}$ $\text{8}$ $\text{7000}$ $\text{6}$ $\text{8000}$ $\text{4}$ $\text{9000}$ $\text{3}$ $\text{10000}$ $\text{1}$ Total $\text{60}$.

Ans. The formula for  calculating the mean is give by:

$Mean=\frac{\sum{{{f}_{\text{i}}}{{\text{x}}_{\text{i}}}}}{\sum{{{f}_{\text{i}}}}}$

The value of $\sum{{{f}_{\text{i}}}{{\text{x}}_{\text{i}}}}$ and $\sum{{{f}_{\text{i}}}}$ can be calculated as follows:

 Salary (in Rs.) (${{\text{x}}_{\text{i}}}$) Number of workers (${{f}_{\text{i}}}$) ${{f}_{\text{i}}}{{\text{x}}_{\text{i}}}$ $3000$ $16$ $\text{3000 }\!\!\times\!\!\text{ 16=48000}$ $4000$ $12$ $\text{4000 }\!\!\times\!\!\text{ 12=48000}$ $5000$ $10$ $\text{5000 }\!\!\times\!\!\text{ 10=50000}$ $6000$ $8$ $\text{6000 }\!\!\times\!\!\text{ 8=48000}$ $7000$ $6$ $\text{7000 }\!\!\times\!\!\text{ 6=42000}$ $8000$ $4$ $\text{8000 }\!\!\times\!\!\text{ 4=32000}$ $9000$ $3$ $\text{9000 }\!\!\times\!\!\text{ 3=27000}$ $10000$ $1$ $\text{10000 }\!\!\times\!\!\text{ 1=10000}$ Total $\sum{{{\text{f}}_{\text{i}}}}\text{=60}$ $\sum{{{\text{f}}_{\text{i}}}{{\text{x}}_{\text{i}}}}\text{=305000}$.

So, Mean salary $\text{=}\frac{\text{305000}}{60}$.

Therefore, the mean salary of $\text{60}$ workers is $\text{Rs}\text{. 5083}\text{.33}$.

6. Give one example of a situation in which

i. The mean is an appropriate measure of central tendency.

Ans: Mean is an appropriate measure of central tendency when the observations are relatively close to each other.

Median is an appropriate measure of central tendency when the observations are relatively far from each other.

Consider the following example − the following data represents the heights of the members of a family:

$\text{154}\text{.9 cm, 162}\text{.8 cm, 170}\text{.6 cm, 158}\text{.8 cm, 163}\text{.3 cm, 166}\text{.8 cm, 160}\text{.2 cm}$

In this case, mean will be calculated as an appropriate measure of central tendency because the observations in the given data are close to each other.

ii. The mean is not an appropriate measure of central tendency, but the median is an appropriate measure of central tendency.

Ans: Mean is an appropriate measure of central tendency when the observations are relatively close to each other.

Median is an appropriate measure of central tendency when the observations are relatively far from each other.

Consider the following data representing the marks obtained by $\text{12}$ students in a test.

$\text{48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99}$

In this case, the median will be calculated as an appropriate measure of central tendency because there are some observations which are very far from other observations.

NCERT Solutions for Class 9 Maths

NCERT Solution Class 9 Maths of Chapter 14 All Exercises

 Chapter 14 - Statistics Exercises in PDF Format Exercise 14.1 2 Questions & Solutions (2 Short Answers) Exercise 14.2 9 Questions & Solutions (9 Long Answers) Exercise 14.3 9 Questions & Solutions (6 Short Answers, 3 Long Answers) Exercise 14.4 6 Questions & Solutions (2 Short Answers, 4 Long Answers)

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.4

Opting for the NCERT solutions for Ex 14.4 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 14.4 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 9 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 9 Maths Chapter 14 Exercise 14.4 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 9 Maths Chapter 14 Exercise 14.4, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.

Do not delay any more. Download the NCERT solutions for Class 9 Maths Chapter 14 Exercise 14.4 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.

FAQs on NCERT Solutions for Class 9 Maths Chapter 14: Statistics - Exercise 14.4

1. What will I learn in this chapter?

Statistics chapter is one of the simplest chapters among all other chapters of CBSE Class 9 Maths Solutions. This chapter is connected to the arithmetic calculations which includes grouped data, ungrouped data and the measures of central tendencies. This also explains about frequency, mean, median and mode. Our NCERT Solutions for Class 9 Maths Chapter 14 consists of 4 exercises which have 26 questions in total and these questions cover the major topics of the chapter. Solutions provided to these are easy and simple to understand.

2. What are the main concepts that are covered in this chapter?

Statistics is a division of mathematics that deals with the combination of data, organization, analysis, presentation and interpretation. Apart from the math topic, Statistics play a vital role in various fields of human actions. A study dealing with the presentation, collection and interpretation and analysis of information is called statistics.

Topics that are included in this chapter are data, frequency, ungrouped data, grouped data, class interval, regular and irregular class interval, frequency table, sorting, ungrouped frequency table, grouped frequency table, graphical representation of data, bar graphs, variable being a number, histogram, frequency polygon, midpoint of the class interval, equality of areas and measures of central tendency which includes average, mean, mode and median.

It is used to examine about the things happening around us, the existing position of per capita income, community growth rates, schooling, unemployment, housing, medical, facilities, for forecasting the weather, marks of a student to predict the age and lot more.

3. How many questions are there in this exercise?

There are a total of 6 questions in this exercise. In question 1 and question 2, you’ll have to find the mean, median and mode of the scores made by a team. In question 3 you will be provided with the median of the data and you’ll have to find the value of x in it. Question 4 is based on the mode, you’ll be provided with the frequency and for which you need to find the mode.

Question 5 is based on the mean concept. You will be given the table based on the salary for which you need to find the mean for it. Question 6 is a scenario-based question, which is totally based on the mean concept.

4. Why are NCERT solutions much needed for the CBSE exam preparation?

Our NCERT Solutions for Class 9 Maths are provided with a complete explanation and relevant examples. These solutions are in a methodical way which helps you in increasing up a strong base of all the topics. We make sure that all the points and sub-topics are covered from each and every chapter and we also have sketched these solutions in a way to initiate your learning process more fun, interesting and delightful.

You can learn and revise these solutions as they will make your task simpler. These solutions follow a logical flow to make your conceptual knowledge stronger. Our NCERT solutions to the exercise question and in-between exercise questions are in a well-structured manner to make your learning fast and effective.

5. Is this the only exercise available on Statistics for Class 9?

Exercise 14.4 is the fourth exercise that deals with Statistics in Class 9 Maths. The previous exercises cover various other topics and concepts that are relevant to Statistics. This exercise deals with the concepts of mean, median, and mode. The questions in this exercise help students in grasping and getting a tight hold of these concepts, which will ultimately prove beneficial in the examination. You can also check for the NCERT Solutions of Class 9 Maths Chapter 14 Ex-14.4 on the Vedantu app as well as the website.

6. Why must one look towards the NCERT solutions for Class 9 Maths Chapter 14?

The NCERT solutions are designed to provide students with a strong base before they are met with complicated questions in the examination. The various exercises that the solutions offer will help the student attain a stronghold of the concepts of Class 9 Maths Chapter 14. With the practise of these exercises, the student will be able to answer any question that is asked from this particular chapter. The student can download these solutions for free from the website of Vedantu and the app.

7. What routine should one follow to be able to solve these questions?

To solve a question, one needs to be fully acquainted with the basics. Therefore, before solving a question, practising the basics becomes extremely important. Thus, one has to be aware of the concepts to solve a question, not only in this exercise but also in the examination. The routine, therefore, has to be based on polishing their concepts and understanding of the topics first and then solving numerous exercises on that topic to get a hold over it. For checking the answers, you can visit the page NCERT Solutions of Class 9 maths.

8. What are the real-time applications of the concepts present in this exercise?

The mean, median and mode help present different perspectives of the same data. These concepts are widely used in the healthcare industry and by insurance analysts. For instance, it helps insurance analysts to calculate the mean age of the individuals to whom they provide insurance. Thus, it helps them analyse the mean age of their customers.

9. What are the basics to understand while solving questions concerning mean, median, and mode?

The mean of a particular dataset is usually deduced by adding all numbers given in that particular dataset and then dividing it by the number of values present in the set. The median is the middle value when the data is arranged from the least to the greatest and mode is the number that appears the most in a particular data set. To have further knowledge on these topics, download the PDF of NCERT Solutions of Class 9 maths free of cost from the Vedantu website.