# NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Ex 14.4)

In students’ academic careers, Class 10 is a crucial stage. During this year, students are supposed to sit for board exams. Thus, the emphasis on studies is considerably enhanced. The students need to cover the topics much more thoroughly and comprehensively. Having proper guidance can help them a lot in this academic endeavour. Students may find it perplexing to access reliable and trustworthy reference materials for technology-aided learning due to the wide variety of academic content available online. Quality academic reference material can be found online, provided that the quality of the content isefficacious.

Students in Class 10 who are looking for Exercise 14.4 Class 10 NCERT Solutions can visit the website of Extramarks. Extramarks provides the best quality NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4. These NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 can make even the most challenging concepts easy to understand and interesting to practice. In these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 every concept and topic related to Class 10 Maths Chapter 14 Exercise 14.4 is explained in an in-depth manner. Students will gain a thorough understanding of the chapter after going through these NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.4.Thus, they would be better able to deal with the various topics embedded in the chapter in a more subtle and appropriate way.

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## NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Ex 14.4) Exercise 14.4

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For Statistics Class 10 Solutions 14.4, students can visit the Extramarks website. On the Extramarks learning portal, as  part of NCERT Solutions Class 10, a PDF of NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 is available. Students can also conveniently download NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 for offline access. Students can revise these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 efficiently on a daily basis for comprehensive understanding. With a firm grasp of the concepts of Statistics, they will be rendered able to effectively respond to any question of Statistics. Thus students may opt for these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 available on the Extramarks website to prepare for board exams more effectively.

The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 are also available on the Extramarks Learning App. Students can access these NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.4 by downloading the Learning App.Access NCERT Solution for Class 10 Maths Chapter 14 – Statistics

The contemporary world is highly data-oriented. The relevant information about every field is represented by sets of various kinds of data.  In the most subtle terms, statistics is a branch of mathematics that deals with the representation of data in a meaningful way .In many real-life scenarios, the fundamentals of Statistics are used to represent a set of data either in tabular form or through graphs or pie charts. There are a number of methods discussed in Chapter 14 of Class 10 Mathematics dealing with Statistics. Some of these methods include the Step Deviation Method, the Direct Method, finding the Mode and Median of Grouped Data, Converting Frequency Distribution and Establishing the Relation between Mode, Mean and Median etc. All these topics require thorough understanding. Extramarks’ NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 discuss the concepts related to the themes of Cumulative Frequency and Grouped Data. Using these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4, students can understand the concepts in a detailed way and can attain proficiency in the questions related to this chapter with regard to the board exams in a convenient manner. It is possible to revise more effectively with the assistance of resources such as past years’ papers. Students benefit greatly from a detailed analysis of important topics in the simplest language possible.

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## NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercise 14.4

Choosing Extramarks’ NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4  is a wise step for the CBSE students of Class 10 when it comes to examination preparation for Chapter 14 Mathematics. Out of four exercises, students can access NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 in PDF format. Students can avail of these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 either online or offline, as the same can be downloaded by visiting the Extramarks website or mobile application.

The subject matter experts of Extramarks have curated the solutions to the questions inculcated in Class 10 Maths Chapter 14 Exercise 14.4 with utmost precision, following all the guidelines recommended by CBSE. Class 10 students who are well-versed with all the concepts from this chapter of Mathematics in the NCERT textbook can solve all the problems of Class 10 Maths Ex 14.4. Thus, with the aid of NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4, any student can achieve excellence in the questions related to Statistics in the board exams. Further, NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 are also accompanied by learning assets like sample papers and past years’ papers. With the help of these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4, students can understand the pattern of questions that may appear in the examination with regard to this chapter in a comprehensive manner. In addition, they can obtain information about the topic weightage in Chapter 14 of Mathematics by referring to the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4.

Besides the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 which pertain to Exercise 14.4, there are a number of exercises in this chapter containing a huge number of questions, the solutions to which can be found on Extramarks. All these solutions are of superior quality and can be referred to by anyone during the time of examination preparation. In order to score maximum marks in the examination, it is really vital to understand all the concepts given in the NCERT textbook of Mathematics and solve the questions given in the exercises.

As part of a comprehensive preparation strategy, students should download the NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.4 from the Extramarks website.Their knowledge will be increased, and their preparation will be enhanced as a result.

Q.1 The following distribution gives the daily income of 50 workers of a factory.

 Daily income (in ₹) 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its graph.

Ans

$\text{We find less than type cumulative frequency table as below.}$

 Daily income (in ₹) Cumulative Frequency Less than 120 12 Less than 140 12 + 14 = 26 Less than 160 26 + 8 = 34 Less than 180 34 + 6 = 40 Less than 200 40 + 10 = 50

$\begin{array}{l}\text{Now, taking upper class limits of class intervals on x-axis and their respective frequencies on y-axis we draw its}\\ \text{ogive as following.}\end{array}$

Q.2 During the medical check-up of 35 students of a class, their weights were recorded as follows:

 Weight (in kg) Number of students Less than 38 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52 0 3 5 9 14 28 32 35

Draw a less than type graph for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Ans

$\text{Following is the given cumulative frequency distributions of less than type}$

 $\begin{array}{l}\text{Weight}\left(\text{in kg}\right)\\ \text{upper class limits}\end{array}$ $\begin{array}{l}\text{Number of students}\\ \text{(Cumulative frequency)}\end{array}$ Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35

Now locate 17.5 (half of 35) on y-axis and draw a line parallel to x-axis to cut the graph at a point.
Draw a perpendicular from this point to x-axis. The point where this perpendicular meets the x-axis
determines the median of the data. From the graph we see the median is 46.5.

$\begin{array}{l}\text{Now, we mark the point A(17.5, 46.5). So median of the given data is 46.5.}\\ \text{We find class intervals with their respective frequencies as the following.}\end{array}$

 Weight (in kg) Frequency (f) Cumulative Frequency Less than 38 0 0 38 – 40 3 – 0 = 3 3 40 – 42 5 – 3 = 2 5 42 – 44 9 – 5 = 4 9 44 – 46 14 – 9 = 5 14 46 – 48 28 – 14 = 14 28 48 – 50 32 – 28 = 4 32 50 – 52 35 – 32 = 3 35 Total (n) 35

$\begin{array}{l}\frac{\mathrm{n}}{2}=\frac{35}{2}=17.5\\ \text{Cumulative frequency just greater that 17.5 is 28 which belongs}\\ \text{to class interval}46-48.\\ \therefore \text{Median class}=46-48\\ \text{Now, we have}\\ \mathrm{l}=46,\\ \text{Cumulative frequency (}\mathrm{cf}\text{) of the class preceding the}\\ \text{median class}=14,\\ \text{Frequency of median class (}\mathrm{f}\right)=14,\text{\hspace{0.17em}\hspace{0.17em}}\\ \text{Class size (}\mathrm{h}\right)=2\end{array}$

$\begin{array}{l}\text{We know that}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Median}=\mathrm{l}+\left(\frac{\frac{\mathrm{n}}{2}-\mathrm{cf}}{\mathrm{f}}\right)×\mathrm{h}\\ \therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Median\hspace{0.17em}}=46+\left(\frac{\frac{35}{2}-14}{14}\right)×2\\ \text{or\hspace{0.17em}\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}Median\hspace{0.17em}}=46.5\\ \text{So median of the given data is}46.5.\\ \text{Hence, value of the median is verified.}\end{array}$

Q.3 The following table gives production yield per hectare of wheat of 100 farms of a village.

 Production yield (in kg/ha) 50-55 55-60 60-65 65-70 70-75 75-80 Number of farms 2 8 12 24 38 16

Change the distribution to a more than type distribution, and draw its graph.

Ans

$\text{Following is the cumulative frequency distributions of more than type of the given data..}$

 $\text{Production yield (in kg/ha)}$ $\begin{array}{l}\text{Number of farms}\\ \text{(Cumulative frequency)}\end{array}$ More than or equal to 50 100 More than or equal to 55 100 – 2 = 98 More than or equal to 60 98 – 8 = 90 More than or equal to 65 90 – 12 = 78 More than or equal to 70 78 – 24 = 54 More than or equal to 75 54 – 38 = 16

Now, draw the graph by plotting the points : (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16).

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### 1. What are the benefits of utilising Extramarks’ NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 to understand the concepts of Class 10 Maths Chapter 14 Exercise 14.4?

Extramarks provides NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 to the students of Class 10 in a PDF format. These aptly designed NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 as well as solutions to other exercises can be accessed by the students visiting the Extramarks website. If students have any doubts regarding any concept of Chapter 14 of Mathematics, referring to these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 can prove beneficial to them. The NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 are prepared by mentors in accordance with the latest examination pattern and syllabi recommended by CBSE. The availability of these NCERT solutions in an exercise-wise division enhances its utility value. Thus using these NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4, students can avail tremendous benefits.

### 2. What are the main topics that are covered in Extramarks NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4?

In total there are four exercises in Chapter 14 of Maths Class 10. Out of these, the last exercise is 14.4. In this exercise, the topics of Cumulative Frequency Interpretation and Median ff Grouped Data have been covered. Apart from this, questions requiring a Graphical Representation of the Cumulative Frequency Curve and the Ogive for the Median Calculated from the given Set of Grouped Data are also a part of this exercise. These topics have been covered thoroughly in NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 available on the Extramarks website and Learning App. If needed, students can download the NCERT Solutions For Class 10 Maths Chapter 14 Exercise 14.4 for help in their homework or examination preparation.

### 3. What tips should one follow to make perfect graphs in statistics?

The best and the easiest way to make perfect graphs in statistics is by practising it many times. Practice is helpful in drawing perfect graphs which can fetch students really good scores in the board exams. The tips to draw a perfect graph are mentioned below: