NCERT Exercise 15.1 Class 11 Maths Solutions: NCERT Solutions for Class 11 Maths deal with various important concepts from the’ Statistics’ chapter. These NCERT Solutions for statistics exercise 15.1 Class 11 allow students to work at their own pace to clarify concepts and solve difficult problems. To strengthen their skills, students can download the NCERT solutions for Class 11 Maths and practise them offline.

The mean deviation from the mean and mean deviation about the median is calculated in this statistics exercise. Students will benefit from the solution presented in this exercise in order to gain a better knowledge of the topics. It will also be beneficial to provide a firm foundation for learning complex statistics topics. In this article, we have provided all the information regarding NCERT exercise 15.1 Class 11 Maths solutions to help students score well in the exams.

NCERT Exercise 15.1 Class 11 Maths Solutions: Overview

Statistics is the study of data gathered for specific reasons. Decisions can be made by evaluating and understanding the data. In previous classes, you have learned how to express data graphically and in tabular form. Now you will learn about data representation, as well as some of the data’s most important aspects and attributes. It assists students in developing an understanding of the many uses of statistics and its relevance to their lives and fields of study.

Before jumping into further details, let us have an overview of NCERT exercise 15.1 Class 11 Maths solutions:

Class	CBSE Class 11
Book Name	NCERT Class 11 Maths
Solutions	Exercise 15.1 Class 11 Maths Solutions
Available on	Embibe
Price	Free

NCERT Exercise 15.1 Class 11 Maths Solutions: PDF

The mean deviation, which is a measure of dispersion, is used in NCERT Solutions for Class 11 exercise 15.1. Range, standard deviation, and quartile deviation are the four primary types of dispersion metrics. The range of any given set of data provides a general sense of variability, but it does not reveal the data’s dispersion from a measure of central tendency.

As a result, the standard deviation and mean are used. These calculations can be carried out on both grouped and ungrouped data. Discrete frequency distribution and continuous frequency distribution are the two types of a frequency distribution that can be applied to grouped data. Students can practice these concepts from the NCERT exercise 15.1 Class 11 Maths solutions PDF link available below:

Q.1. Find the mean deviation from the mean for the data.
4, 7, 8, 9, 10, 12, 13, 17

Solution: The given data is
4, 7, 8, 9, 10, 12, 13, 17
We proceed step-wise and get the following:
Step 1 Mean of the data x ̄=4+7+8+9+10+12+13+178=808=10
Step 2 The deviations of the respective observations from the mean x, i.e. xi-x ̄, for each of the values.
Step 3 The absolute values of the deviations, i.e. |xi-x ̄|, are
6, 3, 2, 1, 0,2, 3, 7
Step 4 The required mean deviation about the mean is M·D·x ̄=∑i=18|xi-x-|8=6+3+2+1+0+2+3+78=248=3
Therefore, the mean deviation from the median for the given data is 3.

Q.2. Find the mean deviation about the mean for the data

Height in cms	Number of Boys
95-105	9
105-115	13
115-125	26
125-135	30
135-145	12
145-155	10

Solution: The following table is formed. 

Height in cms	Number of boys fi	Mid-point xi	fixi		xi-x¯ fixi-x¯
95-105	9	100	900	25.3	227.7
105-115	13	110		1430 15.3	198.9
115-125	26	120	3120	5.3	137.8
125-135	30	130	3900	4.7	141
135-145	12	140		1680 14.7	176.4
145-155	10	150		1500 24.7	247

Here, N=∑i=16fi=100, ∑i=16fixi=12530 ∴x ̄=1N∑i=16fixi=1100×12530=125.3 M.D. (x ̄)=1N∑i=16fixi-x ̄=1100×1128.8=11.28 Therefore, the mean deviation about
the mean for the given data is 11.28.

Q.3. Find the mean deviation about the median for the following data: 

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of Girls	6	8	14	16	4	2

Solution: The following table is formed. 

Marks	Number of girlsfi	Cumulative frequency c.f.	Mid-Point xi	xi-M	fixi-Med.
0-10	6	6	5	22.85	137.1
10-20	8	14	15	12.85	102.8
20-30	14	28	25	2.85	39.9
30-40	16	44	35	7.15	114.4
40-50	4	48	45	17.15	68.6
50-60	2	50	55	27.15	54.3
–	50	–	–	–	517.1

The class interval containing the N2th or 25th item is 20-30. Therefore, 20-30 is the median class.
It is known that,
Median=l+N2-Cf×h
Here, l=20, C=14, f=14, h=10 and N=50 ∴ Median=20+25-1414×10=20+11014=20+7.85=27.85
Thus, mean deviation about the median is given by,
M.D.M=1N∑i=16fixi-M=150×517.1=10.34
Therefore, the mean deviation of the given data about the median is 10.342.

DOWNLOAD NCERT EXERCISE 15.1 CLASS 11 MATHS SOLUTIONS

About NCERT Exercise 15.1 Class 11 Maths Solutions

When tackling the NCERT solutions for exercise 15.1 Class 11 Maths, keep in mind that one must be able to recognise the type of data presented in the question in order to apply the proper calculation. Students will not make blunders in solving problems once they have mastered this skill. The mean deviation, which is a measure of dispersion, is used in NCERT Solutions for Class 11 Maths Chapter 15 exercise 15.1 statistics.

The range of data provides a basic understanding of variability or scatter, but it does not provide information about the data dispersion from a measure of central tendency. The mean and standard deviation are used for this. Both ungrouped and grouped data are subjected to these tests. A discrete and continuous frequency distribution can be applied to grouped data. Students also learn how to calculate the mean deviation from the median. The procedure for determining each measure differs; students must remember all of the steps in order to get the correct answers. There are 12 problems in NCERT Solutions for Class 11 Maths exercise 15.1 based on the mean deviation formulas.

NCERT Exercise 15.1 Class 11 Maths Solutions: Chapter Summary

NCERT Solutions for Class 11 chapter 15 is not only a crucial lesson for current year exams, but it is also important for Class 12 board exams. As students proceed through their educational journey, the concepts taught in this chapter will serve as the foundation for introducing more complex concepts. As a result, students should make it a point to be well-versed in statistics formulas and theories, as these will undoubtedly appear on future board exams. Statistics is defined as the process of gathering and classifying data, as well as the interpretation and presentation of data and data analysis.

Statistics can also be described as the process of obtaining conclusions from sample data obtained through trials. Statistics is used in a wide range of subjects, including sociology, psychology, geology, probability, and more. In the NCERT solutions for Class 11 Maths, students examine statistical measurements such as mean deviation, standard deviation, and variance of grouped and ungrouped data in greater depth. This chapter has detailed several formulas for determining the values of the concepts, as mentioned earlier. Moreover, Embibe provides students with lessons that integrate the fundamentals of statistics with more advanced concepts.

Benefits of NCERT Exercise 15.1 Class 11 Maths Solutions

Solving the NCERT exercise 15.1 Class 11 Maths solutions comes with its own perks. Keeping that in mind, we have provided some of the benefits of practising the NCERT solutions for exercise 15.1 Class 11 Maths:

1. NCERT solutions provide in-depth knowledge of the chapter’s complex concepts, helping students score more in the exams.
2. NCERT solutions help students know the areas they are weak in and help them cope with their fears regarding the chapter.
3. NCERT solutions are very descriptive and are presented in a step-by-step manner to help students with their exam preparations.
4. Students learn some complex problem-solving skills while practising from the NCERT textbooks. This helps them achieve higher grades in the exams.
5. Students also learn how to solve the question paper in a time-bound as NCERT books offer good practice scope.
6. NCERT exercise 15.1 Class 11 Maths helps students understand the correct method to solve the in-text exercise questions.
7. Statistics exercise 15.1 Class 11 Maths gives students an insight into the level of questions asked in the final exams.
8. NCERT solutions are the most reliable study material as they strictly follow the CBSE guidelines, helping students score well in the exams.
9. Solving the NCERT solutions for exercise 15.1 Class 11 Maths will help students with the revision and help them achieve excellent grades.
10. Lastly, students must keep practising from the NCERT textbooks to understand and grasp the basic knowledge to solve any questions in the exam quickly.

FAQs on NCERT Exercise 15.1 Class 11 Maths Solutions

Some of the frequently asked questions on NCERT exercise 15.1 Class 11 Maths solutions are mentioned below:

Q.1: Where can I find the NCERT solutions for exercise 15.1 Class 11 Maths?
Ans: Students can find the NCERT exercise 15.1 Class 11 Maths solutions on Embibe as they are easily accessible.

Q.2: Are the NCERT solutions for Class 11 Maths exercise 15.1 available for?
Ans: Yes, the NCERT solutions for chapter 15 Class 11 Maths are available for on Embibe.

Q.3: How many questions are there in the NCERT textbook for chapter 15?
Ans: There are a total of 34 questions in chapter 15 – Statistics. Students must solve all the questions to score excellent marks.

Q.4: What are the important topics covered in statistics exercise 15.1 Class 11?
Ans: The topics include measures of dispersions, mean deviation, and variance of grouped and ungrouped data. Variance and standard deviation of discrete and continuous frequency distributions and coefficient of variation are included in other sections.

Q.5: Which is the best textbook to study statistics from?
Ans: Students must study from the NCERT textbooks for their exams as they follow the CBSE guidelines.

We hope this article on NCERT Solutions for Statistics Exercise 15.1 Class 11 Maths helps you. If you have any questions then feel to post them here. We will get back to you at the earliest.