statistics class 11 assignment

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Statistics Class 11

Statistics class 11 notes.

In statistics class 11 , the importance of statistics in studying the measures of dispersion and the methods of calculating the grouped and ungrouped data has been explained. In applied mathematics, statistics is a branch that deals with the collection, organization and interpretation of data. It is similar to the study of the probability of events occurring based on the collection of data or the known quantities of data. Some of the concepts with examples and the scope of the statistics are explained in the Class 11 maths chapter 15 Statistics.

Statistics Class 11 Chapter 15 Concepts

The concepts covered in this chapter 15 of Class 11 Statistics are:

• Introduction 

Measures of Dispersion

Mean deviation.

• Variance and Standard Deviation
• Analysis of Frequency Distributions

Let’s have a look at the brief explanation of all these concepts with examples given below:

A measure of central tendency gives us a rough idea of wherever data points are centred. However, to better understand the data, we should know how the data are scattered or how much they are bunched around a measure of central tendency. However, the measures of central tendency are not adequate to give exhaustive information about a given data. Variability is another essential factor that is expected to be studied in statistics. Similar to the measures of central tendency, we need to have a unique number that describes the variability, and this single number is called a measure of dispersion. In this chapter, you will learn some of the important measures of dispersion and the methods for calculating these measured for both ungrouped and grouped data.

The dispersion or scatter in the data is measured based on the observations and the types of the measure of central tendency. The different types of measures of dispersion are:

• Quartile deviation
• Mean deviation
• Standard deviation.

In Class 11 statistics, you get an explicit knowledge of all the measures of dispersion except quartile deviation, which will be studied in your higher classes.

The range is the difference between the maximum value and the minimum value

Range = Maximum Value – Minimum Value

Click here to understand the range in a better way.

Mean deviation is the basic measure of deviations from value, and the value is generally a mean value or a median value. In order to find out the mean deviation, first take the mean of deviation for the observations from value is d = x – a Here x is the observation, and a is the fixed value.

The basic formula to find out the mean deviation is

Mean Deviation = Sum of absolute values of deviations from ‘a’ / Number of observations

To learn more about mean deviation, visit here .

Mean Deviation for Ungrouped Data

Calculation of mean deviation for ungrouped data involves the following steps :

Let us assume the observations x 1 , x 2 , x 3 , …..x n

Step 1:  Calculate the central tendency measures to find the mean deviation and let it be ‘a’.

Step 2 : Find the deviation of x i from a, i.e., x 1 – a, x 2 – a, x 3 – a,. . . , x n – a

Step 3: Find the absolute values of the deviations, i.e., | x 1 – a |, | x 2 – a |, |x 3 – a|,. . . ,|x n – a| and drop the minus sign (–), if it is there,

Step 4: calculate the mean of the absolute values of the deviations. This mean obtained is the mean deviation about a, i.e.,

Where M = Median

Mean Deviation for Grouped Data

The data can be grouped into two ways namely,

• Discrete frequency distribution
• Continuous frequency distribution

The methods of finding the mean deviation for both the types are given below

Discrete Frequency Distribution

Here, the given data consist of n distinct values x 1 , x 2 , x 3 ,….x n has frequencies f 1 , f 2 , f 3 ,….f n respectively. This data is represented in the tabular form as and is called discrete frequency distribution , and the data are given below

Mean Deviation About Mean

Where the numerator denotes the sum of products of observations x i with the respective frequencies f i and the denominator denotes the sum of frequencies.

Now take the absolute values,

Therefore, the required mean deviation about the mean is given by

Mean Deviation About Median

To find the mean deviation about the median for the given discrete frequency distribution. First arrange the observation in ascending order to get cumulative frequency which is equal to or greater than N/2, where N is the sum of the frequencies.

Therefore, the mean deviation for median is given by,

Also, check:

• Mean deviation about Median
• Mean absolute deviation
• Mean deviation for Continuous frequency distribution
• Mean deviation Calculator

Continuous Frequency Distribution

To find the mean deviation for the continuous frequency distribution , assume that the frequency in each class is centred at its midpoint. After finding the midpoint, proceed further to find the mean deviation similar to the discrete frequency distribution.

Standard Deviation

The positive square root of the variance is called standard deviation (S.D) and it is denoted by the symbol, 𝝈 and the formula to find S.D is given by

Where the variance is denoted as 𝝈 2 and it is given by

To understand more about standard deviation, visit here .

Watch The Below Video To Learn Statistics Class 11 Concepts

Class 11 Statistics Examples

Question 1: Find the range and mean deviation about the mean for the following data: 

6, 7, 10, 12, 13, 4, 8, 12

Given data: 6, 7, 10, 12, 13, 4, 8, 12

Range = Maximum value – Minimum value

= 13 – 4 = 9

Now, we need to calculate the mean.

Mean ( x̄) = (6 + 7 + 10 + 12 + 13 + 4 + 8 + 12)/8 = 72/8 = 9

Let us calculate the deviations, i.e. x i – x̄

6 – 9, 7 – 9, 10 – 9, 12 – 9, 13 – 9, 4 – 9, 8 – 9, 12 – 9, 

–3, –2, 1, 3, 4, –5, –1, 3

The absolute deviations are:

3, 2, 1, 3, 4, 5, 1, 3

As we know, the formula of mean deviation about the mean is

So, M.D(x̄) = (3 + 2 + 1 + 3 + 4 + 5 + 1 + 3)/8 = 22/8 = 2. 75

Mean deviation about the mean = 2.75

Question 2:

Obtain the variance and standard deviation for the following data :

Data in tabular form :

Here, N = 30 = f i

= 1374/30 = 45.8

Variance = 45.8

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Chapter 13 Class 11 Statistics

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Updated for NCERT 2023-24 Edition.

Get solutions of Chapter 13 Class 11 Statistics of free at teachoo. Answers to all NCERT questions and examples are solved in a step-by-step basis, with detailed explanations of each and every question.

In previous classes, we learned what data is, what mean, median, mode is. 

Mean, median, mode are called central tendency. In this chapter, we will find dispersion. Dispersion means how the data is different from the central tendency. Like if we find mean, how the data is different from the mean.

Like in the figure

Both red and blue graphs have the same mean - 100.

We see that values of the blue graph are very left and right from the mean, that is, they are dispersed from the mean.

And, for the red graph, they are very close to the mean, they are less dispersed from the mean.

This is called Dispersion.

In this chapter, we will study how do we find dispersion. 

The topics in the chapter include

• How to find range
• Ungrouped data
• Grouped data - Discrete frequency deviation and Continuous Frequency Deviation
• And, we will also find Mean deviation about Median for ungrouped and grouped data
• (In Mean Deviation about Mean and Median, we will use the concepts of finding Mean and Median from Class 10 Statistics )
• Then, we study another form of dispersion, known as Standard Deviation and Variance .
• We will learn formulas of Standard Deviation for Discrete Frequency Distribution, Continuous Frequency Distribution and shortcut method as well.
• Then, to compare two groups of numbers, we find Coefficient of Variation.
• And we also do some mix questions like Multiplication of observations, Finding remaining observations, Correcting incorrect observations.

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• NCERT Book Class 11 Statistics PDF
• NCERT Books

CBSE Class 11 NCERT Books for Statistics PDF - Free Download

There are almost 20,299 schools in India that are affiliated to CBSE. Also, NCERT is in charge of the publication of textbooks for every subject in these schools, and others, for example, NCERT books for Class 11 Economics Statistics. They are also responsible for framing syllabus for CBSE examinations. 

Students appearing for CBSE Class 11 final examination must mandatorily refer to NCERT Statistics book, for it provides a great insight into the subject.

A Subject like statistics often seems complicated to students because of its dependency on data and numerical figures. However, NCERT book of Statistics for Class 11 is there to help you out by making the entire learning process fun and easy to grasp.

NCERT Books Class 11 Statistics

NCERT Books for Class 11

Ncert solutions for class 11, ncert books for cbse class 11 statistics pdf free download, an introduction to ncert statistics book class 11.

A subject like statistics requires special attention and a systematic approach to comprehend the concepts well. Along with that, making the basics clear is equally essential. Only then students can score well in their board exams. NCERT books for Class 11 Economics Statistics thus aims at extending adequate guidance to students so that practising with the book alone can benefit them comprehensively.

Class 11 Statistics NCERT books strictly adhere to the CBSE syllabus. It makes sure that students do not need to prepare with multiple study books for a syllabus-oriented lesson. Therefore, you can download NCERT books for Class 11 Statistics PDF to get an at-length grasp of the syllabus.

Chapter-Wise Summary of Class 11 NCERT Statistics

Chapter 1: introduction.

The opening chapter of Statistics for Economics Class 11 NCERT book focuses on the several vital components of economics. Then, it proceeds to the definition of statistics and what it comprises for a general understanding of the subject’s scope. Based on the meaning of statistics by Bowley, this chapter presents the significant features of statistics in a plural sense.

This chapter also gives an account of statistics in its singular scope, as mentioned by Seligman. Students also get to know about the significance of statistics in economics. The chapter ends with the limitation of the subject.

An exercise after the chapter also contains some questions that students can answer to test their grasp of knowledge.

Chapter 2: Collection of Data 

Moving on to the next chapter of NCERT book for Class 11 Economics Statistics, students get to learn about the two sources and types of data. They are primary and secondary data, and the difference between them is also established in this chapter itself.

This chapter also gives a detailed account of the statistical methods used for data collection. Following are those methods.

Direct personal investigation

Indirect oral investigation

Information from correspondents or local sources

Information gathered through schedules and questionnaires

Sample 

Apart from that, this chapter also sheds light on several methods through which samples are collected and their reliability. 

Chapter 3: Organisation of Data

The third chapter of NCERT Statistics book Class 11 deals with a significant concept of statistics, i.e., classification. Starting from the objective to characteristics of good classification, this chapter covers it all.

Students also learn about the different types of statistical series from this chapter. They primarily include - 

Individual series 

Frequency series

Frequency distribution is a critical part of this subject that is discussed in this chapter in great details. It also contains an exercise with the questions that may possibly come in the examination. Hence, solving these problems over and over again, students will be able to answer any kind of questions in the exam hall.

Chapter 4: Presentation of Data 

There are several modes of presentation of data in statistics, and they are incorporated in this chapter of NCERT books for Class 11 Economics Statistics. Following are the different types.

Diagrammatic

Each of these types also has some distinct characteristics that are highlighted in this chapter. Students become aware of the use of graph in statistics and different types of it from this chapter easily.

Nonetheless, one just cannot draw a graph as he/she has to abide by some particular rules. Following the rules, one can get the desirable and correct quantitative data. Finally, the chapter concludes by stating the merits of graphical representation of data and its limitation.

Chapter 5: Measures of Central Tendency

Central tendency measurements deal with the central value of a statistical series. This chapter primarily focuses on the several aspects of statistical measurements. From this chapter of NCERT books for Class 11 Economics Statistics, students of economics can develop an understanding of how to calculate the arithmetic mean step by step. Following this book, students can easily learn the tricks and methods to calculate several statistical data. For example, usages of Median, Percentile, Quartiles, and Mode can often become complicated and troublesome.

However, the NCERT books have made understanding all these aspects student-friendly so that they can learn the concepts quickly without wasting much time. Moreover, solving the exercise at the end, you can make your concept clear at once.

Chapter 6: Measures of Dispersion

Dispersion is a crucial term in Statistics that measures the variation of a data. This chapter of NCERT books for Class 11 Economics Statistics primarily highlights the various aspects of dispersion. Students will get to know about the different ways to measure dispersion. Following are some of them -  

Mean deviation

Quartile deviation

Standard deviation

All of these topics are discussed in minute details in this chapter. Often, these calculations seem incoherent and critical to students, and eventually, they lose interest in these vital concepts.

However, consulting this book, they can easily interpret the process of these methods and their appropriate usage that will bring the most accurate result possible. 

Chapter 7: Correlation

Correlation refers to a method that determines the quantitative relationship between two different variables, such as demand and price. It is primarily of two types.

Positive correlation

Negative correlation

Along with that, learners will also develop their knowledge about the degree of correlation from this chapter. Additionally, there are different methods that aid in estimating correlation. Karl Pearson’s theory on the coefficient of correlation also forms a vital constituent of this chapter in the NCERT book for Class 11 Economics Statistics.

Moreover, this method also follows some specific rules, for instance, short-cut and step deviation methods, to derive the final output. This book makes all these concepts lucid and simplified with examples and in-depth analysis of the theory.

Chapter 8: Index Numbers

Another pivotal statistical device is the index number, which students need to learn to get a firm grip on the subject. If you are a board exam aspirant or preparing for any other national entrance test, gaining a sound understanding of this topic is mandatory. Only then you will be able to tackle any kind of question to be asked in the examination. 

Download NCERT books for Class 11 Economics Statistics for a simplified approach to concepts like the construction of index numbers and other allied topics. For example, index numbers are of different types, like simple and weighted index numbers, and hence, their construction methods will be altered accordingly. Reading this chapter, you can differentiate between the two without much hassle.

Chapter 9: Use of Statistical Tools

The concluding chapter of NCERT books for Class 11 Economics Statistics furnishes all the data types that one requires to conduct a statistical operation. The previous chapters dealt with several fundamental concepts of statistics. However, this chapter solely concentrates on the real-life application of those concepts.

For that, Some Step-by-Step Methodologies are Followed. They Include -  

Introduction

Identifying a particular area of study

Target group

Data collection

Presentation of data in an organised way

Analysis 

Submission of project

On successful completion of sequential steps, students can come up with an accurate statistical result.

Since this book provides considerable illustrative examples, students can learn the concepts readily without making any mistakes.

Why are NCERT Books Essential for CBSE Board Exam Preparation?

The market is flooded with several books for Class 11 Statistics. Still, NCERT books often come on the top list for students. What do you think can be the reason for that? To understand that, consider the following few aspects.

Let’s Take a Look!

In-depth Analysis -  Each NCERT book, irrespective of the subject, provides a detailed analysis of every topic so that students can gain a clear idea of the basics. Developing a strong base in any subject helps students excel in the examination and score well. Mere cramming of the concepts almost always does not work for subjects. Therefore, NCERT always thrives on imparting a quality lesson to students so that they can nurture themselves for the subject beyond just scoring in examinations.

Detailed Exercise for Practice -  The exercises after each chapter of the NCERT book for Class 11 Economics Statistics allow the students to get a fair idea of what types of questions they can expect in their board examination. These exercises are curated in such a way that testifies not only the comprehensive idea of the subject but also the conceptual understanding of respective chapters. Moreover, almost 95% of questions in CBSE board exams come from these textbooks. Hence, solving these exercises will let the students answer promptly.

Student-Friendly Examples -  Another characteristic of NCERT books is that they contain simplified diagrams and examples from real life. It helps students relate their classroom lessons to that in the outer environment. Since each topic contains several examples; students do not need to rote the lesson. Instead, they can memorise the concepts even better for proper answering during their exam. Due to this reason, teachers also refer to these books for their classroom lessons.

Easy Availability -  A valid reason behind the popularity of NCERT books is its ready availability. These books are available both online and offline. Students who are not comfortable with online books can purchase the physical copy of them from any reputed book store. On the other hand, students who want to save some on such purchases can download the NCERT books in PDF format and continue with their curricular preparation according to their convenience.

After assessing these factors, it would be easy to understand their increasing popularity. Hence, download NCERT books for Class 11 Economics Statistics today and start preparing for a comprehensive learning and exam preparation.

What Makes Vedantu a Leading E-Learning Site?

The reputation of Vedantu lies in the fact that we are dedicated to bringing the best out of each student. For that, we have all the educational apparatus, starting from notes, online books and PDF to model questions. Due to this, students consider our e-learning platform as a one-stop solution for any academic requirement. 

Hence, if you are struggling with subjects like Statistics, don’t get stressed. Download NCERT books for Class 11 Economics Statistics and start preparing for the upcoming exams. Also, you can join our online session to clear your doubts if any. 

Download Vedantu’s app today on your Smartphone to stay updated with any study-related information.

Other Free Study CBSE Material for Class 11

FAQs on NCERT Book Class 11 Statistics PDF

1. How Many Chapters are There in Class 11 Statistics Under Economics?

There are a total of nine chapters in the CBSE syllabus for Class 11 Statistics, Economics. The first chapter starts with the basic introduction to statistics so that students can get an overall idea of the subject. Then, the next chapters elaborate the topics essential under Class 11 curriculum. Finally, the ninth chapter ends with necessary statistical tools that you need to provide an accurate statistical report and other real-life applications.

2. Why Should You Gain an in-depth Understanding of Statistics as a Subject?

Gaining a comprehensive understanding of statistics enables you to employ appropriate methods to collect information and data, and using them, you can prepare several reports. Making reports manually often becomes cumbersome and erroneous. To overcome that, statistics is necessary as it uses scientific methods and systematic approaches to bring out the most accurate results. Moreover, it makes the entire process of data arrangement, calculation and analysis hassle-free and saves a lot of time. 

3. How to Improve Your Score in Statistics?

Statistics is a subject with a wide scope; hence, comprehensive learning is required to get a firm hold on the subject. If you are a student of statistics, then start by reading all the chapters of NCERT books for Class 11 Economics Statistics minutely. On completion of the reading, start solving problems from each chapter. Finally, allot some time to revise the whole book before your exam. Following these steps, you can score well in the exam. 

4. Which Books Should CBSE Students Follow for Statistics?

CBSE Class 11 students can first cover the NCERT book for Statistics to get a fair idea of the syllabus. Then, if they need additional consultation from other books for reference purpose, they can follow TR Jain and VK Ohri’s Statistics for Economics. Apart from that, Sandeep Garg’s book for statistics is also a suitable choice. However, no matter what book you are following, proper revision and frequent practise are essential to obtain good marks in Statistics.

5. What are class 11 statistics?

In class 11 statistics, the students are given an in-depth understanding of the importance that the subject holds in studying the measures relating to dispersion. It also teaches the students the different methods used to calculate the grouped and the ungrouped data. It is a subject that incorporates the study of the collection, organization and interpretation of data. The student can access the text for class 11 statistics from the website of Vedantu. They can easily download the pdf and utilize it offline. The reading and practice from these NCERT texts will help the student in better understanding of the subject matter. 

6. How do the ncert texts help the student?

The question papers set for the class 11 examination, having questions based on the syllabus present in these NCERT texts. These NCERT texts are recommended by the CBSE and are designed by experts to meet the educational needs of the students. 

These chapters not just help the student score good grades in the class 11 examination, but they also help the student in their future prospects, as they help enrich the knowledge and insight of the students. Therefore, it is mandatory for every student to read the NCERT books thoroughly. These books can be easily downloaded from the website of Vedantu for free. 

7. How to prepare for class 11 statistics?

In order to score good grades in the examination, the students should follow the given steps;

Make a well planned timetable and make sure to follow it dedicatedly.

Complete the daily assignments without leaving anything behind. This will help the student complete the syllabus on time before the examinations. The students will also have enough time to revise the important topics.

It is very important for the student to read the NCERT textbooks thoroughly. This will give the student enough exposure and insight into the subject. While reading the chapters, the students should also mark the important areas so that it gets easier to refer to them while preparing for the exam.

The students are also advised to make personal notes, and practice the concepts again and again to be able to remember them during the exam.

Additionally the students should also refer to the study materials and the guide books.

Following these simple steps will help the students immensely in securing good grades in their exams. 

8. Is the website of Vedantu trustworthy?

Yes, the website of Vedantu is very trustworthy. The website aims at providing the best guidance and assistance for the students appearing for the exams. The website makes sure that all the information and materials are updated regularly so that the student is never kept hidden from the information necessary for their academics. The students can download the important materials and refer to the information while preparing for their examination. With enough practice and guidance the students will definitely be able to score good grades in their exams.  

9. What are the important chapters in class 11 Statistics?

It is advised to the students to not follow the short way in preparing for the exam. This will result in the deduction of marks due to the lack of proper preparation. In order to not find the syllabus very taxing on oneself, the student should plan accordingly and complete the chapters well before time. This will give them enough time to read and revise before the examinations. Reading the NCERT books will prove to be a great boon for the students, as all the questions asked in the examination revolve around the syllabus present in their curriculum.  

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Introduction Class 11 Statistics Notes And Questions

Please refer to Introduction Class 11 Statistics notes and questions with solutions below. These Class 11 Statistics revision notes and important examination questions have been prepared based on the latest Statistics books for Class 11. You can go through the questions and solutions below which will help you to get better marks in your examinations.

Class 11 Statistics Introduction Notes and Questions

1. CONCEPT OF ECONOMICS We advise the young learners of Class XI to comprehend the concept of economics through the following discussion relating to ordinary (or routine) business (or activities) of our life.

Every individual, ranging from a child to an old man, is engaged in some economic activity or the other. Consumption is an important economic activity; and we all are consumers, consuming different goods and services for the satisfaction of our wants.

Who is a Consumer? A consumer is one who consumes goods and services for the satisfaction of his wants.

What is Consumption? Consumption is the process of using up utility value of goods and services for the direct satisfaction of our wants. Utility value of goods means inherent capacity of goods and services to satisfy human wants.

Production is another economic activity, and many of us are producers, engaged in the production of different goods and services for the generation of income.

Who is a Producer? A producer is one who produces and/or sells goods and services for the generation of income.

What is Production? Production is the process of converting raw material into useful things. Things become useful as they acquire utility value in the process of production. Saving and investment are also economic activities, and many of us are savers and investors. We save a part of our income for future consumption or for investment in shares and bonds to generate income.

What is Saving? It is that part of income which is not consumed. It is an act of abstinence from consumption.

What is Investment? It is expenditure by the producers on the purchase of such assets which help to generate income. Thus, we are consumers, producers, savers and investors. We are all engaged in diverse economic activities. Economic activities include consumption, production, saving, investment, and many more.

What is Economic Activity? It is an activity which is related to the use of scarce means (also called scarce resources). Means are always scarce in relation to our wants. Imagine yourself as the richest person on the earth. Still you can’t have everything you wish to have at a point of time. It implies the scarcity of your means/ resources in relation to your wants.

Engaged in diverse economic activities, we are performing ‘ordinary business of life’, according to Alfred Marshall, a great pro founder of Modern Economics. Thus, he defines economics as “the study of mankind in the ordinary business of life.”

Scarcity is the Undercurrent of Economic Problem and therefore of Economics

Resources are always scarce in relation to our wants. Also, resources have alternative uses: A ten-rupee note in your pocket may be spent on a cup of coffee or a cold drink. Likewise, a worker may render his services in factory A, rather than B and C. Because, resources are scarce and have alternative uses, we cannot escape from the problem of allocation of limited means to alternative uses. This is what we call economic problem or the problem of choice.

What is Economic Problem? It is the problem of choice (or the problem of allocating scarce resources to alternative uses) arising on account of the fact that resources are scarce and these have alternative uses. Economics is essentially the study of economic problems that we must confront owing to the fact that our means are scarce in relation to our wants, and that the means have alternative uses. If there is no scarcity, there is no economic problem, and there is no economics if there is no economic problem. Thus, Robbins defines economics as “A science that studies human behaviour as a relationship between ends and scarce means which have alternative uses.”

Three Distinct Components of Economics: Consumption, Production and Distribution Consumption Here, we, as students of economics, study behaviour of human beings as consumers or buyers of different goods and services for the satisfaction of their wants. As consumers, people have limited means, while their wants are unlimited. How do they allocate their given means (or income) to the purchase of different goods and services, (given their market prices) so that their satisfaction is maximised? This is the study of consumption or the study of consumer behaviour. When we formulate a set of standard relationships (like the inverse  elationship between price of good and its purchase) explaining how consumers tend to behave, we call it consumption theory.

Production Producers also have limited means while they have a wide range of goods and services to choose from for their firms and factories. Given prices of different inputs, how do they choose such combination(s) which are least expensive, so that they are able to minimise their cost of production. Also, given prices of different goods, how do they choose to produce those, the production of which offers them maximum revenue, so that their profit (profit = revenue – costs) is maximised. This is the study of production, or the study of producers’ behaviour. When we formulate a set of standard relationships (like greater the productivity of a factor, greater is its employment) explaining the behaviour of producers or their production decisions, we call it production theory.

Distribution As students of economies we are also interested in knowing how income (generated in the process of production) is distributed among those who have worked as agents of production. Who are agents of production? These are owners of factors of production, viz. land, labour, capital and entrepreneurship. A part of income generated will go to the owners of land (used in production) in the form of rent; a part will go to labourers (for rendering their services) in the form of wage; a part will go to the owners of capital (used in production) in the form of interest; and a part will go to the entrepreneurs in the form of profits. Distribution of income refers to the distribution of GDP (gross domestic product) among the owners of the factors of production (land, labour, capital and entrepreneurship). What are the economic principles on the basis of which income is distributed among owners of the factors of production? Such a study is called distribution theory in economics.

Besides these three major components of economics, the economists also address such questions which are of social significance, like the question of poverty and unemployment, the question of growth with social justice and the question of environmental degradation as linked to various economic activities. Issues of social significance or collective significance are categorised as issues of macroeconomics. These are distinct from the issues of microeconomics which revolve around the problems of choice confronted by microeconomic units like a household, a firm or an industry.

                                                Microeconomics and Macroeconomics

Microeconomics deals with economic issues or economic problems related to microeconomic units like a household, a firm or an industry. These issues and problems are studied and addressed largely with a view to maximising individual welfare. Macroeconomics deals with economic issues or economic problems at the level of economy as a whole. These issues or problems are studied and addressed keeping in mind the goals of social welfare or collective welfare.

2. WHAT IS STATISTICS? Even to a layman this should not be a difficult question. If asked to define Statistics, we can expect a layman to say that Statistics is something like a store of quantitative information. Yes, it is true. Statistics means quantitative information or quantification of the facts and findings. But, how do we get quantitative information? There must be a system, method or technique to collect quantitative information. Also, statistical information may be a raw information. It needs to be classified, tabulated or it needs to be systematically presented. One must learn the system of presentation and classification of data. Also, there must be a set of methods and techniques to condense the data. May be, we find averages or percentages. And above all, there must be a set of methods or techniques on the analysis and interpretation of quantitative information. A student of economics has to study all these methods and techniques to understand and master the subject matter of Statistics.

Thus, unlike a layman, a student of economics cannot relax taking Statistics just as a pool of quantitative information. Instead he is also to look into the methods or techniques relating to its collection, classification, presentation, analysis as well as interpretation.

In view of such a vastness of the subject matter, Statistics is defined both in singular sense and plural sense, as under:

Statistics—A Plural Noun In its plural sense, Statistics refers to information in terms of numbers or numerical data, such as Population Statistics, Employment Statistics, Statistics concerning Public Expenditure, etc. However, any numerical information is not Statistics. Example: Ram gets Rs. 100 per month as pocket allowance is not Statistics (it is neither an aggregate nor an average) whereas average pocket allowance of the students of Class X is Rs. 100 per month, or there are 80 students in Class XI compared to just 8 in Class XII of your school are Statistics.

The following table shows a set of data which is Statistics, and another set which is not Statistics. The figures used are hypothetical.

Distinction between Quantitative and Qualitative Data This is related to the distinction between quantitative variables and qualitative attributes. There are quantitative variables like income, expenditure and investment which can be expressed in numerical terms, viz., per capita income in India was (say) Rs. 40,000 per month, per capita expenditure was (say) Rs. 30,000 per month, and net investment (or capita formation) was (say) Rs. 10,000 crore in the year 2017-18. All such data are called quantitative data. On the other hand, there are qualitative attributes like ‘IQ’ level of different individuals or beauty of the individuals which cannot be expressed in numerical terms.

These attributes refer to qualitative characteristics of the objects. These can be ranked or rated as good, very good, or excellent. We may give them ranks as 1, 2, 3, etc. All such data are called qualitative data. Briefly, while quantitative data refers to quantitative variables, qualitative data refers to qualitative attributes of the different objects.

Thus: All Statistics are data, but all data are not Statistics. Definition In its plural sense, this is how Statistics is defined by different authors: “Statistics are numerical statements of facts in any department of enquiry placed in relation to each other. ”  —Bowley “By Statistics we mean quantitative data affected to a marked extent by multiplicity of causes. ”  —Yule and Kendall Features or Characteristics of Statistics in the Plural Sense or as Numerical Data Main characteristics of Statistics in terms of numerical data are as follows:

(1) Aggregate of Facts:  A single number does not constitute Statistics. No conclusion can be drawn from it. It is only the aggregate number of facts that is called Statistics, as the same can be compared and conclusions can be drawn from them. For example, if it is stated that there are 1,000 students in our college, then it has no statistical significance. But if it is stated that there are 300 students in arts faculty, 400 in commerce faculty and 300 in science faculty in our college, it makes statistical sense as this data conveys statistical information. Similarly, if it is stated that population of India is 121 crore or that the value of total exports from India is Rs. 14,41,420 crore, then these aggregate of facts will be termed as Statistics. It can, therefore, be concluded ‘All Statistics are expressed in numbers but all numbers are not Statistics’.

(2) Numerically Expressed:  Statistics are expressed in terms of numbers. Qualitative aspects like ‘small’ or ‘big’; ‘rich’ or ‘poor’; etc. are not called Statistics. For instance, to say, Irfan Pathan is tall and Sachin is short, has no statistical sense. However, if it is stated that height of Irfan Pathan is 6 ft and 2-inches and that of Sachin is 5 ft and 4-inches, then these numericals will he called Statistics.

(3) Multiplicity of Causes:  Statistics are not affected by any single factor; but are influenced by many factors. Had they been affected by one factor alone then by removing that factor they would lose all their significance. For instance, 30 per cent rise in prices may have been due to several causes, like reduction in supply, increase in demand, shortage of power, rise in wages, rise in taxes, etc.

(4) Reasonable Accuracy:  A reasonable degree of accuracy must be kept in view while collecting statistical data. This accuracy depends on the purpose of investigation, its nature, size and available resources.

(5) Mutually related and Comparable:  Such numericals alone will be called Statistics as are mutually related and comparable. Unless they have the quality of comparison they cannot be called Statistics.

For example, if it is stated “Ram is 40 years old, Mohan is 5 ft tall, Sohan has 60 kg of weight”, then these numbers will not be called Statistics, as they are not mutually related nor subject to comparison. However, if the age, height and weight of all the three are inter-related, then the same will be considered as Statistics.

(6) Pre-determined Objective:  Statistics are collected with some pre-determined objective. Any information collected without any definite objective will only be a numerical value and not Statistics. If data pertaining to the farmers of a village is collected, there must be some pre-determined objective. Whether the Statistics are collected for the purpose of knowing their economic position, or distribution of land among them or their total population, or for any other purpose, all these objectives must be pre-determined.

(7) Enumerated or Estimated:  Statistics may be collected by enumeration or are estimated. If the field of investigation is vast, the procedure of estimation may be helpful. For example, 1 lakh people attended the rally addressed by the Prime Minister in Delhi and 2 lakh in Mumbai. These Statistics are based on estimation. As against it, if the field of enquiry is limited, the enumeration method is appropriate. For example, it can be verified by enumeration whether 20 students are present in the class or 10 workers are working in the factory.

(8) Collected in a Systematic Manner:  Statistics should be collected in a systematic manner. Before collecting them, a plan must be prepared. No conclusion can be drawn from Statistics collected in haphazard manner. For instance, data regarding the marks secured by the students of a college without any reference to the class, subject, examination or maximum marks, etc., will lead to no conclusion. In short, it can safely be concluded that “all numerical data cannot be called Statistics but all Statistics are called numerical data. ”

Statistics-A Singular Noun In the singular sense, Statistics means science of Statistics or statistical methods. It refers to techniques or methods relating to collection, classification, presentation, analysis and interpretation of quantitative data.

Focus of the Study Statistics as a singular noun is focus of the study for the students of Class XI. You are to learn and understand how to collect data, organise data, present data as well as analyse and interpret data.

Definition “Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data. ”  —Croxton and Cowden

“Statistics is the science which deals with the collection, classification and tabulation of numerical facts as a basis for the explanation, description and comparison of phenomena. ” — Lovitt  “

Statistics is the science which deals with the methods of collecting, classifying, presenting, comparing and. interpreting numerical data, collected to th row some light on any sphere of enquiry. ”  —Seligman

Stages of Statistical Study Studying Statistics as a singular noun implies the knowledge of various stages of statistical study. These stages are:

Obviously, at the first stage, we collect statistical data. Second, we organise the data in some systematic order. Third, we present the data in the form of graphs, diagrams or tables. Fourth, we analyse the data in terms of averages or percentages. Fifth, and finally, we interpret the data to find certain conclusions.

Statistical Tools Each stage of the statistical study involves the use of certain standard techniques or methods. These techniques or methods are called statistical tools. Thus, there are statistical tools used for the collection of data, like the ‘Sample’ and ‘Census’ techniques. Array of data and tally bars are the standard techniques used for organisation of data. Tables, graphs and diagrams are the well-known statistical tools for the presentation of data.

Averages and percentages are the commonly used techniques for the analysis of data. Interpretation of data is often done in terms of the magnitude of averages, percentages or coefficients of correlation/regression. The following table gives an overall view of the various stages of statistical study and the related sets of statistical tools.

What are Statistical Tools?  These refer to the methods or techniques used for the collection, organisation and presentation of data, as well as for the analysis and interpretation of data. Stages of Statistical Study and the Related Statistical Tools

3. SCOPE OF STATISTICS Study of the scope of statistics includes: (1) Nature of Statistics, (2) Subject Matter of Statistics, and (3) Limitations of Statistics. Nature of Statistics Here, the basic question is whether Statistics is a science or an art. Prof. Tippet, has rightly observed that “Statistics is both a science as well as an art.” As a science, Statistics studies numerical data in a scientific or systematic manner. As an art, Statistics relates to quantitative data to the real life problems. By using statistical data, we are able to analyse and understand real life problems much better than otherwise. Thus, the problem of unemployment in India is more meaningfully analysed when the size of unemployment is supported with quantitative data.

Subject Matter of Statistics Subject matter of statistics includes two components: Descriptive Statistics and Inferential Statistics.

The Concept of Universe or Population It should be interesting for the students of Clsss XI to note that the concept of universe or population has a specific meaning in Statistics. It refers to the aggregate of all items or units relating to your statistical study. Example:

Universe or population size is 1,000 if you are studying 1,000 students for your statistical study.

(1) Descriptive Statistics:  Descriptive Statistics refers to those methods which are used for the collection, presentation as well as analysis of data. These methods relate to such estimations as ‘measurement of central tendencies’ (average mean, median, mode), ‘measurement of dispersion’ (mean deviation, standard deviation, etc.), ‘measurement of correlation’, etc. Example: Descriptive statistics is used when you estimate average height of the secondary students in your school. Likewise, descriptive statistics is used when you find that marks in science and mathematics of the students in all classes are intimately related to each other.

(2) Inferential Statistics:  Inferential Statistics refers to all such methods by which conclusions are drawn relating to the universe or population on the basis of a given sample. (In Statistics, the term universe or population refers to the aggregate of all items or units relating to any subject.) For example, if your class teacher estimates average weight of the entire class (called universe or population) on the basis of average weight of only a sample of students of the class, he is using inferential statistics.

Limitations of Statistics In modern times. Statistics has emerged to be of crucial significance in all walks of life. However, it has certain limitations. Thus, writes Newshome that, “Statistics must be regarded as an instrument of research of great value but barring severe limitations which are not possible to overcome.” Following are some notable limitations of Statistics:

(1) Study of Numerical Facts only:  Statistics studies only such facts as can be expressed in numerical terms, it does not study qualitative phenomena like honesty, friendship, wisdom, health, patriotism, justice, etc.

(2) Study of Aggregates only:  Statistics studies only the aggregates of quantitative facts. It does not study statistical facts relating to any particular unit. Example: It may be a statistical fact that your class teacher earns Rs. 50,000 per month. But, as this fact relates to an individual, it is not to be deemed as a subject matter of Statistics. However, it becomes a subject matter of Statistics if we study income of school teachers across all parts of the country, for purpose of finding regional differences in income.

(3) Homogeneity of Data, an essential Requirement:  To compare data, it is essential that statistics are uniform in quality. Data of diverse qualities and kinds cannot be compared. For example, production of food grains cannot be compared with the production of cloth. It is because cloth is measured in meters and food grains in tonnes. Nevertheless, it is possible to compare their value instead of the volume.

(4) Results are True only on an Average:  Most statistical findings are true only as averages. They express only the broad tendencies. Unlike the laws of natural sciences, statistical observations are not error-free. They are not always valid under all conditions. For instance, if it is said that per capita income in India is Rs. 50,000 per annum, it does not mean that the income of each and every Indian is Rs. 50,000 per annum. Some may have more and some may have less,

(5) Without Reference, Results may Prove to be Wrong:  In order to understand the conclusions precisely, it is necessary that the circumstances and conditions under which these conclusions have been drawn are also studied. Otherwise, they may prove to be wrong.

(6) Can be used only by the Experts:  Statistics can be used only by those persons who have special knowledge of statistical methods. Those who are ignorant about these methods cannot make sensible use of statistics. It can, therefore, be said that data in the hands of an unqualified person is like a medicine in the hands of a quack who may abuse it, leading to disastrous consequences. In the words of Yule and Kendall, “Statistical methods are most dangerous tools in the hands of an inexpert.”

(7) Prone to Misuse:  Misuse of Statistics is very common. Statistics may used to support a pre-drawn conclusion even when it is absolutely false. It is usually said, “Statistics are like clay by which you can make a god or a devil, as you please.” Misuse of statistics is indeed its greatest limitation.

4. FUNCTIONS AND IMPORTANCE OF STATISTICS IN ECONOMICS Following words of Prof. Tippet very aptly capture the importance of Statistics in economics: “A day might come when the department of economics in the universities will go out of the control of economic theoreticians and come under the control of statistical workshops, in the same manner as the department of physics and chemistry have come under the control of experimental laboratories.” Indeed, Statistics has emerged as the lifeline of economics. It is because of the growing use of Statistics by the economists that the subjects like econometrics have been added to the horizons of economics. Students of Class XI may note the following points to highlight the significance (functions and importance) of Statistics in economics.

(1) Quantitative Expression of Economic Problems: Consider any economic problem, be it the problem of unemployment, the problem of price rise or the problem of shrinking exports. The first task of the economists is to understand its magnitude through its quantitative expression.

For example, if it is the problem of unemployment, we make its quantitative expression stating that (say) 20 per cent of the India’s working population is unemployed or that between the years 1995-2010 the percentage of unemployed working population has tended to increase from 18 per cent to 9.4 per cent.

(2) Inter-sectoral and Inter-temporal Comparisons:  Economists do not stop merely at the quantitative expression of the problems. They would try to further comprehend it through inter-sectoral and inter-temporal comparisons. From inter-sectoral comparisons we mean, comparisons across different sectors of the economy. Thus, analysing the problem of unemployment, the economists would like to know the magnitude of unemployment across rural and urban sectors of the economy. They would like to know what percentage of rural population is unemployed compared to the urban population. Inter-temporal comparison means understanding of change in the magnitude of the problem over time. This would mean making a comparison (say) over different plan periods of the rural and urban unemployment.

(3) Working out Cause and Effect Relationship: Economists try to find out cause and effect relationship between different sets of data. This enables them to attempt an effective diagnosis of the problem and accordingly to suggest some effective remedies. Thus, through their statistical studies, if the economists come to know that it is because of the decline in demand that investment in the economy has tended to shrink, they can suggest the government to adopt such measures as would increase the level of demand in the economy.

Two Important points on the Significance of Statistics in Economics (i) Statistics facilitates inter-sectoral and inter-temporal comparison. (ii) Statistics helps to establish cause and effect relationship between different economic variables that have facilitated the construction of economic theories.

(4) Construction of Economic Theories or Economic Models:  What is economic theory? It is an established statistical relationship between different sets of statistical data, offering conclusions of economic significance. The well-known inverse relationship between price of a commodity and its demand (i.e., more is purchased when price falls) is an established statistical relationship, and therefore, is a part of economic theory. Is the construction of theoretical relationships or models possible without statistical experiments? Certainly not. (5) Economic Forecasting:  Economists do forecasting through statistical studies. By the term forecasting we do not mean some astrological predictions. We only mean to assess and ascertain the future course of certain events which are of economic significance. Thus, on studying the behaviour of price level over several years, the economists can make statistical forecasting about the likely trend or pattern of the price level in the near future. This helps us in future planning. (6) Formulation of Policies:  How does the finance minister decide to increase or decrease taxation as a source of government revenue? Obviously through statistical studies. It is through statistical investigations that the finance minister gets a feedback on the taxpaying capacity of the people, and revenue needs of the government. Accordingly, tax rates are fixed to get maximum possible revenue with minimum possible discomfort to the people. (7) Economic Equilibrium:  What is economic equilibrium? It is a state of balance for the producer or the consumer where the producer finds that his profits are maximum or where the consumer finds that his satisfaction is maximum. It is through the use of statistical methods that the economists have evolved some eco-fundamentals (which you will study in Class XII) telling us how profits of the producers are maximised or how consumers get maximum satisfaction. Thus, so much is the significance of Statistics in economics that Marshall (a great economist of the past century) had to concede that “Statistics are the straw out of which I, like every other economist, have to make bricks.” Surely, Statistics is the hub of the wheel of economic studies, and the beginners of Class XI must focus on the hub to precisely understand the movement of the entire wheel.

Statistical Methods are No Substitute for Common Sense This is a statement of caution to the students of Statistics. It urges the students not to use Statistics devoid of their common sense. You may find some spurious relationships, like larger the number of doctors in an area greater are the deaths in that area. It may be true statistically, but does not match with common sense. Hence, never propagate any statistical conclusion in case it offends your common sense. Likewise, average size of shoes for the 50 students in your class may be ‘six’. But it would be foolish if the school authorities place an order of 50 shoes of the size-six for all of you. Surely this size may not fit many of you.

Distrust of Statistics Some people have misgivings about Statistics and make observations like the following: (i) Statistics is a rainbow of lies. (ii) Statistics are tissues of falsehood. (iii) Statistics can prove anything. (iv) Statistics cannot prove anything. (v) Statistics are like clay of which you can make a god or a devil, as you please. According to Disraeli, “There are three kinds of iies-lies, damned lies and Statistics.”

Indeed, one can present statistical information in a manner that tends to distort the facts and thereby mislead the people. For instance, the government claimed that in 2018, per capita income in India increased by about 17 per cent. On the other hand, the opposition party claimed that in 2018, per capita income increased by 5 per cent only. But the difference lies in the fact that whereas government estimates are based on current prices, those of the opposition party are based on the 2011-12 prices, it is difficult for a layman to understand this difference. He will just be confused or perhaps be fooled by the claims and counterclaims of the government and the opposition party.

What Causes Distrust? Distrust of Statistics arises not because there is anything wrong with Statistics as a subject matter. It arises because the users of Statistics tend to manipulate it to suit or support their pre-drawn conclusions or observations. Main causes for the distrust of Statistics are as under: (i) Different kinds of Statistics are obtained in respect of a given problem. (ii) Statistics can be altered to match the predetermined conclusions. (iii) Authentic Statistics can also be presented in such a manner as to confuse the reader. (iv) When Statistics are collected in a partial manner, the results are generally wrong. Consequently, people lose faith in them.

However, it may be noted that if Statistics are presented wrongly, then the fault does not lie with Statistics as a subject matter. The fault lies with those people who collect wrong Statistics or those who draw wrong conclusions. Statistics, as such, do not prove anything. They are simply tools in the hands of the statisticians. If a statistician misuses the data, then the blame lies squarely on him and not on the subject matter, A competent doctor can cure a disease by making good use of the medicine but the same medicine in the hands of an incompetent doctor becomes a poison. The fault in this case is not of the medicine but of the unqualified doctor. In the same way, Statistics is never faulty but the fault lies with the users.

In fact, Statistics should not be relied upon blindly nor distrusted outright. “Statistics should not be used as a blind man uses a lamp post for support rather than for illumination, whereas its real purpose is to serve as illumination and not as a support.”

In making use of Statistics one should be cautious and vigilant. In the words of King, “The science of Statistics is the most useful servant, but only of great value to those who understand its proper use.”

It is the duty of the students of economics to make use of know-how of Statistics to discover the truth rather than to cover the truth.

How to Remove Distrust? Following are some essential remedies of the distrust of Statistics: (i) Consideration of Statistical Limitations:  While making use of Statistics, limitations of Statistics must be taken care of. (ii) No Bias:  The user should be impartial. He should make use only of the relevant data and draw conclusions without any bias or prejudice. (iii) Application by Experts:  Statistics should be used only by the experts to minimise the possibility of misuse.

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Assignments For Class 11 Mathematics Statistics

Assignments for Class 11 Mathematics Statistics have been developed for Standard 11 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 11 Mathematics Statistics from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 11 Mathematics Statistics. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Statistics book and get good marks in class 11 exams.

Assignments for Class 11 Mathematics Statistics as per CBSE NCERT pattern

All students studying in Grade 11 Mathematics Statistics should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Statistics exam for standard 11. We have made sure that all topics given in your textbook for Mathematics Statistics which is suggested in Class 11 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 11 Mathematics Statistics

• Solving Assignments for Mathematics Statistics Class 11 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignment given in your class by Mathematics Statistics teacher for class 11 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Statistics class test
• You will be able to revise all topics given in the ebook for Class 11 Mathematics Statistics as all questions have been provided in the question banks
• NCERT Class 11 Mathematics Statistics Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 11 Mathematics Statistics teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 11 Mathematics Statistics Assignments PDF.

You can download free assignments for class 11 Mathematics Statistics from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 11 Mathematics Statistics from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 11, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

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Yes all test papers for Mathematics Statistics Class 11 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

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Statistics and probability

Unit 1: analyzing categorical data, unit 2: displaying and comparing quantitative data, unit 3: summarizing quantitative data, unit 4: modeling data distributions, unit 5: exploring bivariate numerical data, unit 6: study design, unit 7: probability, unit 8: counting, permutations, and combinations, unit 9: random variables, unit 10: sampling distributions, unit 11: confidence intervals, unit 12: significance tests (hypothesis testing), unit 13: two-sample inference for the difference between groups, unit 14: inference for categorical data (chi-square tests), unit 15: advanced regression (inference and transforming), unit 16: analysis of variance (anova).

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CBSE Worksheets for Class 11 Maths

CBSE Worksheets for Class 11 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 11 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 11 Maths Worksheets for the students of Class 11. All our CBSE NCERT Class 11 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 11 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 11 Maths Number of Worksheets: 42

CBSE Class 11 Maths Worksheets PDF

All the CBSE Worksheets for Class 11 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 11 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 11 Maths Worksheet. CBSE Worksheets for Class 11 Math can also use like assignments for Class 11 Maths students.

Binomial Theorem

• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 1
• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 2

Complex Numbers and Quadratic Equation

• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 1
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 2
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 3
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 4
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 5
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 6

Conic Sections

• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 1
• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 2

Introduction To 3Dimensional Geometry

• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 1
• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 2

Linear Inequalities

• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 1
• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 2

Permutations and Combinations

• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 1
• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 2

Principle of Mathematical Induction

• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 1
• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 2

Probability

• CBSE Worksheets for Class 11 Mathematics Probability Assignment 1
• CBSE Worksheets for Class 11 Mathematics Probability Assignment 2

Relations and Functions

• CBSE Worksheets for Class 11 Mathematics Relations and Functions Assignment

Sequences and Series

• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 4
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 5
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 6
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 7
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 8
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 1
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 2
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 1
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 2

Straight Lines

• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 1
• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 2

Trigonometric Ratios

• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 1
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 2
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 3
• CBSE Worksheets for Class 11 Mathematics Mathematical Reasoning Assignment

Advantages of CBSE Class 11 Maths Worksheets

• By practising NCERT CBSE Class 11 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 11 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 11 Math Worksheets encourages classroom activities.

Worksheets of CBSE Class 11 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 11 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 11 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 11 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 11 Math revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 11 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 11 Math Worksheets to secure good score.

CBSE Worksheets For Class 11

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How to Perform Well in Your Online Statistics Class

Table of Contents

Online learning has brought convenience and flexibility to students’ lives. Hence, it has become increasingly prevalent. However, when it comes to online statistics classes, one needs to have a unique approach, unlike traditional classes. Only effective strategies, planning, and dedication can help you get through your online statistics class without much difficulty. So, if your statistics class make you feel overwhelmed then don’t worry! You are not alone and we have got you covered. With the right strategies, we can excel in this challenging subject. In this blog by All Assignment Help , we will learn about tips that will help you perform well in your online statistics class.

Understand the Course Structure

The very first step to succeeding in any subject matter is to understand the structure of the course well. When you are aware of the syllabus, course material, and other requirements, it makes your learning hassle-free. In addition to this, you have to keep yourself updated with all the deadlines, exams, assignments, quizzes, etc. Knowing and having an understanding of course structure also helps students in planning their study schedule effectively.

Moreover, are you worried about your online statistics class? Are too many assignments leaving you with no time to focus on the lectures? Are you facing any technical issues which are preventing you from taking your online statistics class? Regardless of your reason, the ultimate problem of not being able to attend your statistics online classes should be dealt with. Therefore, when you are left with no option, you can hire an online expert to take your online class on your behalf. You can find a long list of websites offering the service when you google your queries like, how can I find an expert to take my online statistics class ? Once the list appears in front of you, choose the best website depending on its reviews, cost-effectiveness, etc. Moreover, provide the experts with information like your login details. After this, the experts will take your class on your behalf keeping the internet safety protocol in mind. 

Stay Organized and Engage Actively

If you are wondering what is stopping you from being successful in your online statistics class, then there are chances you have not organized the study space yet. A cluttered study space would not let you focus on your goal as there will be so many distractions in the environment. Therefore, it is needed to have a dedicated study space free from any kind of distractions. Moreover, it will help you focus on your coursework solely. Furthermore, you can use planners, calendars, online tools, etc. to keep track of study sessions, due dates, assignments, and a lot more. Also, you can break your work into manageable portions so that you do not procrastinate.

Alongside being organized, it is important that you actively participate in your online statistics class discussions and forums, etc. Active engagement with your classmates and teachers will also help you in developing a sense of community. Moreover, it will effectively enhance your knowledge of statistical concepts as you are exchanging ideas now.

Also read: How to Excel in Your Online Programming Classes?

Seek Clarification and Practice Regularly

Some students never clear their doubts regarding statistics complex topics. There can be hesitation or sometimes students just feel embarrassed to ask questions. However, leave everything behind and it’s time to seek clarification even when you come across a minute problem in the subject. Never hesitate to reach out to your teacher or professor if you need any clarification on any topic of the course material. Professors are there to help you understand the subject through and through. Furthermore, most online statistics classes offer various means of communication, for example, virtual office hours, email, discussion boards, etc. You can use any of these communication media to clear your doubts. Doing so will help you prevent any misunderstanding regarding the subject and facilitate your learning process.

Apart from clarifying your doubts, it is also needed that you practice statistics regularly. The subject requires consistent practice. So, give it all it needs. In order to do so, you can dedicate specific time to yourself in the day to study and practice your problems. Moreover, there are online resources, textbooks, and supplementary materials that you can use to keep your understanding of statistics techniques and key concepts clear. Also, during your online statistics class, if you get assignments then do not forget to complete them on time. It affects your performance. However, if you find it complex to deal with the assignment alone, you can ask for assignment help online from websites to assist you with excellent quality work.

Use Interactive Tools

There are multiple interactive tools and software available on the internet to help you learn statistics during your statistics online class. Moreover, you will get simulations, practice exercises, and tutorials on various online platforms with which you can learn to apply the methods of statistics in real-world situations. Furthermore, these hands-on experiences will make your problem-solving skills better and deepen your subject understanding. Also, if there are reasons becoming hurdles in your online learning journey then you can hire an online class helper to take your class on your behalf. They will provide you with class notes that will support your subject learning.

Also read: How to Study for the SAT

Form Study Groups  

If you have complex topics that you want to understand easily then forming a study group is the best way to do so. When you share and discuss things with your peers in the study groups , it helps you in easy understanding of the complex topics. Moreover, you can discuss study strategies and review course material together. Studying together is a great way for mutual learning. Furthermore, it helps in the easy reinforcement of the concepts.

Practice Self-Assessment and Stay Motivated

Self-assessment is needed to check your progress. Keeping a regular check of your progress during your online statistics class helps you in overcoming the loopholes of learning. Moreover, you can review your past assignments, exams, and quizzes to check where you are lacking in the subject. Furthermore, identify areas where you think you need to work harder and give yourself and the topic some extra time to strengthen your understanding of those topics. With the help of self-assessment, you do not only track your growth but also tailor your study approach.

Now comes keeping yourself motivated. In order to do so, you can set realistic goals and milestones and encourage yourself to work on them. Regardless of how small or big your achievements are, celebrate them. Also, make sure you have a positive attitude towards learning. Keep reminding yourself that statistics is important and relevant in various fields. Furthermore, seek assignment writing help in case of academic complexity.

Seek Additional Resources

If there are particular challenges you are facing with the concepts in your statistics online class or you think you need extra help never hesitate to look for additional resources like academic support services, online tutorials, textbooks, etc. Because these additional resources can enhance your subject understanding and clarify complex topics.

Conclusion  

In conclusion, you need to be diligent, engage much in your class, and apply effective study strategies if you wish to be successful in your online statistics class. When you follow these tips and remain loyal to your learning goals, nothing can stop you from getting through the virtual learning environment with confidence and achieving success in your online statistics class. Also remember, if you master statistics it will not only enhance your analytical skills but expose you to a plethora of career opportunities in data research, analysis, and beyond.

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What Students Are Saying About Why School Absences Have ‘Exploded’

Chronic absenteeism has increased in American schools since the Covid-19 pandemic. We asked teenagers what they make of the trend.

By The Learning Network

Nationally, an estimated 26 percent of public school students were considered chronically absent last school year, up from 15 percent before the Covid-19 pandemic, according to the most recent data, from 40 states and Washington, D.C., compiled by the conservative-leaning American Enterprise Institute.

The increases have occurred in districts big and small, and across income and race.

In “​ Why School Absences Have ‘Exploded’ Almost Everywhere ,” Sarah Mervosh and Francesca Paris explain:

The trends suggest that something fundamental has shifted in American childhood and the culture of school, in ways that may be long lasting. What was once a deeply ingrained habit — wake up, catch the bus, report to class — is now something far more tenuous. “Our relationship with school became optional,” said Katie Rosanbalm, a psychologist and associate research professor with the Center for Child and Family Policy at Duke University.

In a related Student Opinion question , we asked teenagers if that explanation resonated with them. Had their relationship to school — and school attendance — changed since the pandemic? And if so, what did they make of this shift?

Many students said, yes, school feels different now. Why? They pointed to remote learning changing their routines, an increase in anxiety and a decrease in motivation, the ease of making up schoolwork online and much more. Read their responses in full below.

Thank you to everyone who participated in the conversation on our writing prompts this week, including students from Central Bucks South High School in Warrington, Pa .; Norwood High School in Norwood, Mass.; and West Salem High School in Salem, Ore.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

Remote learning made students comfortable with missing school.

I believe that there are two main contributors to missing school too much. The first is online school. Myself included. It was very easy to simply leave the call after taking attendance and the teacher wouldn’t realize. Skipping class was easy and you could still get high grades. Transitioning back to real school, kids still held that true. They knew that they could miss school and still do well because covid taught that to them. The second reason is punishment. When you miss school, nothing happens. Class goes on and you have a little extra homework the next day but that’s it. What is the issue with missing class is a very common thought and it’s true. There is very minimal downside to missing school. When I had surgery, I missed a full week of school and within a day and a half, I was fully caught up again. Missing school has just become all too easy.

— Xavier, Pennsylvania

2020 was when our lives completely changed for the worst. We all had to stay inside and stay separate from each other. It was terrible, not being able to talk to my friends, and seeing the death toll on news constantly rise. However, after a year into the pandemic, I believe students realized the power they now had, including me. Now that I am a highschooler, I am going to admit that sometimes I would just mute my class and do whatever I wanted. School became shorter and easier to pass than ever before. That’s why when we all transitioned back into school, it was weird. We all still wanted to get through class the “easy way,” yet now that we were back, it wasn’t possible. This is why we started increasing our absences. The threat of absence has become weak, students are not as afraid to stay out of school. Furthermore the threat of being infected gave just one more reason to be out of school, for the sake of “preventing others from getting sick,” when in reality you feel fine. That is most likely why the absences in school had an exponential increase.

— Joshua, Pennsylvania

Students feel like expectations are lower than they were before the pandemic.

As a student in high school, I’ve come to realize the horrible state our attendance has been in since the pandemic. The reason can be simplified into one idea: laziness. We are lazy, willing to do only enough to get by, no more, no less. If a student doesn’t need to come to a class to obtain the grade they wish to achieve, then they won’t show up. Classes are not challenging enough to make students feel that they are worth going to. My mom is used to getting texts from me during the school day, begging to be excused from a class where “we’re doing nothing” or, “I already finished the work,” which is true, yet I abuse the opportunity to miss class because I know there will be no greater coincidence, I will still be getting an A. Due to my laziness, I would rather be at home taking a nap than sitting in a class with no greater impact on my life.

— Clara, Salem, Oregon

Since the pandemic, schooling has been focused on getting students caught up to where we’re supposed to be. Consequently, more allowances are made for students who don’t do assignments or don’t even show up. And with the switch to all online because of the pandemic, things have never shifted back. If a student misses a day or even a week, they can easily see what they missed and do it and submit it from home. With this option giving them the exact same grade as it would if they actually went to school, it’s no wonder why students are choosing to stay at home or skipping class. Additionally, the pandemic had heightened anxiety levels in students, specifically social anxiety, making them less likely to show up. The allowances made by the school district for students has created a space for students to be lazy and get away with it. This is fostering a negative impact on student work ethic not only now, but also in the future when this generation will be entering the work force.

— Emma, West Salem High School

The period of school shutdowns got students out of their school routines.

When I think back to virtual learning, my brain automatically goes to how stress free it was. I was in sixth grade when Covid first hit and going through a period of my life where I was extremely anxious at school. I believe that this break is exactly what I needed at the time. However, I do believe that in the long run, this online learning time period got a lot of people into the routine of not having a routine. A lot of people at my school would turn their camera off and fall asleep or go on their phones during online learning. I believe that there were times that I did this as well. I also think that this mindset carried through into the grades where I did not have an online/hybrid option. In eighth and ninth grade, I happened to stay home sick, go into school late, or leave early a lot. I think this is due to me not taking school as seriously due to the grading methods that were being used and how some of my teachers were not grading harshly. Now that I am a sophomore in high school, I think I have finally gotten back into the routine of actual schooling and not staying home sick unless I actually feel extremely sick.

— Madison, Pennsylvania

Before the pandemic and as I was growing up, I was the kind of student that wanted perfect attendance. For some odd reason, it made me feel like a better student if I never missed a day. This included turning my parents down when they offered me to go on trips, even though I was only in fourth grade and the work that I would have missed wouldn’t have made an impact in my academic career. However, after the pandemic school began to feel optional. We felt what it was like to fall out of the routine that going to school was and were never able to fully recover from it. I think that having experienced attending school from your bed, in your pajamas has played a major role in the current trend of students receiving more absences. For me, it made me realize that the “0” next to your number of absences didn’t matter as much as I had once thought. As a now highschooler, the school days are long and every class requires an abundance of work and undivided attention that whenever there is a substitute or not much going on, it is easy to decide to leave school. With senior year approaching, everything’s purpose is college and the fact that colleges aren’t able to see how many absences a student has when they apply, does play a role in the increasing number of absences.

— Ava, Miami Country Day School

Because assignments and other materials are online, students find they can keep up with their classes even if they don’t attend school.

Schools have adjusted rules so much that it makes school feel optional. Don’t want to attend class publicly? Take online classes. Don’t want to take “required” state testing? Opt out. Before, school seemed strict, we didn’t have the option to opt out of tests, we didn’t think of taking online school. Yet now, schools make it so easy to skip because everything is simply online. Our assignments, lectures, and teachers are all online. There are no longer requirements in school. What’s the point of attending if we can graduate without taking state testing or attending advisory — also a requirement, yet I no longer have an advisory because my counselors said I don’t need to take it to graduate. It’s confusing. Students have been enabled for over 4 years now since quarantine started. School doesn’t feel mandatory, it’s optional. I’m currently enrolled into 2 AP classes, so I try my best not to miss school. But it’s inevitable, I get sick, I have family situations or maybe I simply don’t feel like attending school. But I see people skip school like nothing. “I didn’t feel like going” is a constant statement I hear. Not many students have the motivation to attend, and simply don’t go because they have a comfort in their head that they can graduate while missing multiple days of school nearly everyday.

— Olivia, Salem, OR

Current absenteeism rates have significantly impacted my learning experience for the past few years. Since the pandemic, there has been a noticeable shift in the perception of the value of education and whether or not attendance is an important factor in a student’s academic success. In the years following 2020, I found myself struggling to make it to class everyday due to my new found efficiency of working at home with my computer. I felt that even if I was not in class personally, I would be able to keep up with my work easily as it was all online regardless. Due to this I would go on trips or skip class purely because I was under the impression that I would be able to continue achieving virtually.

— Ruby, RFHS

Before the pandemic, my attendance was stable but after the pandemic, my absences were piling on. It was difficult to get back in the rhythm of in person school when I had already done a whole year online, but now my attendance in school is definitely getting better. On the other hand, students in my school tend to miss school and it is a rare sight to see a full class. Some students go as far as showing up to class once a week and just do the classwork online. After the pandemic, schools went from paperwork to all online, which is a big reason why students miss all the time, knowing that school work can just be done at home. It has definitely affected students’ grades and goals in life, but hopefully in the future, absences can lower back down.

— Emily, Atrisco Heritage Academy High School

Going to school, and finding the motivation to have as good an attendance record as possible, now feels like more of a struggle.

As students, we’ve developed a comfort in staying in bed during school without having to get ourselves ready to go outside. We had the ability to wake up five minutes before “school” started to get on our zoom calls. Now, we must wake up an hour and a half prior, and make breakfast and pack lunch, before driving to school. The process is tenuous as the article states, but because we’ve accustomed to a different lifestyle, it just makes this one seem like so much more work. I, myself have noticed my difference in attendance after COVID-19. I used to be very obsessed with perfect attendance, but I had 11 absences in my sophomore year, right after coming back from online school. Nowadays, I’m more lenient on myself when it comes to taking a mental health day, because the process can be overwhelming. School is very important, so of course I try to always come in, but sometimes it can be hard. I have not noticed this trend in the world, as well as with myself until this article. It’s enlightening to know that this had not only an effect on me, but all over the country. Hopefully the rates of absenteeism will decrease as time goes on, because we are the future.

— Anisha, New Jersey

Before virtual learning, I never made much of a habit of not turning in work or showing up for class. It was so much easier then but since virtual learning, it had become incredibly difficult for me to focus as well as keep up motivation to continue school. It was easy to skip and nobody really said much about it so it easily became a bad habit. That bad habit eventually leaked into normal school as well and it always sounds so much easier to break out of than it actually is.

— Tayy, NRHS

As the average high school class skipper (only sometimes), in my personal experience, missing out on classes hasn’t really been because of mental health concerns, but more of just lasting laziness from the pandemic. I feel as though I was relatively hard working in middle school/elementary but after a few years off with only half effort assignments, I have grown to become more sluggish and reluctant when it comes to more advanced work while in school. And it makes the option of missing out on classes because of my own reluctance a lot more appealing.

— Luke, Bali, Indonesia

My schedule during the week is get up, get ready for school, go to school, go home, do homework, go to sleep and then I repeat that everyday for 5 days. As much as I don’t want to dread going to school, it’s exhausting having the same schedule repeated everyday of the week. While in school, you have assignments assigned nearly everyday. I feel as though school has had a change in its meaning because of the COVID-19 pandemic. While in quarantine, we were looking at a screen for the whole day and lacked motivation to get assignments done. When we shifted to in person school again, it didn’t change. I now look at school as a task that I need to complete to shape my future. I need to have all my assignments perfect and turned in on time. The meaning of school has turned into a draining task rather than a place that you look forward to going to.

— Jamisan, Salem, Oregon

Some students face challenges in attending class that may have nothing to do with the pandemic.

I don’t believe that students are skipping because it is so easy to catch up and pass, despite their absences. In fact, I know that a lot of people who skip aren’t passing most of their classes. They do this because their parents don’t hold them accountable, and there is always something deeper going on in that student’s life that makes it that much harder for them to find the motivation to go to class. I don’t think making the classes harder will hold students more accountable, but in fact deter them from going to class at all. If a student is aware that they are failing and doesn’t understand the concept of the class, and the class proceeds to become harder, they are going to quickly become unmotivated to go to class in the first place, feeling out of place compared to the other — passing — students in the class. While I don’t have a solution for this problem, myself, I feel that the problem is much broader than we suspect, and the answer will be a much deeper journey to find.

— Kylie, West Salem HS

Schools can do more to get students back in class.

I attend a French school in London and attendance is closely monitored. Absences have to be justified by your parents or you could get into trouble. I think it’s important to attend school as we did before Covid - because as well as learning the curriculum, it is crucial to socialise with your friends and classmates, which is good for your mental health … I wonder if social media could be a factor? If students did not have access to social media or the internet, would they prefer to be in school with their friends? This increase in absenteeism could affect students’ chances of getting into University when they come to finish school or even their opportunities later in life. Students need to be reminded of this more and more perhaps. School helps you to learn not just about facts but also helps to build your emotional quotient & social intelligence — which are all valuable for life.

— Alexandre 14, London

As a current high school junior, my experiences with skipping have been minimal at best, however, I feel strongly that the reason behind skipping is pretty simple. Students don’t care as much about school and the system encourages it. When faced with the choice of sitting in a class and learning about the Patagorian theorem or hanging out with friends, many students are now choosing the latter. The lack of care or effort being put forth in school doesn’t even affect their grades! This is due to certain classes having minimal grades set at 50%, which is 10% away from a pass. This system is actively encouraging people to put minimal effort into a class just to get a pass and graduate. Removing courses like this would certainly raise the importance of getting the work done. Another solution to this problem would be having attendance as a grade, if your grade depends on you being in classes then most would show up. If you have to show up to class to pass then more students would be inclined to do so. The emphasis is on not bending the knee to people who don’t want to show up to class, not giving them a minimal 50%, we should mark attendance for a passing grade, and letting them fail. If we keep letting students skip with minimal consequences then their attitudes won’t change and thus hinder our students’ growth.

— Henry, Salem, OR

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