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NCERT Solutions

Class 11

Statistics

Chapter 5 Measures Of Central Tendency

CBSE Class 11 Statistics NCERT Solutions Chapter 5 – Measures of Central Tendency [2025-26]

Q: 1. What are the main formulas in Class 11 Statistics Chapter 5?

The key formulas from Class 11 Statistics Chapter 5 – Measures of Central Tendency include the mean, median, and mode calculations, all essential for CBSE 2025 exams.Important formulas:Arithmetic Mean (Ungrouped Data): Mean = (Sum of all observations) / (Number of observations)Arithmetic Mean (Grouped Data): Mean = (Σfixi) / (Σfi)Median (Ungrouped Data): Middle value after arranging data in orderMedian (Grouped Data): Median = l + [(n/2 – cf)/f] × hMode (Grouped Data): Mode = l + [(f1 – f0)/(2f1 – f0 – f2)] × hThese formulas represent central tendency measures and are crucial for calculations in all NCERT exercises and exam questions.

Q: 2. How do I calculate median for grouped data in NCERT Exercise 5?

To calculate the median for grouped data (as asked in NCERT Exercise 5):Follow these steps:Find the cumulative frequency (cf) for the classes.Locate the median class: the class where (n/2) falls, where n is the total number of observations.Use the formula: Median = l + [(n/2 – cf)/f] × hwhere:l = lower class boundary of median classcf = cumulative frequency before median classf = frequency of median classh = class widthAlways arrange frequencies and classes accurately for correct median calculation.

Q: 3. Is there a free PDF for Class 11 Statistics Chapter 5 solutions?

Yes! Vedantu provides a free PDF download of NCERT Solutions for Class 11 Statistics Chapter 5 – Measures of Central Tendency.All solutions strictly follow the CBSE 2025 syllabus.PDF is provided for offline exam preparation and revision.No sign-up required.Simply use the ‘Download PDF’ button provided on the solution page to access the file instantly.

Q: 4. How to use Vedantu's NCERT solutions for last-minute revision?

For last-minute revision of Class 11 Statistics Chapter 5:Begin with the quick revision guide and formula blocks.Review solved examples for mean, median, and mode step-by-step solutions.Practice unsolved exercises and then check the answers.Download the free PDF for offline study on exam day.This will boost confidence and accuracy before your CBSE exams.

Q: 5. Are these CBSE-approved answers for 2025 board exams?

Yes, all answers are CBSE-approved for Class 11 Statistics Chapter 5 (2025 syllabus).Solutions are mapped to the latest official NCERT and CBSE curriculum.Updated regularly by experienced statistics educators.Follows proper marks-weightage and exam pattern.Use these solutions for reliable preparation and full syllabus coverage.

Q: 6. What are Measures of Central Tendency?

Measures of Central Tendency are statistics used to represent a large set of data with a single value that best describes the entire distribution.Main types:Mean: The average of all data valuesMedian: The middle value when data is arranged in orderMode: The value that occurs most frequently in the data setThese are core concepts in statistics covered in Class 11 Chapter 5 for CBSE 2025.

Q: 7. Which topics are included in NCERT Class 11 Statistics Chapter 5 syllabus for 2025?

The 2025 CBSE syllabus for Class 11 Statistics Chapter 5 covers:Definition and types of Averages (Mean, Median, Mode)Calculating mean (arithmetic mean, step deviation, weighted mean)Finding median in ungrouped and grouped dataMode calculation (simple and grouped data)Application-based and theory questionsAll content strictly follows the latest CBSE guidelines.

Q: 8. How do I avoid common mistakes while solving measures of central tendency questions?

To avoid common errors in measures of central tendency:Memorise each formula and understand when to apply which (mean vs median vs mode).Read questions carefully to determine if data is grouped or ungrouped.Double-check calculations, frequencies, and cumulative totals.Write all steps clearly in your solutions (as modelled in NCERT and Vedantu solutions).Practicing solved examples from official NCERT solutions ensures accuracy and clarity.

Q: 9. How can I get more practice questions for mean, median, and mode?

For more practice on mean, median, and mode in Class 11 Statistics:Use the Vedantu Important Questions and Worksheets for Chapter 5.Attempt previous year papers and sample exercises.Try chapter-end unsolved and extra questions.Explore online MCQs and case-based problems provided in the study material section.This will provide broad coverage and boost your confidence for exams.

Download Free PDF of Measures of Central Tendency for Class 11 Statistics Chapter 5

You're about to strengthen your understanding of statistics through the lens of Class 11 Measures of Central Tendency. This CBSE-aligned solution guide unpacks mean, median, and mode, using simple steps and exam-focused examples. Here, you will find clear explanations that remove confusion around which formula to use for each question type—a common challenge in statistics chapter 5 exercise solutions.

Table of Content

This chapter holds a weightage of around 12 marks in the Statistics & Probability unit, which makes every mark count for your board results. You’ll practice essential skills like mean calculation and comparison of statistical averages, while building confidence to handle both theory and application-based questions. Vedantu's solved answers follow the latest 2025 syllabus, so every solution is current and reliable for your CBSE exam needs.

If you’re searching for class 11 statistics chapter 5 notes or extra support, these solutions are designed as a quick revision companion. Each solution explains the reasoning behind every calculation step, empowering you to master central tendency and score higher this year.

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.

CBSE Class 11 Statistics Chapter 5 Other Study Materials

S. No	Important Study Material Links for Chapter 5 Measures of Central Tendency
1.	Class 11 Measures of Central Tendency Important Questions
2.	Class 11 Measures of Central Tendency Revision Notes

Chapter-wise NCERT Solutions for Class 11 Statistics

S. No	NCERT Solutions Class 11 Statistics Chapter-wise List
1	Chapter 1 - Introduction to Statistics Solutions
2	Chapter 2 - Collection of Data Solutions
3	Chapter 3 - Organisation of Data Solutions
4	Chapter 4- Presentation of Data Solutions
5	Chapter 6 - Correlation Solutions
6	Chapter 7 - Index Numbers Solutions
7	Chapter 8 - Use of Statistical Tools Solutions

Important Related Links for CBSE Class 11 Statistics

S.No	Study Material for Class 11 Economics
1.	CBSE Class 11 Economics NCERT Books
2.	CBSE Class 11 Economics Important Questions
3.	CBSE Class 11 Economics Sample Papers
4.	CBSE Class 11 Economics NCERT Solutions
5.	CBSE Class 11 Economics Sandeep Garg Solutions
6.	CBSE Class 11 Economics Notes
7.	CBSE Class 11 Economics Syllabus

FAQs on CBSE Class 11 Statistics NCERT Solutions Chapter 5 – Measures of Central Tendency [2025-26]

1. What are the main formulas in Class 11 Statistics Chapter 5?

The key formulas from Class 11 Statistics Chapter 5 – Measures of Central Tendency include the mean, median, and mode calculations, all essential for CBSE 2025 exams.
Important formulas:

Arithmetic Mean (Ungrouped Data): Mean = (Sum of all observations) / (Number of observations)
Arithmetic Mean (Grouped Data): Mean = (Σf_ix_i) / (Σf_i)
Median (Ungrouped Data): Middle value after arranging data in order
Median (Grouped Data): Median = l + [(n/2 – cf)/f] × h
Mode (Grouped Data): Mode = l + [(f₁ – f₀)/(2f₁ – f₀ – f₂)] × h

These formulas represent central tendency measures and are crucial for calculations in all NCERT exercises and exam questions.

2. How do I calculate median for grouped data in NCERT Exercise 5?

To calculate the median for grouped data (as asked in NCERT Exercise 5):
Follow these steps:

Find the cumulative frequency (cf) for the classes.
Locate the median class: the class where (n/2) falls, where n is the total number of observations.
Use the formula:
Median = l + [(n/2 – cf)/f] × h
where:
- l = lower class boundary of median class
- cf = cumulative frequency before median class
- f = frequency of median class
- h = class width

Always arrange frequencies and classes accurately for correct median calculation.

3. Is there a free PDF for Class 11 Statistics Chapter 5 solutions?

Yes! Vedantu provides a free PDF download of NCERT Solutions for Class 11 Statistics Chapter 5 – Measures of Central Tendency.

All solutions strictly follow the CBSE 2025 syllabus.
PDF is provided for offline exam preparation and revision.
No sign-up required.

Simply use the ‘Download PDF’ button provided on the solution page to access the file instantly.

4. How to use Vedantu's NCERT solutions for last-minute revision?

For last-minute revision of Class 11 Statistics Chapter 5:

Begin with the quick revision guide and formula blocks.
Review solved examples for mean, median, and mode step-by-step solutions.
Practice unsolved exercises and then check the answers.
Download the free PDF for offline study on exam day.

This will boost confidence and accuracy before your CBSE exams.

5. Are these CBSE-approved answers for 2025 board exams?

Yes, all answers are CBSE-approved for Class 11 Statistics Chapter 5 (2025 syllabus).

Solutions are mapped to the latest official NCERT and CBSE curriculum.
Updated regularly by experienced statistics educators.
Follows proper marks-weightage and exam pattern.

Use these solutions for reliable preparation and full syllabus coverage.

6. What are Measures of Central Tendency?

Measures of Central Tendency are statistics used to represent a large set of data with a single value that best describes the entire distribution.
Main types:

Mean: The average of all data values
Median: The middle value when data is arranged in order
Mode: The value that occurs most frequently in the data set

These are core concepts in statistics covered in Class 11 Chapter 5 for CBSE 2025.

7. Which topics are included in NCERT Class 11 Statistics Chapter 5 syllabus for 2025?

The 2025 CBSE syllabus for Class 11 Statistics Chapter 5 covers:

Definition and types of Averages (Mean, Median, Mode)
Calculating mean (arithmetic mean, step deviation, weighted mean)
Finding median in ungrouped and grouped data
Mode calculation (simple and grouped data)
Application-based and theory questions

All content strictly follows the latest CBSE guidelines.

8. How do I avoid common mistakes while solving measures of central tendency questions?

To avoid common errors in measures of central tendency:

Memorise each formula and understand when to apply which (mean vs median vs mode).
Read questions carefully to determine if data is grouped or ungrouped.
Double-check calculations, frequencies, and cumulative totals.
Write all steps clearly in your solutions (as modelled in NCERT and Vedantu solutions).

Practicing solved examples from official NCERT solutions ensures accuracy and clarity.

9. How can I get more practice questions for mean, median, and mode?

For more practice on mean, median, and mode in Class 11 Statistics:

Use the Vedantu Important Questions and Worksheets for Chapter 5.
Attempt previous year papers and sample exercises.
Try chapter-end unsolved and extra questions.
Explore online MCQs and case-based problems provided in the study material section.

This will provide broad coverage and boost your confidence for exams.

10. Why should I trust Vedantu’s NCERT Solutions for Class 11 Statistics Chapter 5?

Vedantu’s NCERT Solutions for Class 11 Statistics Chapter 5 offer:

Accuracy: All answers are prepared and reviewed by expert CBSE educators.
Updated Syllabus Coverage: Solutions follow the latest 2025 CBSE and NCERT guidelines.
Stepwise Explanations: Every question is solved in a clear and exam-oriented manner.
Free Download & Peer Review: All material is fact-checked and free to access for students.

This combination ensures trustworthiness and top marks in board exams.