Miscellaneous Exercise Class 11 Maths NCERT Solutions: NCERT Solutions for Class 11 Maths Chapter 15 Statistics contains solutions for all Miscellaneous Exercises. The exercise will help students study and comprehend the difficulty level of the chapter’s questions by challenging and testing students’ knowledge of the subject. Students can achieve appropriate exposure to different problems.

Students looking for detailed and comprehensible solutions for the Miscellaneous Exercise Chapter 15 Class 11 Maths can find it in this article. Embibe’s subject matter experts have designed the NCERT Solutions to help students improve their arithmetic, logic, and reasoning skills, and clear their queries and doubts. The NCERT Solutions help candidates prepare for the Class 12 board exams and competitive exams as well like JEE Main, BITSAT, NEET, and more. Continue reading the article to know more details regarding the exercise and the link to download the NCERT Solutions for.

NCERT Solutions for Miscellaneous Exercise Class 11 Maths: Overview

Candidates can go through the table below to get a complete overview of the Miscellaneous Exercise Chapter 15 Class 11 Maths:

Particulars	Details
Class	Class 11
Subject	Mathematics
Name of the Chapter	Statistics
Topic Name	Miscellaneous Exercise
Language	English
Solution Type	Questions and Answers
Number of Exercises in the Chapter	4 Exercises Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.4 (Miscellaneous Exercise)
Official Website	https://ncert.nic.in/

NCERT Solutions for Class 11 Miscellaneous Exercise Chapter 15: Download PDFs

Students can download the Miscellaneous Exercise Chapter 15 Class 11. The solutions are crafted by Embibe experts and the challenging difficulties have been solved and explained to make learning more simpler and help students clear doubts and confusion.

NCERT Class 11 Maths Solutions are considered the best resources while preparing for competitive exams. Therefore, we have provided the solutions in PDF and text format. Students can download the solutions for and prepare to score well in their final examination even when they are offline. Below are the step-wise question-answer solutions for Miscellaneous Exercise Chapter 15 Class 11.

About NCERT Solutions for Class 11 Maths Miscellaneous Exercise Chapter 15

Before we dive into the detailed solutions of the exercise, let us have a quick summary of the Miscellaneous Exercise in Chapter 15 for Class 11.

Measure of Dispersion
Dispersion is the measure of variations in the values of the variable. It measures the degree of scatteredness of the observation in the distribution around the central value.

Range
The measure of dispersion is easy to understand and easy to calculate in the range.
The range is defined as the difference between two extreme observations of the distribution.

Range of distribution = Largest observation – Smallest observation.

Mean Deviation
Mean deviation for ungrouped data.
For n number of observations x₁, x₂, x₃,…, x_n, the mean deviation about their mean x¯ is given by

(formulas need to be added)

The mean deviation about their median M is as follows

(formulas need to be added)

Mean Deviation for Discrete Frequency Distribution
Let the given data consist of discrete observations x₁, x₂, x₃,……., x_n occurring with frequencies f₁, f₂, f₃,……., f_n respectively

The mean deviation about their Median M is given as

Mean Deviation for Continuous Frequency Distribution

The xi is the mid-points of the classes, and x¯ and M are respectively, the mean and median of the distribution.

Variance
Variance is the arithmetic mean of the square of the deviation about mean x¯.
Let x₁, x₂, ……x_n be the n observations with x¯ as the mean, then the variance denoted by σ², is given by

Standard Deviation
If σ² is the variance, then σ is called the standard deviation is given by:

The standard deviation of a discrete frequency distribution is given by:

The standard deviation of a continuous frequency distribution is given by:

Coefficient of Variation
To compare two or more frequency distributions, compare their coefficient of variations. The coefficient of variation is defined as follows:

NCERT Solutions for Class 11 Maths: Important Questions from Chapter 15

Candidates can go through the below list of questions to know the important questions of Class 11 NCERT Solutions for the Statistics chapter:

• The variance of 10 observations is 16 and their mean is 12. If each observation is multiplied by 4, what are the new mean and the new variance?
• The mean and standard deviation of the data having 18 observations were found to be 7 and 4 respectively. Later it was found that 12 was wrongly copied as 21 in the calculation. Find the correct mean and the correct standard deviation.
• Find the mean deviation from the mean of A.P: a, a + d, a + 2d… a + 2nd.

NCERT Solutions for Class 11 Maths: Important Topics from Chapter 15

The following is the list of important topics students must cover while practising the Class 11 Chapter 15:

Statistics	Statistics is defined as the process of collection and classification of data, interpretation, presentation and analysis of data. Also, statistics is defined as drawing conclusions from the sample data that is collected using experiments.
Measures of Dispersion in Statistics	The dispersion in the data is measured based on the observations data and measure of central tendency.  The different types to represent the measures of dispersion are: Range Mean deviation Quartile deviation Standard deviation.
Range in Statistics	Range = Maximum Value – Minimum Value
Mean Deviation in Statistics	The term is defined as the difference between the observed value of a data point and the expected value.
Variance and Standard Deviation	The two important topics in Statistics. Variance is a measure of how data values vary from the mean. Standard Deviation is the measure of the distribution of statistical data.
Analysis of Frequency Distributions	Frequency Distribution represents the frequency of items of a data set in a graphical or a tabular format.

Is the Miscellaneous Exercise Chapter 15 Class 11 Tough?

Chapter 15 of 11th-grade Mathematics is neither simple nor difficult. Some of the examples and questions in this chapter are easy to solve and some are challenging and complex. However, the level of difficulty of each chapter varies from student to student. Some students find it complicated, while others find it simple. With the right study plan, practice, and revision students can complete the chapter easily.

Benefits of Studying from Embibe’s NCERT Solutions for Class 11 Maths Chapter 15

The following are the benefits students gain through solving Class 11 NCERT solutions at Embibe:

• The NCERT Class 11 detailed and comprehensive solutions are provided by Embibe’s subject-matter experts.
• They help students cover the syllabus and prepare their level best for the exams.
• One of the best sources for preparations and revision or last moment preparations.
• Students can easily access the NCERT Solutions for Class 11 at Embibe in PDF and text format.
  • The PDFs will help students prepare for the exam in offline mode as well.
• Ex 15.4 Class 11 is solved in a step-by-step manner to help students understand the answers easily, clear their doubts and queries, and be able to solve them in their final exam.

FAQs on NCERT Solutions for Miscellaneous Exercise Chapter 15 Class 11 Maths

Below are the most frequently asked questions on Miscellaneous Exercise Chapter 15 Class 11 Maths:

Q1: Where can I download the Miscellaneous Exercise Chapter 15 of Class 11 for?
Ans: Students can download the Miscellaneous Exercise Chapter 15 of Class 11 for at Embibe, i.e., from this article.

Q2: What important topics are covered in Chapter 15 of Class 11 Maths NCERT Solutions?
Ans: The important topics covered in Chapter 15 of Class 11 Maths NCERT Solutions are Statistics, Measures of Dispersion in Statistics, Range in Statistics, Mean Deviation in Statistics, Variance and Standard Deviation, and Analysis of Frequency Distributions.

Q3: How do NCERT Solutions help in solving Miscellaneous Exercise Chapter 15 Class 11?
Ans: The NCERT Solutions for Miscellaneous Exercise Chapter 15 Class 11 are provided by Embibe’s subject-matter experts. These step-by-step detailed solutions help students clear their doubts and queries and help them prepare well for the exams.

Q4: Where can I get chapter-wise Class 11 Maths NCERT Solutions mock test series for practice?
Ans: Students can solve the chapter-wise Class 11 Maths NCERT Solutions mock test series at Embibe for.

Q5: How many questions are there in the Miscellaneous Exercise Chapter 15 Class 11?
Ans: There are 12 questions in the Miscellaneous Exercise Chapter 15 Class 11.

Download NCERT Solutions for Class 11 Maths for different chapters from the table below:

Class 11 NCERT Maths Chapter 14 Solutions

Class 11 NCERT Maths Chapter 15 Solutions

Class 11 NCERT Maths Chapter 16 Solutions

We hope the above article has helped you with the PDFs of NCERT Solutions for Miscellaneous Excercise Chapter 15 Class 11 Maths. Embibe wishes you good luck and all the best.

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