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# NCERT Solutions for Class 11 Maths Chapter 15 : Statistics

Statistics Class 11 Maths Chapter 15 deals with the study of data collection for specific purposes. After that, we can make decisions based on the data by analyzing and interpreting it. Class 11 Maths Chapter 15 explains the key concepts of statistics. Class 11 Maths Chapter 15 Statistics will help students to gain a thorough understanding of this concept and its practical applications. The expert faculty of Toppr produced these solutions to assist students with their first-term exam preparations.

Statistics Class 11 Chapter 15 also covers topics such as Measures of dispersions, range, mean deviation, variance of grouped and ungrouped data, variance and standard deviation of discrete and continuous frequency distributions, and coefficient of variation. Students will quickly learn about these concepts if they practice Chapter 15 Maths Class 11 NCERT Solutions of Statistics. All of these solutions have been created with the new CBSE pattern in mind, ensuring that students have a thorough understanding of their exams. It goes over all major concepts in depth, allowing students to better understand the ideas.

Chapter 15 Maths Class 11 Questions and Answers can help you get good grades in tests and properly prepare for all of the important concepts. Several examples provided in the solutions will assist students with a better understanding of Statistics. Statistics Class 11 NCERT Solutions Chapter 15 is available below in pdf format, and a few solutions are also included in the exercises. These solutions explain the topics covered with examples so that students can easily relate to the notion being discussed.

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## Access NCERT Solutions for Class 11 Maths Chapter 15 : Statistics

Exercise 15.1
Question 1
Find the mean deviation about the mean for the data:

Medium
Solution Verified by Toppr

Question 2
Find the mean deviation about the mean for the data
Medium
Solution Verified by Toppr
The given data is

Mean

The deviations of the respective observation from the mean  i.e. are .

The absolute values of the deviations i.e. are

The required mean deviation about the mean is

Question 3
Find the mean deviation about the median for the data
Medium
Solution Verified by Toppr
Given: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 19
n = 12
median =
=
=  Question 4
Find the mean deviation about the median for the data
Medium
Solution Verified by Toppr
Given =36,72,46,42,60,45,53,46,51,49
n = 10
median
mean deviation above median =
=
=
=  Question 5
Find the mean deviation about the mean for the data in Exercises 5 and 6.
5   10   15   20  25
7   4   6   3  5

Hard
Solution Verified by Toppr  Question 6
Find the mean deviation about the mean for the data in
Medium
Solution Verified by Toppr
Question 7
Find the mean deviation from the mean for the following data:
Medium
Solution Verified by Toppr
Computation of mean deviation about mean

We have, , and

Mean

Mean deviation

Mean deviation
Question 8
Find the mean deviation from the median for the following data:

Medium
Solution Verified by Toppr
 15 3 3 15 45 21 5 8 9 45 27 6 14 7 42 30 7 21 0 0 35 8 29 5 40
We have

The cumulative frequency just greater than i.e, is

. The corresponding value ob variable is . So median

Mean deviation

Question 9
Find the mean deviation about the mean for the data:
 Income per day Numbers of persons 0-100 4 100-200 8 200-300 9 300-400 10 400-500 7 500-600 5 600-700 4 700-800 3
Medium
Solution Verified by Toppr
 Income  per day Number  of persons Mid-point 0-100 4 50 200 308 1232 100-200 8 150 1200 208 1664 200-300 9 250 2250 108 972 300-400 10 350 3500 8 80 400-500 7 450 3150 92 644 500-600 5 550 2750 192 960 600-700 4 650 2600 292 1168 50 17900 7896
Here

Question 10
Find the mean deviation about the mean for the data
 Height of cms Number of boys 95-105 9 105-115 13 115-125 26 125-135 30 135-145 12 145-155 10
Medium
Solution Verified by Toppr
The following table is formed
 Height of cms Number of boys mid-point 95-105 9 100 900 25.3 227.7 105-115 13 110 1430 14.3 198.9 115-125 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

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## NCERT Solutions for Class 11 Maths Chapter 15 Statistics – Brief Overview

1. Statistics

It is defined as the process of gathering and categorizing data, interpreting and presenting data, and analyzing data. Statistics is sometimes defined as extracting inferences from sample data gathered through trials.

1. Measures of Dispersion

The dispersion or scatter in data is measured based on the observations and the types of central tendency measures used.

• Range - The range is defined as the difference between the maximum and minimum values in the given data set.

Range = Maximum Value – Minimum Value

• Mean Deviation - The difference between the observed and expected values of a data point is defined as the mean deviation.

Mean Deviation = Sum of absolute values of deviations from 'a' / no. of observations

Mean Deviation for ungrouped data = ∑|xi - x̅| / n

Mean Deviation for grouped data = ∑|xi - x̅| / N; where N = ∑ fi

1. Variance

The variance of data values is a measure of how far they deviate from the mean. It is denoted by σ2

Variance (σ2) = ∑(xi - x̅)2 / n

1. Standard Deviation

The standard deviation is a measure of statistical data distribution. It is written as the positive square root of the variance.

Standard deviation = σ

1. Coefficient of Variation

The coefficient of variation is a unit-independent measure of variability (denoted as C.V.). The coefficient of variation is defined as,

C.V. = ( σ / x̅ ) x 100

where σ and x̅ are the standard deviation and mean of the data

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### Frequently Asked Questions on NCERT Class 11 Maths Chapter 15 : Statistics

Q1. Explain the difference between Variance and Standard Deviation.

Answer: The standard deviation of a set of numbers is the distance between them and the mean. The variance is a measure of how much each point deviates from the mean on average. Variance is the average of all data points inside a group, whereas standard deviation is the square root of the variance.

Q2. How many exercises are there in Statistics Class 11 NCERT Solutions?

Answer: The NCERT Solutions Class 11 Maths Chapter 15 Statistics has 34 sums separated between three exercises and one miscellaneous activity. They range from simple formula-based problems to difficult word problems. The solutions to the exercise-specific questions are also accessible in PDF format, with the goal of assisting students in performing well in the yearly exam.

Q3. What are the key subtopics in Statistics Class 11 Maths Chapter 15 that could be tested?

Answer: All the topics covered in NCERT Solutions Class 11 Maths Chapter 15 are equally important. Statistics is a topic that is commonly used in the financial and economic industries for planning and forecasting. They aid in the development of mathematical models and the analysis of time series data. It is not only an important lesson for exams but it is also required of students in the 12th grade. Students can now study and stay up to date on the latest CBSE syllabus by using the NCERT Solutions, which are available in PDF format.

Q4. Is it necessary to practice all of the questions in Statistics Class 11 NCERT Solutions?

Answer: Statistics Class 11 NCERT Solutions are well-designed to help students study basic statistical concepts easily. It thoroughly covers all essential principles, allowing students to grasp the concepts. Students must memorize multiple formulas and do complex calculations. All of the exercises, examples, and practice problems have been meticulously designed to help students gain a rapid and effective comprehension of the various topics.

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