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NCERT Solutions for Class 11 Statistics Chapter 5 - Measures Of Central Tendency

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NCERT Solutions for Class 11 Statistics Chapter 5 - Measures of Central Tendency

Class 11 Statistics Chapter 5 Measures of Central Tendency is a significant part of Statistics that teaches students how to use certain mathematical tools to calculate central tendency for a list of data. This chapter needs supreme attention from the students to prepare. To make it easier, the subject experts of Vedantu have compiled accurate NCERT solutions for all the exercises. Find the answers to check how to solve such questions and develop your conceptual foundation.


The NCERT Solutions for Class 11 Statistics Chapter 5 provides an excellent knowledge of Statistics to the students. They provide updated and revised solutions for which well-experienced subject experts prepare the content. These are available in three different languages, namely Urdu, English, and Hindi. Students can gain knowledge along with good marks with the help of NCERT solutions.


Class:

NCERT Solutions for Class 11

Subject:

Class 11 Statistics

Chapter Name:

Chapter 5 - Measures Of Central Tendency

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes



The NCERT Solutions for Class 11 Statistics Chapter 5 PDF will be uploaded soon.

NCERT Solutions for Class 11 Statistics Chapter 5 Measures of Central Tendency

Class 11 Statistics NCERT Solutions chapter 5 is available in a PDF format on the official website of Vedantu for free of cost. The students should avail of this opportunity to get more knowledge. Using a soft copy or hard copy is up to the student. If they are willing to take a hard copy, then it can be easy for them to study without worrying about the internet connection. It also helps to prepare for competitive exams and other board exams.


Measures of Central Tendency

1. Introduction 

NCERT Solutions Class 11 Statistics Chapter 5 wants to introduce the measures available for the central tendency in Statistics as the students have learned the collection of data and the representation of data. The next one is analyzing and interpreting the data. To analyze the data, we have three different measures of central tendencies, such as arithmetic means, median, and mode.


2. Arithmetic Mean

The arithmetic mean is a broadly used measure to calculate the average of the given data. NCERT Solutions for Class 11 Statistics Chapter 5 also explains two different variations called, mean for grouped data and mean for ungrouped data. For any kind of method, the arithmetic mean is the sum of all observations divided by the number of observations. A formula can represent it, and the students can proceed to calculate the mean for given data.


Statistics Class 11 NCERT Solutions' Measures of Central Tendency specify that the calculation of mean for ungrouped data and grouped data has three different kinds of methods. They are a direct method, assumed method, step division method. Each method may differ from grouped data and ungrouped data.


The NCERT Solutions Class 11 Statistics Chapter 5 clearly explains available on the official website of Vedantu with an illustration. Again the grouped data has two kinds of series namely-discrete series and continuous series.


3. Median

In this section, the students are advised to learn another measure of central tendency, median. The NCERT Class 11 Statistics Chapter 5 Measures of Central Tendency explains that the median is a simple concept. It can be calculated as taking the middle value, which separates both sides of the values will be equal. But it is possible only if the size of the series is an odd number. If the students are asked to find out the median for a set of even number values, then we need to take the two middle terms and find out the average for those two terms.


Quartiles are another topic explained to the students. If the whole size is divided into four equal parts, then it is called quartile. It can be calculated separately for both series by themselves.


Percentiles are a  topic for which the whole size is divided into 99 Parts which reaches the cent.

 

4. Mode 

Class 11 of Statistics Chapter 5 is explained by our NCERT solutions that specifies the students to understand each measure of central tendency. Because if the students can understand the meaning and formula, it is difficult to forget. Even though the mode is the last measure of central tendency, it has a lot of significance. The mode is a French word that means the fashionable or frequent value which occurred in the set. In simple words, we can say that the mode is the value which has the highest occurrences. For the direct method, we can calculate directly by seeing itself. For the continuous method, there is a particular formula to find out the value of mode.


5. Relative position of arithmetic mean, median, and mode

The NCERT solutions of Class 11 Statistics Chapter 5 have also explained the students about the positions of three measures of central tendency. If we can stir the magnitude of three measures in any direction, the median should be in the middle. Mode and the arithmetic mean will be at either of the extreme positions.


6. Conclusion

Thus the Chapter 5 of measures of central tendency has been explained very well by professional teachers to the students. The material is provided with different examples of all six concepts.


Key Takeaways of NCERT Solutions for Class 11 Statistics Chapter 5 PDF

NCERT solutions for Class 11 Statistics Chapter 5 offered by Vedantu is a good choice for students. Here are the following benefits:

  • It allows students to enrich their conceptual knowledge and to boost their scores. 

  • Our tailor-made solutions are available for a free download in the PDF format. 

  • Several subject experts under Vedantu are ready to clarify the doubts of students through live chat are available in a chatbox on the official website.

  • It is useful to gain sound knowledge as well as to participate in the Olympiads and national level talent tests etc.


Importance of Class 11 Statistics Chapter 5 Measures of Central Tendency NCERT Solutions

Learning the advanced concepts of measuring central tendency will require complete study material. Apart from the textbook part, students will need notes and the solutions to all the exercise questions given in the chapter. Once the chapter has been prepared well, students will proceed to solve the exercise to check whether they can use the mathematical concepts and formulas properly or not.


This is where the solutions framed by the experts can be used perfectly. The solutions have been framed by following the latest syllabus to properly cover all the topics and exercises. The answers in these solutions are designed by following the Class 11 standards so that students can easily comprehend them.


While practising solving these questions, students can refer to the solutions given so that they can quickly find the answers. These answers are accurate and can be followed to practice for the development of concepts. Hence, the NCERT exercise solutions will deliver the highest convenience to the students to prepare this chapter well.


Advantages of Class 11 Statistics Chapter 5 Measures of Central Tendency NCERT Solutions

  • All the exercises of Class 11 Statistics Chapter 5 Measures of Central Tendency have been solved by the experts to offer a consolidated set of solutions in one place. You can access them online or can download the entire file for more convenience.

  • Resolve doubts related to exercise problems instantly by using the solutions. Leave no doubts unattended and make your preparation for this chapter perfect.

  • Find out how the experts have solved these problems by using simple stepwise methods. Practice and imbibe these methods to develop your answering skills. Learn how to use mathematical concepts and statistical tools to calculate the central tendency to score more in exams.


Download Class 11 Statistics Chapter 5 Measures of Central Tendency NCERT Solutions PDF

Get the free PDF version of these solutions and complete your study material for this chapter. Refer to the solutions whenever you are practising solving exercise questions and take your preparation to the next level. Understand how to score more in the exams by mastering the answering patterns and methods explained in these solutions.

FAQs on NCERT Solutions for Class 11 Statistics Chapter 5 - Measures Of Central Tendency

1. Find the mean, median, and mode for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average is, 

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

The median is the middle value, so first, we have to rewrite the list in numerical order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the size is an odd number. 

13, 13, 13, 13, 14, 14, 16, 18, 21

Hence, the median is 14.

A mode is a number that is repeated more times.

Hence, 13 is the mode.

2. What is the difference between Mean and Median?

Mean is the average of all the values given in the set. On the contrary, the median is the exact middle number when a list of values will be written in order. So both are completely different and how they have unique advantages in the field of Statistics.

3. What are the concepts covered in Chapter 5 of Statistics Class 11?

The Chapter 5 deals with 'Measures of Central Tendency' and the statistical concepts like central tendency, statistical averages, etc. The concepts covered in the chapter are:

  • Central Tendency

  • Types of statistical averages: Mathematical and Positional

  • Arithmetic mean and its types

  • Methods of Calculating Arithmetic Mean

  • Median and Mode

  • Quartiles and Percentiles

All these concepts are discussed in a student-friendly language in NCERT Solutions drafted by experts available on the official website of Vedantu and the Vedantu app.

4. What are the important formulae in Statistics Chapter 5 For Class 11?

Formulae form a very important and unavoidable part of this chapter of Statistics because statistical problems do not exist without formulae. As such, students of class 11 need to remember some important formulae if they are to solve problems from this chapter. The formulae are listed out below, and students can refer to NCERT Solutions for this chapter for an easy understanding of these formulae to solve problems.

  • Arithmetic Mean, X=x1+x2+x3+…+xn/N or ∑x/N

  • Weighted Mean, XW=∑WX/∑W

  • Median, M=Size of [N/2]th term+Size of [N/2+1]th term/2

  • Mode, Z=L1+ (f1-f0/2f1-f0-f2)xi

5. What are the benefits of using NCERT Solutions for learning Statistics Chapter 5  in Class 11?

NCERT Solutions for Statistics Chapter 5  is available all over the internet in PDF formats, the best being solutions provided by Vedantu. Students are recommended to make use of this opportunity to download them because they are a very rich source of statistical material that can help students gain excellent knowledge and ideas about the topic of statistics. Since these solutions keep revising their topics in accordance with the CBSE syllabus, students also receive the most important references.

6. What are the definitions of Median and Mode in Class 11 Statistics?

In a given data set, median is that statistical data that gives the value of the variable dividing the group into two equal parts. On the other hand, the mode of a given data set is the value of the variable occurring the most number of times in the series of data values.  

7. What are quartiles and percentiles in Chapter 5 of Class 11 Statistics?

A quartile is a statistical term where a series is divided into four equal parts. The end value of each of these parts forms a quartile. A percentile is a statistical term used to show the division of the series into 100 equal parts.