important questions from presentation of data class 11

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CBSE Presentation of Data Class 11 MCQs of Statistics for Economics Chapter 4

Presentation of data class 11 mcqs: find here multiple choice questions and answers for cbse class 11 statistics for economics chapter 4, presentation of data. these have been prepared as per cbse’s latest syllabus 2023-2024..

Presentation   of Data Class 11 MCQs: This article consists of a list of 10 Multiple Choice Questions (MCQs) for CBSE Class 11 Statistics for Economics Chapter 4, Presentation of Data. Also, find attached a PDF download link for the same. Students don’t have to worry while referring to this list since they are completely based on the updated CBSE Syllabus 2023-2024 curriculum. They can use this list as a source of practice for the preparation of annual examinations.

• Easy form of assessment
• Less time consuming
• Tests in-depth knowledge
• Develops soft skills like brainstorming, problem-solving, critical thinking, and lateral thinking
• Covers multiple aspects of theory for assessment
• It can be easily analyzed
• On-the-spot feedback/result
• Mobile-friendly

Here, we have mentioned some of the most important benefits of MCQs. You can find many more such by actually involving in the process of solving MCQs. It is essential for students to practice MCQs and develop a habit of solving them within the deadlines, which happens to be the most critical task for students under pressure.

CBSE Class 11 Economics Syllabus 2023-2024

CBSE Class 11 Economics Deleted Syllabus 2023-2024(PDF)

Revision Notes for Class 11 Economics 2023-2024

MCQs for CBSE Class 11 Economics Collection of Data (2023-2024)

MCQs for CBSE Class 11 Economics Organization of Data (2023-2024)

MCQs for CBSE Class 11Economics Presentation of Data (2023-2024)

MCQs for CBSE Class 11 Statistics for Economics Chapter 4, Presentation of Data are presented below:

1. Which of the following is not a method of presenting data?

(a) Tabulation

(b) Diagrammatic representation

(c) Statistical analysis

(d) None of these 

2. Which of the following is not a basis for the classification of a table?

(a)According to time

(b) According to space

(c) According to size

(d) According to the order 

3. Which of the following is not a graphical method of presenting data?

(a) Bar diagram

(b) Pie chart

(c) Histogram

(d) Frequency polygon

4. Which of the following is not a limitation of tabulation?

(a) It is not suitable for large data sets.

(b) It is not suitable for comparing data sets.

(c) It is not suitable for presenting data in a clear and attractive manner.

5. Which of the following is not a limitation of diagrammatic representation?

(a) It is not suitable for presenting large data sets.

(d) It is not suitable for showing the relationship between different variables. 

6. The number of rows in a table is known as the _______.

(d) Columns 

7. The number of columns in a table is known as the _______.

(d) Rows 

8. The title of a table is placed _______.

(a) Above the table

(b) Below the table

(c) In the middle of the table

9. The headings of the rows and columns of a table are called _______.

(a) Captions

(c) Subtitles

10. The data in a table is arranged in _______ order.

(a) Sequential

(b) Alphabetical

(c) Numerical

CBSE Class 11 Syllabus 2023-24 (All Subjects)

CBSE Class 11 Deleted Syllabus 2023-24 (All Subjects)

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Chapter 4 Presentation of Data (Statistics)

Important questions for class 11 economics (statistics) chapter 4 presentation of data.

HT expert teachers having years of teaching experience for class 11 Economics (Statistics) prepared Important Questions for Class 11 Economics (Statistics) Chapter 4 Presentation of Data. These Important Questions for Chapter 4 Presentation of Data consists of detailed solutions and explanation as per the CBSE Board recommendations. Read the Chapter 4 Presentation of Data before solving the questions asked in the Important Questions sheet prepared and uploaded by HT experts and solve all the questions of sheet Chapter 4 Presentation of Data by yourself. Use Important Questions for Class 11 Economics (Statistics) Chapter 4 Presentation of Data for the final revision of your unit test or final exam for Chapter 4 Presentation of Data. Check out chapter-wise Important questions for class 11 Economics before solving this do solve NCERT Exercise with the help of HTs NCERT Solutions for class 11 Economics . 

Find below the pdf for Important Questions for Class 11 Economics (Statistics) Chapter 4 Presentation of Data 

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• NCERT Solutions for Class 11 Statistics Chapter 4 - Presentation Of Data
• NCERT Solutions

NCERT Solutions for Class 11 Statistics Chapter 4 - Presentation of Data

Commerce students of Class 11 have Statistics as one of the core subjects in their curriculum. When it comes to Statistics, students require an in-depth understanding of each concept. Regular practice and revision are equally essential to score well in this subject. Thus, apart from textbooks , students also need proper reference material for the lessons. NCERT Solutions are an excellent resource to refer to for Statistics lessons. The first part of the Class 11 Economics syllabus is dedicated to Statistics. Part A or Statistics for Economics include:

Introduction

Collection, Organisation, and Presentation of Data

Statistical Tools and Interpretation

NCERT Solutions for Class 11 Statistics Chapter 4 Presentation of Data

Chapter 4 in this section, is the Presentation of Data. NCERT solutions for class 11 statistics for economics chapter 4 is also available, which covers every topic of the concerned chapter.

Data Can Be Represented In Two Forms. They Are As Follows

Textual Presentation

Tabular Presentation

Diagrammatic Presentation

In a textual presentation of data, data form a part of the text or description pf the subject matter. The tabular presentation of data, on the other hand, shows a systematic presentation of numerical data. The tabular presentation includes various components. They are:

Table number

Body or field

Under diagrammatic presentation, bar diagrams are one of the most popular types of data presentation. Different types of bar diagram are:

Simple Bar Diagram

Multiple Bar Diagram

Percentage Bar Diagram

Sub Divided Bar Diagram

All of the above topics have been serially detailed in NCERT solutions class 11 statistics chapter 4. The 15 questions included in this chapter provide a proper insight into “Presentation of Data’.

Questions Given in the NCERT Solutions for Class 11 Statistics for Economics Chapter 4

Each question in the NCERT solutions is followed by a precise, appropriate, and relevant answer. The answers which are given in the solution also follow the CBSE pattern of the exam. This helps students get a brief idea regarding the types of questions they might face in the final exams. Here’s a gist of all the questions included in the Statistics class 11 NCERT solutions chapter 4:

Question 1: The very first question in this chapter of NCERT solution is regarding bar diagrams. The question asks whether the bar diagram is a one-dimensional, two-dimensional or non-dimensional diagram. Bar diagrams are single-dimensional. Although it contains two axes in the form of rectangular bars, the width plays no role in data presentation. Only length plays a part in bar diagrams.

Question 2: The second question NCERT solutions for class 11 statistics for economics chapter 4 is directed towards histograms. It asks students the use of histograms. Histograms are used to represent the value of mode of frequency distribution through graphs with the help of the highest rectangle.

Question 3: The third question is regarding ogives. It asks if ogives can be helpful in graphically locating the mean, mode, or median. The answer to this question would be ‘median’. The point of intersection of more than and less than ogives shows the median of data.

Question 4: The 4 th question is NCERT solutions class 11 statistics chapter 4 asks what data represented through arithmetic line graph depict. The options in this question include ‘long-term trend’, ‘cyclicity in data’, and ‘seasonality in data’. Arithmetic line graph assists in understanding the periodicity and trend observed in long-term continuous data.

Question 5: The 5 th question is based on a true/false statement. The statement given is whether the width of bars in a bar diagram can be unequal. This statement is, however, false. The rectangular bars in a bar diagrams need to be of equal width for any given data.

Question 6: The statement given in this question is ‘Width of rectangles in a histogram should essentially be equal’. It is a false statement. The width of rectangles in a histogram can be uneven.

Question 7: Here, the statement in question is ‘Histogram can only be formed with a continuous classification of data’. This is a true statement. Histograms are always drawn for continuous data. Even if the given data is discrete or discontinuous, it is first changed into continuous form to form a histogram.

Question 8: The statement in this question is Histograms and column diagram are a similar way of presentation of data. However, this is a false statement. The histogram is a two-dimensional diagram which is drawn for continuous data. The rectangles do not have any space between them. On the other hand, the column diagram is a one-dimensional diagram which has space between each column or bar. 

Question 9: The 9 th question has ‘Mode of a frequency distribution can be known graphically with the help of histogram’ as a statement. This statement in NCERT solutions for class 11 statistics for economics chapter 4 is true. The rectangle with the highest measure in a histogram gives the value of mode of a frequency distribution. 

Question 10: The statement given in this question is that the median of a frequency distribution cannot be assessed from the ogives. This is false. The point of intersection of less than along with more than ogives shows the median.

Question 11: The 11 th question in this chapter asks students to provide relevant forms of diagrams to represent different data. There are three sub-parts to this question. They are:

Monthly annual rainfall

Composition of Delhi’s population by religion

Components of the factory’s expenses

The relevant answers to the above questions are bar diagram, component bar diagram, and a pie chart respectively.

Question 12: This question in NCERT solutions for class 11 statistics for economics chapter 4 would require students to represent data in a tabular form. The question provides data related to the share of non-workers and lower urbanisation level in India.

Question 13: The 13 th question is how the procedure of drawing histograms differ when class intervals are unequal compared to equal class intervals in a frequency table.

Question 14 and Question 15 also include data, based on which students will have to form a relevant presentation.

Students can find the PDF of the Statistics lessons in the Vedantu App. The App also provides a free download option of NCERT solutions for class 11 statistics for economics chapter 4. Along with that, students also get online classes, one-on-one guidance, and revision notes to prepare well for exams.

FAQs on NCERT Solutions for Class 11 Statistics Chapter 4 - Presentation Of Data

1. What are the different ways of representing data?

Ans: Data can be presented in the form of text, table or diagrams. It depends on the nature and category of data being represented. Under diagrammatic presentation of data, there can be different types. They are bar diagram, pie or circular diagram, frequency diagram data, histogram, polygon, frequency curve, arithmetic line graph, ogive or cumulative curve, etc.

2. What are the advantages of diagrammatic or graphical presentation of data?

Ans: Many times the diagrammatic presentation of data is considered more convenient over the other forms. So, the advantages of diagrammatic and graphical presentation of data include:

Informative and catchy

Simple to understand

Easy to compare data

Needs less training or specialisation to create graphs

Helps in the study of correlation

3. Which types of questions are provided in the NCERT solutions for class 11 statistics for economics chapter 4?

Ans: Chapter 4 in Class 11 Statistics NCERT solutions includes 15 questions. Some of these questions are conceptual and objective. A few questions in this chapter are based on a ‘true or false’ statement. In some questions, students will have to represent the data given to them.

 4. What is Chapter 4 of the Class 11 Statistics textbook about?

Ans: The chapter talks about the presentation of data. Data is the information that is collected and needs to be organized to study a hypothesis or to reach a conclusion. The chapter mentions textual presentation, tabular presentation as well as diagrammatic presentation of data. The data when presented makes it easier to study and analyze and it is also more appealing to the eyes. Data presented in a clear manner makes it easy to understand. 

5. Is Chapter 4 of Class 11 Statistics important?

Ans: The chapter of the Statistics textbook of Class 11 is titled as Presentation of data. The chapter enables us to understand how one can present and analyze the data. We all, consciously or unconsciously, deal with data, arrange it and use it for getting better results. Understanding the presentation of data also allows us to smartly plan our studies and preparation as well as allows us to understand how we can utilise minimum resources to achieve maximum results. The knowledge gained from the chapter will come in handy in education and in real life.

6. How can I approach the chapter Presentation of Data of Class 11 Statistics?

Ans: The chapter is a part of your statistics textbook and is also a crucial part of the border economics discipline. Understanding the concepts given in the chapter will also facilitate to an extent your understanding of economics. You can start by reading the chapter and understanding the various methods of presenting the data. Make useful notes in your notebook along with the visual representation of the methods. You should also attempt the questions given at the end of the chapter. Make sure you revise your notes on a regular basis.

7. How useful are Vedantu solutions for the preparation of Chapter 4 Presentation of Data of Class 11 Statistics?

Ans: When you are studying Statistics, it is imperative that you have a strong understanding of the core concepts of the discipline. The solutions which are prepared by the expert faculty at Vedantu helps you to clear any doubts or confusion you might have with regard to the concepts of the chapter. They will also come in handy during revision as they cover the chapter in its entirety. You will also get a basic idea about how one should write and present the answers. These solutions are available at free of cost on Vedantu(vedantu.com) and mobile app. 

8. Explain diagrammatic presentation of data.

Ans: The diagrammatic presentation of data is one of the methods through which you can present the data. The data is presented in a comprehensible form that makes the data easy to comprehend and analyze. In this method, numbers or numerical data are represented through diagrams. The diagrammatic presentation can be further categorized into bar graphs, pie charts or circular diagrams, frequency diagrams, and arithmetic line graphs. It is also an attractive way of presenting the data and catches the attention of the reader.

RBSE Class 11 Economics Important Questions Chapter 4 Presentation of Data

Rajasthan Board  RBSE Class 11 Economics Important Questions  Chapter 4 Presentation of Data Important Questions and Answers. 

Rajasthan Board RBSE Solutions for Class 11 Economics in Hindi Medium & English Medium are part of RBSE Solutions for Class 11 . Students can also read RBSE Class 11 Economics Important Questions for exam preparation. Students can also go through RBSE Class 11 Economics Notes to understand and remember the concepts easily.

Very Short Answer Type Questions

Presentation Of Data Class 11 Important Questions Question 1. What is meant by presentation of data? Answer: The presentation of data means exhibition of the data in a clear and attractive manner such that they can be easily understood and analysed. 

Presentation Of Data Class 11 Extra Questions And Answers Question 2.  When is it suitable to use textual presentation of data? Answer: It is suitable to use textual presentation of data when the quantity of data is not too large.

Presentation Of Data Class 11 Numericals Question 3.  What is a table? Answer: A table is the organisation of data in rows and columns.

Presentation Of Data Class 11 Questions And Answers Question 4.  Define tabulation?         Answer: Tabulation involves an orderly and systematic presentation of numerical data to elucidate the problem under consideration.

Class 11 Statistics Chapter 4 Important Questions With Answers Question 5.  Name the classifying variable in temporal classification.  Answer: Time is the classifying variable in temporal classification.

Questions On Presentation Of Data Class 11 Question 6.  Give the examples of classifying variables in spatial classification. Answer: The examples of classifying variables in spatial classification are village, district, state and country, etc.

Presentation Of Data Questions And Answers Question 7.  List the main components of a table. Answer: The main components of a table are: (i) Table number     (ii) Title     (iii) Captions or column headings (iv) Stubs or row headings     (v) Body of the table (vi) Unit of measurement (vii) Source note     (viii) Footnote

Tabular Presentation Of Data Class 11 Questions Question 8.  Write a feature of the ‘title’ of a table. Answer: The title of a table has to be very clear, brief and carefully chosen so that clear interpretations could be derived from the table.

Presentation Of Data Class 11 Question Bank Question 9.  Give another name for column and row heading in the table. Answer: Column heading is also known as caption and row heading is also known as stub.

Presentation Of Data Class 11 Extra Questions Question 10.  How is the location of a figure determined in a table? Answer: The location of a figure in a table is determined by the row and column of the table.

Class 11 Statistics For Economics Chapter 4 Important Questions Question 12.  List the different kinds of diagrams. Answer: The different kinds of diagrams are: (i) Geometric diagrams - bar diagram and pie diagram (ii) Frequently diagrams - histogram, frequency polygon, frequency curve and ogive (iii) Arithmetic line diagram or time-series graph

Class 11 Statistics Chapter 4 Questions And Answers Question 13.  How are data presented in bar diagram? Answer: In bar diagrams, data are presented in the form of bars or rectangles.

Questions On Tabular Presentation Of Data Question 14.  List the variables which can be best represented by bar diagram? Answer: Discrete variables such as family size, grades in an exam, etc. and attributes such as gender, religion, caste, etc. can be best represented by bar diagram.

Presentation Of Data In Statistics Questions And Answers Question 15.  State the use of multiple bar diagram. Answer: Multiple bar diagrams are used to show two or more sets of data simultaneously.

Statistics For Economics Class 11 Chapter 4 Questions And Answers Question 16.  What is a component bar diagram? Answer: A component bar diagram represents the bar and its sub-divisions into two or more components.

Question 17.  Why is there no open space between two consecutive rectangles of a histogram?     Answer: While preparing a histogram, the lower class boundary of a class interval coincides with the upper class boundary of the previous interval. Thus, all the rectangles are adjacent and there is no open j space between two consecutive rectangles.          Question 18.  Define frequency polygon. Answer: Frequency polygon is a plane connected by line segments, formed by joining the middle-top points of all rectangles in a histogram.

Question 19.  What type of distribution is represented by an ogive? Answer: An give represents cumulative frequency distribution.

Question 20.  How is arithmetic line graph prepared? Answer: Time is plotted along x-axis and the value of the variable along y-axis. The plotted points are joined to obtain arithmetic line graph.

Short Answer Type Questions

Question 1. State the advantages and disadvantages of textual presentation of data. Answer: Advantages of Textual Presentation of Data (i) It provides useful and supportive evidence to the text in case of small volume of data. (ii) It enables one to emphasise the important points of the presentation. Disadvantage of lextual Presentation of Data (i) It requires going through the complete text to draw facts.

Question 2.  Write the important features of tabulation. Answer: The important features of tabulation are as below: (i) It organises the raw data, making it easy and definite. (ii) It makes data comparable. (iii) It facilitates calculation of statistical indices and data analysis. (iv) It clearly indicates the features of the data.

Question 3.  Explain the various types of tables. Answer: The various types of tables are explained below: (i) One-way Table: This type of table presents only single characteristic of the data. For example, a table showing the number of students in a college.  (ii) Two-way Table: It presents two features of data simultaneously. For example, a table showing the male and female population of a village. (iii) Three-way Table: This table presents three features of the data. For example, presentation of population of a village on the basis of age, gender and education.

Question 4.  Explain temporal classification of data with the help of an example. Answer: In temporal classification, data is classified with reference to time such as days, weeks, months, quarters, years, etc. The table below shows the exports of Maruti Suzuki cars in terms of years. Here, the classifying characteristic is year and takes values in the scale of time.

Question 6. State the rules for constructing diagrams.     Answer: Following are the rules for constructing diagrams:     (i) The diagram should be drawn strictly according to the scale.     (ii) Title of diagram should not only be easy, definite and attractive but also self-explanatory.  (iii) Necessary instructions and colours should be used along with their clarification. (iv) The use of words and numbers should be minimum.     (v) Diagram should be neatly bordered with thick and double lines.     (vi) Diagram should always be easy and understandable.     (vii) Diagram formation should always be from left to right and up to down.     (viii) Basis of data should be clearly mentioned.    

Question 7. Write the features of bar diagrams. Answer: The main features of bar diagrams are: (i) Height of bar diagram changes with the change in the frequency. (ii) Width of all the bars is same. (iii) Bars can be drawn either vertically or horizontally. (iv) The distance between the bars should be equal.

Question 8. Explain the various types of bar diagrams. Answer: The various types of bar diagrams are explained below: (i) Simple Bar Diagram: In simple bar diagrams, data are presented through equi-width and equidistant bars or rectangles. Bars of different heights are made corresponding to a particular characteristic, say population, production, literacy, etc. at various points of time or of different states to construct a simple bar diagram.

(ii) Multiple Bar Diagram: Multiple bar diagrams are used to show two or more sets of data simultaneously. For example, sales and profits, exports and imports, production of vegetables and foodgrains can be shown using multiple bar diagrams.

(iii) Component Bar Diagram: A component bar diagram represents the bar and its sub-divisions into two or more components. It is very useful in comparing the sizes of different components. For example, distribution of population into males, females and children; expenditure pattern in a typical Indian family; etc.

Question 9. What are the different types of component bar diagrams. Answer: There are two types of component bar diagrams: (i) Simple Component Bar Diagram: It helps in comparing the size of various elements or components and also shows relationship between the integral parts. These are represented in absolute values. Comparative bars are differentiated with colours or shades.

(ii) Percentage Component Bar Diagram: The area of the bar is proportionally divided among various sets of data or components. It is used when the values have high magnitude. The value of total bar length is considered as 100 and value of all the items is calculated as percentage and presented in the form of diagram.

Question 10.  Differentiate between simple bar diagram and histogram. Answer: Following are the points of difference between simple bar diagram and histogram:

Question 11. Write the steps to determine mode graphically. Answer: The steps to determine mode graphically are given below: (i) Represent the given data in the form of a histogram. The height of the rectangles in the histogram shows the frequencies of the class interval.  (ii) Identify the highest rectangle. The class interval corresponding to the highest rectangle is the modal class of the series. (iii) Join the top left comer of the modal rectangle with top right comer of the rectangle on the right. Also, join the top right comer of the modal rectangle with top left comer of the rectangle on the left. (iv) Draw a perpendicular line from the point of intersection onto the x-axis. (v) The value at which the perpendicular meets the x-axis will give the mode.

Question 12. State the difference between: (i) ‘Less than’ and ‘more than’ ogive (ii) Frequency polygon and frequency curve Answer: (i)  In ‘less than’ ogive, frequencies less than the upper class limit are shown. On the other hand, in ‘more than’ ogive, frequencies greater than the lower class limit are shown. (ii) Frequency polygon is a plane connected by line segments, formed by joining the middle- top points of all rectangles in a histogram. On the other hand, frequency curve is a smooth freehand curve, which passes very closely through the points of the frequency polygon.

Question 13.  Write a short note on the quadrants of a graph. Answer: X-axis and Y-axis divide the graph paper into four parts. Each part is called a quadrant The numbers and their signs as marked in all the four quadrants of a graph are as follows:

Question 14.  Define diagrams. Are there any limitations of diagrammatic presentation of data? Explain. Answer: A diagram is a drawing that represents information and relationships. Though diagrammatic presentations are quite effective methods, they do have certain limitations. (i) Diagrams are only approximations.  (ii) Diagrams cannot represent minute differences in values. (iii) Large differences in values can make the diagram look unattractive. (iv) They can present only limited data. (v) Minor mistake in studying measurement unit may produce wrong conclusion.

Question 15.  State the advantages of diagrammatic presentation of data,     Answer: Following are the advantages of diagrammatic presentation of data:     (i) Diagrams present data in an attractive manner.     (ii) Technical knowledge is not required to read diagrams.     (iii) Huge volume of data can be seen at a glance through diagrams.     (iv) Less time and efforts are required to interpret results using diagrams.     (v) Diagrams present the data in proper perspective.     (vi) Diagrams carry with them an effective impression.     Long Answer Type Questions

Frequency Distribution of Monthly Incomes of 50 Households in a Locality

(iii) Spatial Classification: In spatial classification, data is classified according to place. The table below shows data related to sugar production in different states of India.

(iv)Temporal Classification: In temporal classification, data is classified with reference to time such as days, weeks, months, quarters, years, etc. The table below shows the exports of Maruti Suzuki cars in terms of years:

Exports of Maruti Suzuki Car

Question 2.  Describe in detail the components of a table. Answer: The main components of a table are: (i) Table Number: An appropriate number should be assigned to a table for its identification and easy reference in future. It is given at the top or at the beginning of the title of the table. (ii) Title: It is a brief statement of the contents of the table. It is placed at the head of the table. The title should be short and complete. (iii) Stubs or Row Headings: It is the extreme left part of the table, which gives description of the matter presented in the rows. (iv) Captions or Column Headings: This is the upper part of the table giving description of different columns. (v) Body of the Table: It is the main component of the table which contains the numerical information. Each figure or data is kept in the box fixed by a row and column. (vi) Unit of Measurement The units of measurement of the figures in the table must be provided with the title. However, if different units are used for row and column, they must be stated along the stubs and captions. (vii) Source Note: It states the origin of the available information at the bottom of the table. (viii) Footnote: This component shows the explanations of specific items given in the table. 

Question 3. Explain the types of component bar diagram. Also, give numerical examples. Answer: Component bar diagrams are of two types:

(i) Simple Component Bar Diagram: It helps in comparing the size of various elements or components and also shows relationship between the integral parts. These are represented in absolute values. Comparative bars are differentiated with colours or shades. Example: The details of monthly expenditures of Family A and Family B are given. On the basis of this data, we will prepare a simple component bar diagram:

(ii) Percentage Component Bar Diagram: The area of the bar is proportionally divided among various sets of data or components. it is used when the values have high magnitude. The value of total bar length is considered as 100 and value of all the items is calculated as percentage and presented in the form of diagram.

Example: The details of population of City A and City B are given. On the basis of this data, we will prepare a percentage component bar diagram: 

The following are steps for the construction of a pie diagram: (i) Convert all the values as percentage of the total value. (ii) Find the corresponding value in degrees for each percentage value, using the formula \(\text { Angle }=\frac{\text { Percentage }}{100} \times 360^{\circ}\) (iii) Draw a circle of any radius. (iv) Present the converted angle into it by drawing a radius. In this method, cumulative angles are used.

Question 5.  How would you draw the histogram for unequal class intervals. Answer: Width of rectangles in the histogram varies if the class intervals in a distribution are unequal. In order to draw a histogram for unequal class intervals, the frequencies need to be rearranged by taking a ‘Correction factor as: Correction Factor   \(=\frac{\text { Class interval }}{\text { Least interval }}\)

After this, calculate the frequency density as: Frequency Density  \(=\frac{\text { Frequency }}{\text { Correction factor }}\) The frequencies so obtained are presented in the histogram. 

Question 6. Describe cumulative frequency curve or ogives. Answer:  Ogive is the curve constructed by plotting cumulative frequency data on the graph paper, in the form of a smooth curve. Cumulative frequency curve is of two types. (i) ‘Less than’ Ogive: In ‘less than’ ogive, the cumulative frequencies are plotted against the respective upper limits of the class intervals. (ii) ‘More than’ Ogive: In ‘more than' ogive, the cumulative frequencies are plotted against the respective lower limits of the class intervals 

Numerical Questions

Question 1. Draw a table to present the educated and uneducated population of India in the Census years 1951, 1961,1971, 1981, 1991 and 2001. Answer: The table below presents the educated and uneducated population of India:

Table 1: Educated and Uneducated Population of India (in %)

Table Population Distribution

Diagrammatic Presentation of Data

Higher Order Thinking Skills

Question 1. State the difference between table and tabulation. Answer:  While tabulation refers to the method or process of presenting data in the form of row and columns, table refers to the actual presentation of data in the form of row and columns. Table is the consequence of tabulation.

Question 2.  Does tabular presentation of data suffer any limitation? Answer:  Yes, tabular presentation of data suffers certain limitation. These are: (i) It is difficult for a layman to comprehend tables. (ii) It does not have a lasting impression. 

Question 3.  Give one point of difference and one point of similarity between frequency polygon and frequency curve. Answer:  Difference: All points in a frequency polygon are joined by using a foot rule while all points in a frequency curve are joined by freehand. Similarity: Both frequency polygon and frequency curve are drawn by joining mid-points of all the tops of a histogram.

Objective Type Questions

Question 1.  Under which type of classification is the collected data is grouped with reference to time? (A) Quantitative  (B) Qualitative (C) Spatial  (D) Temporal Answer: (A) Quantitative 

Question 2.  Caption’ stands for .............. (A) Numerical information  (B) Column headings (C) Row headings  (D) Table headings Answer: (B) Column headings

Question 3. In which form is the data presented in a pie diagram? (A) Percentages  (B) Degrees (C) Absolute value  (D) Fractions Answer: (B) Degrees

Question 4.  Which of the following diagram could be made with the help of histogram? (A) Frequency polygon  (B) Bar diagram (C) Pie diagram (D) Ogive   Answer: (A) Frequency polygon 

Question 5. In a circle, IX is equal to: ........ (A) I° (B) 6°  (C) 3.6° (D) 10° Answer: (C) 3.6°

Question 6. Which of the following is the formula of correction factor? (A)  \(\frac{\text { Class interval }}{\text { Least interval }}\) (B) Class interval + Least interval (C) Class interval x Least interval  (D) Class interval - Least interval Answer: (A) Question 7.  How is a frequency curve drawn? (A) Using ruler  (B) Using compasses (C) Using protractor  (D) Using freehand Answer: (D) Using freehand

Question 8.  How many types of ogives are there? (A) One  (B) Two (C) Three (D) Four Answer: (B) Two

Question 9.  Which statistical index can be determined with the help of ogives?  (A) Mean  (B) Median  (C) Mode  (D) Rank Correlation Answer: (B) Median 

Question 10.  Which of the following is calculated to make the results comparable when bases of a histogram vary in their width? (A) Absolute frequency  (B) Class frequency (C) Frequency density  (D) Cumulative frequency Answer: (C) Frequency density 

I. Fill in the blanks with correct answer.

I. A table is a systematic arrangement of data in ____ and 2. Footnote is written at the ______ of the table. 3. Spatial classification means classification of data according to ______ 4. Classification of data according to standard of education such as illiterate, primary, secondary, graduate, technical, etc. will be known as _______ classification. 5. In bar diagram, comparison is based on _______ of the columns. 6. Sub-diagram is also called _______ bar diagram. 7. In pie diagram, each component is multiplied by _______ 8. Ogives for more than type and less than type distribution intersect at _______ 9. The total area under the frequency curve represents the total _______ 10. In arithmetic line graph _______ is plotted along x-axis. Answers:  1. rows, columns  2. bottom  3. place/location  4. qualitative  5. height 6. component  7. 3.6  8. median  9. frequency  10. time

II. State whether the following statements are true or false.

I. We can use short-forms in the table. 2. A column designation given to explain figures of the column is called ‘caption’. 3. Source note is the last part of the table. 4. Bar diagrams are suitable both for frequency type and non-frequency type variables and attributes. 5. Larger components are given priority in parting the bar in sub-diagram. 6. If the class intervals are of equal width, the area of the rectangles is proportional to their respective frequencies. 7. Histograms can be drawn both for discrete and continuous variables. 8. Frequency polygon is an alternate name for frequency curve. 9. Frequency polygon may not necessarily pass through all the points of the frequency polygon. 10. Less than ogive is never increasing and more than ogive is never decreasing. Answers:  1. False  2. True  3. False  4. True  5. False  6. True 7. False  8. False  9. True  10. False

III. Match the following.

IV. Read the following statement- Assertion (A) and Reason (R). Choose one of the correct alternatives given below:

Assertion (A): Width of bars in a bar diagram need not be equal. Reason (R): Bar diagram comprises a group of equi width rectangular bars for each class of data. Alternatives: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Answer: (d) Assertion (A) is false and Reason (R) is true.

V. Read the following hypothetical case study,carefully and answer the following questions on the base of the same:

Bar diagram comprises a group of equispaced and equiwidth rectangular bars for each class or category of data. Height or length of the bar reads the magnitude of data. The lower end of the bar touches the base line such that the height of a bar starts from the zero unit. Bars of a bar diagram can be visually compared by their relative height and accordingly data are comprehended quickly.

Data for this can be of frequency or non-frequency type. In non-frequency type data, a particular characteristics, say production yield, population, etc. at various points of time or 6f different states can be noted and corresponding bars are made of the respective heights according to the values of the characteristics to construct the diagram. The values of the characteristics retain the identity of each value.

1. A ____ is a drawing that represents information and relationships. (diagram/information) 2. In ____ diagram, data are presented in the form of rectangles. (bar/pie) 3. Bar diagram is a ____ dimensional diagram. (one/two) 4. Bar diagram comprises a group of ____ width rectangular bars for each class of data. (equi/varying) Answers:  1. diagram  2. bar  3. one  4. equl

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NCERT MOST IMPORTANT QUESTIONS CLASS – 11 | Statistics for Economics IMPORTANT QUESTIONS | CHAPTER –4 Presentation of Data |EDUGROWN|

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• NCERT MOST IMPORTANT QUESTIONS CLASS…

Table of Contents

NCERT Most important question:

Q1.Define presentation of data.

Answer:  The presentation of data is a representation of data in an attractively and transparent manner that everybody understands and analyses.

Q2.What is tabulation?

Answer:  Tabulation means presenting data in tabular form.

Q3.Define table.

Answer:  Table refers to the systematic representation of data with rows and columns.

Q4.Explain a simple table.

Answer:  A simple table only displays one characteristic of the data.

Q5.What is a complex table?

Answer:  It is a table that shows more than one characteristic of the data.

Q6.Define a derived table.

Answer:  A derived data is something where the information is not displayed according to the way it was collected. It is first into rations or percentages and then presented.

Q7.What are the two principal parts of a table?

Answer:  The two principal parts of a table are (i) Table number and (ii) Title

Q8.What are the different kinds of a table?

Answer:  Tables can be classified into three parts. (i) Purpose (ii) Originality, and (iii) Construction

Q9.What are the two types of complex table?

Answer:  The two types of a complex table are (i) Double or two-way table and (ii) Manifold table

Q10.What are a different forms of presentation of data?

Answer:  The different form of presentation of data are (i) Textual and descriptive presentation (ii) Tabular presentation, and (iii) Diagrammatic presentation

Q11. What kinds of diagrams are more effective in representing the following? (i) Monthly rainfall in a year (ii) Composition of the population of Delhi by religion (iii) Components of cost in a factory

Answer (i) Monthly rainfall in a year – simple bar diagram as only one variable i.e. monthly rainfall is to be present and compared visually. (ii) Composition of the population of Delhi by religion – Simple bar diagram Plotting different religion on the x-axis and the number of people on the y-axis, one can easily compare the number of the population religion-wise. (iii) Components of cost in a factory – Pie chart as entire circle represents the total cost and various components of costsare shown by different portions of the circle.

Q12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form? Answer

The number of rural non-workers is greater than urban non-workers. The higher number of rural non-workers indicates lower level of urbanisation in India according to 2001 Census data.

Q13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table? Answer When the class intervals are equal then by normal method we can make histogram which has equal width of rectangle. When the class intervals are unequal, heights of rectangles are to be adjusted to yield comparable measurements by using frequency density (class frequency divided by width of the class interval) instead of absolute frequency.

Q14. The Indian Sugar Mills Association reported that, ‘Sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why? (iii) Present these data diagrammatically. Answer

(ii) To present these data in diagrammatic form we can use multiple bar diagram because these are effective in comparing two or more sets of data.

Q15. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.

Represent the data as multiple time series graphs. Answer

Author:  Swati

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Important Questions: Presentation of Data | Economics Class 11 - Commerce PDF Download

Q1: What are the different forms of presentation of data? Ans: The different forms of data presentation are: 

• Textual and descriptive presentation: Describing data using words and sentences.
• Tabular presentation:  Organizing data into rows and columns for systematic analysis.
• Diagrammatic presentation:  Representing data using visual elements such as charts, graphs, and diagrams for easy understanding and comparison.

Q2: What is a complex table? Ans: A complex table is a type of table that presents more than one characteristic or set of data. Unlike a simple table, it displays multiple variables or categories, allowing for a more detailed and comprehensive analysis of the data. Q3: What is tabulation? Ans: Tabulation is the process of organizing and presenting data in a structured tabular form. It involves arranging data systematically into rows and columns, making it easier to compare, analyze, and draw conclusions from the information presented. Q4: How can tables be classified? Ans:  Tables can be classified based on three main criteria:

• Purpose: Determined by the objective of the table (e.g., comparison, correlation).
• Originality: Whether the data is directly collected or derived from existing sources.
• Construction:  The complexity of the table, ranges from simple tables displaying one characteristic to complex tables presenting multiple variables.

Q5: Define a derived table. Ans: In a derived table, data is not presented in its raw form as collected. Instead, the information is converted into ratios, percentages, or other derived measures before being displayed. This conversion allows for a standardized and comparative analysis of the data. Q6: What are the two principal parts of a table? Ans:  The two principal parts of a table are: 

• Table number: A unique identifier for the table.
• Title:  A brief description that summarizes the content or purpose of the table.

Q7: Define the presentation of data. Ans: Presentation of data refers to the clear and visually appealing representation of information in a manner that is easily understandable and analyzable by everyone. It involves transforming raw data into a format that effectively communicates trends, patterns, and insights to the audience. Q8: Define table. Ans:  A table is a systematic arrangement of data in rows and columns. It provides a structured format for presenting information, making it easier to comprehend and interpret the data. Tables are widely used in various fields to display quantitative and qualitative data. Q9: Define a simple table. Ans: A simple table displays only one characteristic or set of data. It presents information in a straightforward manner, typically featuring rows and columns representing a single variable or category. Q10: What are the two types of a complex table? Ans:  The two types of a complex table are:

• Double or two-way table:  Displays data related to two different variables, allowing for comparison and analysis of their relationship.
• Manifold table:  Presents data involving more than two variables, providing a detailed view of multiple aspects of the data.

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Collection of Data Class 11 Statistics Notes And Questions

Please refer to Collection of Data 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 Collection of Data Notes and Questions

Statistics means data or quantitative information capable of some meaningful conclusions. The present chapter focuses on the collection of data, including: (i) sources of data, and (ii) methods of collecting data. The purpose of data collection is to understand, analyse and explain a socioeconomic problem, for example, the problem of unemployment or the problem of poverty. While analysing the problem we also try to understand the causes behind the problem as also the possible solutions. The entire exercise needs a comprehensive support of numerical facts, called data.

1. PRIMARY AND SECONDARY SOURCES OF COLLECTION OF DATA There are two sources of collection of data: (i) Primary Source, and (ii) Secondary Source.

Primary Source : You want to know about the quality of life of the people in your town. You may like to ascertain the quality of life in terms of per capita expenditure of different households in your town. You decide to collect the basic data yourself through statistical survey(s), of course with the help of investigators or field workers. While doing this exercise you are relying on primary source of the data. Thus, primary source of data implies collection of data from its source of origin. It offers you firsthand quantitative information relating to your statistical study. You or your team of investigators are contacting the respondents (people offering basic information) and obtaining the desired quantitative information on per capita expenditure of different households in your town.

Primary source of data implies collection of data from its source of origin. It offers you first-hand quantitative information relating to your statistical study.

Secondary Source : Secondary Source of collection of data implies obtaining the relevant statistical information from an agency, or an institution which is already in possession of that information. To continue with the previous example, data relating to the quality of life of 

the people of your town (or the data on per capita expenditure) may have already been collected by the State Government. You can simply approach the concerned Government department and request for the desired information. This will be a Secondary Source of data for you. Thus, secondary source implies that the desired statistical information already exists and you are simply to collect it from the concerned agency or the department. You are not to conduct statistical survey(s) yourself and you are not to contact the respondents (people offering basic information). OT course, you are not getting first hand information relating to your statistical study. You are simply relying on the information which is already existing.

Secondary source of data implies collection of data from some agency or institution which already happens to have collected the data through statistical survey(s). It does not offer you first-hand information relating to your statistical study. You are to rely on the information which is already existing.

Primary and Secondary Data Primary source of collecting data offers you, ‘Primary Data’ and secondary source offers you Secondary Data’. Let us clarify the difference.

Primary Data: Data collected by the investigator for his own purpose, for the first time, from beginning to end, are called primary data. These are collected from the source of origin. In the words of Wessel, “Data originally collected in the process oj investigation are known as primary data.” Primary data are original. The concerned investigator is the first person who collects this information. The primary data are, therefore, a first-hand information. To illustrate, you may be interested in studying the socio-economic state of those students in your Class XI who secured first division in their matriculation examination. You collect information regarding their pocket allowance, their family income, educational status, their family members and the like. All this information would be termed as primary information or primary data, since you happen to be the first person to collect this information from the source of its origin. Secondary Data:  In the words of  M.M. Blair,  “Secondary data are those which are already in existence, and which have been collected, for some other purpose than the answering of the question in hand.” According to  Wessel , “Data collected by other persons are called secondary data.” These data are, therefore, called second-hand data. Obviously, since these data have already been collected by somebody else, these are available in the form of published or unpublished reports. For example, data relating to Indian Railways which are annually published by the Railway Board, would be secondary data for any researcher.

Principal Differences between Primary and Secondary Data

The following are some principal differences between primary and secondary data: (1) Difference in Originality:  Primary data are original because these are collected by the investigator from the source of their origin. Against this, secondary data are already in existence and therefore, are not original.

(2) Difference in Objective:  Primary data are always related to a specific objective of the investigator. These data, therefore, do not need any adjustment for the concerned study. On the other hand, secondary data have already been collected for some other 

purpose. Therefore, these data need to be adjusted to suit the objective of study in hand.

(3) Difference in Cost of Collection: Primary data are costlier in terms of time, money and efforts involved than the secondary data. This is because primary data are collected for the first time from their source of origin. Secondary data are simply collected from the published or unpublished reports. Accordingly, these are much less expensive.

Of course, it may be noted that, there are no fundamental differences between primary data and secondary data. Data are data, whether primary or secondary. These are classified as primary or secondary just on the basis of their collection: first-hand or second-hand. Thus, a particular set of data when collected by the investigator for a specific purpose from the source of origin, would be primary data. And the same set of data, when used by some other investigator for his own purpose, would be known as secondary data. Thus, Secrist has rightly pointed out, “The distinction between primary and secondary data is one of the degree. Data which are primary in the hands of one party may be secondary in the hands of other.’’

Primary and Secondary Data—The Basic Difference

■ If we are collecting data from its source of origin, for the first time, it is primary data.

■ If we are using data which have already been collected by somebody else, it is secondary data.

Note: If you are getting data from somebody else who collected it from its source of origin but did not use it for his own study, it will be deemed as primary data.

2. HOW BASIC DATA IS COLLECTED: SOME STATISTICAL METHODS/ MODES OF DATA COLLECTION

When basic data is to be collected from its primary source, how do we do it? It involves the study of a set of statistical methods or statistical techniques. The following are some of the well-known methods of collecting primary data:

(1) Direct Personal Investigation, (2) Indirect Oral Investigation, (3) Information from Local Sources or Correspondents, (4) Information through Questionnaires and Schedules

(i) Mailing Method, and (ii) Enumerator’s Method.

(1) Direct Personal Investigation  The direct personal investigation is the method by which data are personally collected by the investigator from the informants. In other words, the investigator establishes direct relation with the persons from whom the information is to be obtained. The success of this method, however, requires that the investigator should be very diligent, efficient, impartial and tolerant.

Direct contact with the workers of an industry to obtain information about their economic conditions is an example of this method.

Suitability This method of collecting primary data is suitable particularly when: (i) the field of investigation is limited or not very large. (ii) a greater degree of originality of the data is required. (iii) information is to be kept secret. (iv) accuracy of data is of great significance, and (v) when direct contact with the informants is required.

Merits Data, thus, collected have the following merits: (i) Originality:  Data have a high degree of originality. (ii) Accuracy:  Data are fairly accurate when personally collected. (iii) Reliability:  Because the information is collected by the investigator himself, reliability of the data is not doubted. (iv) Related Information:  When in direct contact with the informants, the investigator may obtain other related information as well. (v) Uniformity:  There is a fair degree of uniformity in the data collected by the investigator himself from the informants. It facilitates comparison. (vi) Elastic:  This method is fairly elastic because the investigator can always make necessary adjustments in his set of questions.

Demerits However, the method of direct personal investigation suffers from certain demerits, as

under: (i) Difficult to Cover Wide Areas: Direct personal investigation becomes very difficult when the area of the study is very wide. (ii) Personal Bias: This method is highly prone to personal bias of the investigator. As a result, the data may lose their credibility. (iii) Costly: This method is very expensive in terms of the time, money and efforts involved. (iv) Limited Coverage: In this method, area of investigation is generally small. The results are, therefore, less representative. This may lead to wrong conclusions.

Learning by doing   You are to conduct direct personal investigation on the quality of teaching in a school. Who are your informants? What difficulties do you expect to encounter in such an exercise?

(2) Indirect Oral Investigation Indirect oral investigation is the method by which information is obtained not from the persons regarding whom the information is needed. It is collected orally from other persons who are expected to possess the necessary information, these other persons are known as witnesses. For example, by this method, the data on the economic conditions of the workers may be collected from their employers rather than the workers themselves.

Suitability This method is suitable particularly when: (i) the field of investigation is relatively large. (ii) it is not possible to have direct contact with the concerned informants. (iii) the concerned informants are not capable of giving information because of their ignorance or illiteracy. (iv) investigation is so complex in nature that only experts can give information. This method is mosdy used by government or non-government committees or commissions.

Merits Some of the notable merits of this method are as under: (i) Wide Coverage: This method can be applied even when the field of investigation is very wide. (ii) Less Expensive: This is relatively a less expensive method as compared to Direct Personal Investigation. (iii) Expert Opinion: Using this method an investigator can seek opinion of the experts and thereby can make his information more reliable. (iv) Free from Bias: This method is relatively free from the personal bias of the investigator. (v) Simple: This is relatively a simple approach of data collection.

Demerits However, there are some demerits, as under: (i) Less Accurate:  The data collected by this method are relatively less accurate. This is because the information is obtained from persons other than the concerned informants.

(ii) Biased:  There is possibility of personal bias of the witnesses giving information. (iii) Doubtful Conclusions:  This method may lead to doubtful conclusions due to carelessness of the witnesses.

Difference between Direct Personal Investigation and Indirect Oral Investigation

The difference between direct personal investigation and indirect oral investigation is as under: (i) In the case  of direct personal investigation, the investigator establishes direct contact with the informants. On the other hand, in the case of indirect oral investigation, information is obtained by contacting other than those about whom information is sought. (ii) Direct Personal  Investigation is generally possible when the field of investigation is small. On the other hand, indirect oral investigation is generally preferred when the field of investigation is relatively large. (iii) In the Direct  Personal Investigation, the investigator must be well versed in the language and cultural habits of the informants. There is no such requirement in the case of Indirect Oral Investigation. (iv) Direct investigation is relatively costlier than the indirect investigation. (3) Information from Local Sources or Correspondents Under this method, the investigator appoints local persons or correspondents at different places. They collect information in their own way and furnish the same to the investigator.

Suitability

This method is suitable particularly when: (i) regular and continuous information is needed. (ii) the area of investigation is large. (iii) the information is to be used by journals, magazines, radio, TV, etc. and (iv) a very high degree of accuracy of information is not required.

Merits Principal merits of this method are as under: (i) Economical: This method is quite economical in terms of time, money or efforts involved. (ii) Wide Coverage: This method allows a fairly wide coverage of investigation. (iii) Continuity: The correspondents keep on supplying almost regular information. (iv) Suitable for Special Purpose: This method is particularly suitable for some specialpurpose investigations, e.g., price quotations from the different grain markets for the construction of Index Number of agricultural prices.

Demerits Following are some notable demerits of this method: (i) Loss of Originality: Originality of data is sacrificed owing to the lack of personal contact with the respondents. (ii) Lack of Uniformity: There is lack of uniformity of data. This is because data is collected by a number of correspondents. (iii) Personal Bias: This method suffers from the personal bias of the correspondents. (iv) Less Accurate: The data collected by this method are not very accurate. (v) Delay in Collection: Generally, there is a delay in the collection of information through this method.

(4) Information through Questionnaires and Schedules Under this method, the investigator prepares a questionnaire keeping in view the objective of the enquiry. There are two ways of collecting information on the basis of questionnaire: (i) Mailing Method, and (ii) Enumerator’s Method.

(i) Mailing Method Under this method, questionnaires are mailed to the informants. A letter is attached with the questionnaire giving the purpose of enquiry. It is also assured that the information would be kept secret. The informant notes the answers against the questions and returns the completed questionnaire to the investigator.

Suitability This method is most suited when: (a) the area of the study is very wide, and (b) the informants are educated.

Merits The following are the main merits of this method: (a) Economical: This method is economical in terms of time, money and efforts involved. (b) Original: This method is original and therefore, fairly reliable. This is because the information is duly supplied by the concerned persons themselves. (c) Wide Coverage: This method allows wide coverage of the area of study.

Demerits However, there are certain demerits of this method as under: (a) Lack of Interest:  Generally, the informants do not take interest in questionnaires and fail to return the questionnaires. Those who return, often send incomplete answers. (b) Lack of Flexibility:  This method lacks flexibility. When questions are not properly replied, these cannot be changed to obtain the required information. (c) Limited Use:  This method has limited use owing to the fact that the questionnaires can be answered only by the educated informants. Thus, this method cannot be used when the informants are uneducated. (d) Biased:  If the informants are biased, then the information will also be biased. (e) Less Accuracy:  The conclusions based on such investigation have only limited accuracy. This is because some questions may be difficult, and consequently accurate answers may not be offered. (ii) Enumerator’s Method Under this method, a questionnaire is prepared according to the purpose of enquiry. The enumerator himself approaches the informant with the questionnaire. The questionnaires which are filled by the enumerators themselves by putting questions are called schedules. Thus, under this method, the enumerator himself fills the schedules after seeking information from the informants. Enumerators are those persons who help the investigators in collecting the data. The enumerators are given training to fill the schedules and put the questions intelligently to obtain accurate information.

Suitability This method is mostly used when: (a) field of investigation is large. (b) the investigation needs specialised and skilled investigators, and (c) the investigators are well versed in the local language and cultural norms of the informants.

Investigator, Enumerator and Respondent ■ Investigator is a person who plans and conducts an empirical investigation independently or with the help of others. ■ Enumerator is a person who actually collects the desired statistical information or statistical data. Often the enumerators are trained personnel hired by the investigator for field work. ■ Respondent is a person who answers/responds to the set of questions included in the questionnaire.

Merits This method has the following merits: (a) Wide Coverage:  This method is capable of a wide coverage in terms of the area involved. Even illiterates can furnish the required information. (b) Accuracy:  There is a fair degree of accuracy in the results. This is because investigations are done by specialized enumerators. (c) Personal Contact:  Unlike in the case of mailing questionnaires, there is personal contact with the informants in this method. Accordingly, accurate and right answers are obtained. (d) Impartiality:  This method is impartial. This is because the enumerators themselves do not need the required information, so they are impartial to the nature of information that they obtain. (e) Completeness:  Schedules have the merit of completeness because these are tilled in by the enumerators themselves.

Demerits The following are the main demerits of this method: (a) Expensive:  This is a very expensive method of investigation because of the involvement of trained investigators. (b) Availability of Enumerators:  Competent enumerators may not be available. Accuracy of the information accordingly suffers. (c) Time Consuming:  Enumerators may need specialised training for particular investigation. The process of investigation thus becomes time consuming. (d) Not Suitable for Private Investigation:  Since this method is very expensive, it is generally not suitable for private investigation. This method is generally used by the Government institutions. (e) Partial:  If the enumerators are biased, then the data will not be accurate. Construction of Questionnaires and Schedules and their Qualities In the context of collection of Primary data, construction of questionnaires and schedules has the special significance.

The Basic Difference between a Questionnaire and a Schedule Both show a set of questions. But in case of a questionnaire, the answers are to be recorded/written by the respondents themselves, while in the case of a schedule, answers are to be written/recorded by the enumerators specifically hired for the purpose.

The set of questions in questionnaires and schedules are similar. The only difference that lies between the two is that, in questionnaires, the entire information is recorded by the informants themselves. In the schedules, on the other hand, the information as supplied by the informants is recorded by the enumerators.

Qualities of a Good Questionnaire Following are some of the desired qualities of a good questionnaire: (1) Limited Number of Questions: The number of questions in a questionnaire should be as limited as possible. Questions should be only relating to the purpose of enquiry. (2) Simplicity: Language of the questions should be simple, lucid and clear. Questions should be short, not long or complex. Mathematical questions must be avoided. (3) Proper Order of the Questions: Questions must be placed in a proper order. (4) No Undesirable Questions: Undesirable questions or personal questions must be avoided. The questions should not offend the informants. (5) Non-Controversial: Questions should be such as can be answered impartially. No controversial questions should be asked. (6) Calculations: Questions involving calculations by the respondents must be avoided. Investigator himself should do the calculation job. (7) Pre-Testing Pilot Survey: Some questions be asked from the informants on trial basis. If their answers involve some difficulty these can be reframed accordingly. Such testing is technically called pilot survey. (8) Instructions: A questionnaire must show clear instructions for filling in the form. (9) Cross Verification: Such questions may be asked which help cross verifications. (10) Request for Return: Request should be made to the respondents to return the questionnaire completed in all respects. The informant must be assured that the information conveyed by him will be treated as confidential.

Types of Questions: Some Examples There are four possible types of questions, as under: (1) Simple Alternative Questions:  These questions are answered in ‘Yes’ or ‘No’, ‘Right or Wrong’ and ‘Good or Bad.’ Example Do you have a car? Or Yes/No Government decides to introduce 10+2 system in the college. Do you agree? Yes/No

(2) Multiple Choice Questions :  When there are various possibilities of a particular event, multiple choice questions are generally asked. A number of possible answers are given for such questions. The informant is to tick-mark the one that he feels fit. Example What is your mode of conveyance from home to college? 1. On foot 2. Cycle 3. Bus 4. Scooter Correct answer be tick-marked (/) in the box. (3) Specific Information Questions:  Only specific information is obtained through such questions. Example In which class do you read? Or How much pocket allowance do you get? (4) Open Questions:  In such questions, the informant is requested to give his views on specific issues. Example How can prices in India be controlled? Or How can power shortage in the country be overcome?

Example of an Ideal Questionnaire Objective of this questionnaire is to know about the monthly income and expenditure of the 10+2 students living in the hostels. You are requested to fill in this questionnaire, and return at your earliest convenience. Information furnished in this questionnaire will be kept strictly confidential. The information will be used only for the present investigation. 1. Student’s Name 2. Age 3. Faculty …………………………….. Art/Commerce/Science 4. Name of the School I College 5. Father’s name and address 6. Father’s Occupation ……………………………. Income 7. Income (if any) of other members in the family 8. Monthly income received by the student (i) From the family …………………………………………………………………………………… …. (ii) Personal earning ………………………………………………………………………………….. (iii) Scholarship ………………………………………………………………………………………… (iv) Others ………………………………………………………….. .. ………………………………… 9. Monthly Expenditure of the Student Items of Expenditure                           Amount of Expenditure (i) School/College fee                          ……………………………………… (ii) Stationery                                     ……………………………………… (iii) Books                                          ……………………………………… (iv) Conveyance                                 ……………………………………… (v) Hostel expenses                            ……………………………………… (Vi) Entertainment                              ……………………. … …………… (vii) Other items (specify)                    ……………………………………… 10. Is your monthly income enough for you? Yes ………. No 11. If your monthly income is not enough, how do you propose to increase it? 12. Can you save anything from your monthly income? If yes, under which of the abovenoted heads of expenditures can you save and how much?

Principal Steps in the Planning of a Field Survey (or Field Investigation) While planning a field survey, you are required to focus on the following steps: (i) Design questionnaire with utmost care and be sure that: (a) the questionnaire has a reasonable length. (b) the questionnaire includes only precise and short questions. (c) the set of questions in the questionnaire can be cross-checked with each other. (d) the questions do not involve seriousl difficult calculations for the respondent. (ii) Decide the mode of enquiry, viz. direct personal oral investigation (also called interview method) or mailing the questionnaire.

(iii) Arrange a proper training programme for the enumerators, explaining to them the purpose and mode of enquiry and also the nature of various questions in the questionnaire. (iv) Conduct a pilot survey (a small preliminary investigation) when the field of investigation is very large.

Pilot Survey What it is? It refers to a try-out survey covering a very small sample of the universe of your study. Why do it? This is a sort of pre-testing of your questionnaire. This helps you to assess quality of your questionnaire and the way respondents respond to the set of questions. Accordingly, you are able to know in advance the shortcomings/drawbacks of your questionnaire. Required changes in the questionnaire may be introduced before you are set out for a final survey.

Pilot Survey helps: (i) in assessing the quality and suitability of questions (ii) in assessing performance of the enumerators (iii) in designing a set of instructions for the enumerators (iv) in assessing the cost and time involved in the final survey.

Main Sources of Errors in Collection of Data These are the following: (i) Errors related to the measurement of objects which may occur when: (a) the scale of measurement happens to be different for different enumerators, and (b) different enumerators may be allowing different degree of approximation in their measurement, even while using identical scales. (ii) Errors occurring due to wrong responses simply because the respondents are not able to handle/understand the questions precisely. (Hi) Errors occurring due to the lack of response. Some respondents may not respond to the questionnaire. Lack of information thus occurring infuses an element of error in the collection of data. (iv) Errors occurring due to miscalculations, also called arithmetical errors. (v) Errors occurring due to ‘communication gap ’or due to lack of recording of the information.

3. COLLECTION OF SECONDARY DATA There are two main sources of secondary data: (1) Published Sources, and (2) Unpublished Sources.

(1) Published Sources Some of the published sources of secondary data are: (i) Government Publications:  Ministries of the Central and State Governments in India publish a variety of Statistics as their routine activity. As these are published by the Government, data are fairly reliable. Some of the notable Government publications on Statistics are: Statistical Abstract of India, Annual Survey of Industries, Agricultural Statistics of India, Report on Currency and Banking, Labour Gazette, Reserve Bank of India Bulletin, etc. (ii) Semi-Government Publications:  Semi-Government bodies (such as Municipalities and Metropolitan Councils) publish data relating to education, health, births and deaths. These data are also fairly reliable and useful. (iii) Reports of Committees and Commissions:  Committees and Commissions appointed by the Government also furnish a lot of statistical information in their reports. Finance Commission, Monopolies Commission, Planning Commission are some of the notable commissions in India which supply detailed statistical information in their reports. (iv) Publications of Trade Associations:  Some of the big trade associations, through their statistical and research divisions, collect and publish data on various aspects of trading activity. For example, Sugar Mills Association publishes information regarding sugar mills in India. (v) Publications of Research Institutions:  Various universities and research institutions publish information as findings of their research activities. In India, for example, Indian Statistical Institute, National Council of Applied Economic Research publish a variety of statistical data as a regular feature. (vi) Journals and Papers:  Many newspapers such as ‘The Economic Times’ as well as magazines such as Commerce, Facts for You also supply a large variety of statistical information. (vii) Publications of Research Scholars:  Individual research scholars also sometimes publish their research work containing some useful statistical information. (viii) International Publications: International organisations such as UNO, IMF, World Bank, ILO, and foreign governments etc., also publish a lot of statistical information. These are used as secondary data.

(2) Unpublished Sources There are some unpublished secondary data as well. These data are collected by the government organisations and others, generally for their self use or office record. These data are not published. This unpublished numerical information may, however, be used as secondary data. A Note of Caution for the Users of Secondary Data Users of secondary data must check: (i) reliability of data, (ii) suitability of data, and (iii) adequacy of data.

Precautions in the Use of Secondary Data We know that secondary data are collected by others to suit, their specific requirements. Therefore, one needs to be very careful while using these data. Connor has rightly stated, “Statistics especially other people’s Statistics are full of pitfalls for the users.” Some of the notable questions to be borne in mind while dealing with the secondary data are: (i) Whether the data are reliable? (ii) Whether the data are suitable for the purpose of enquiry? (iii) Whether the data are adequate? In order to assess the reliability, suitability and adequacy of the data, the following points must be kept in mind: (1) Ability of the Collecting Organisation:  One should check the ability of the organisation which initially collected the data. The data should be used only if it is collected by able, experienced and impartial investigators. (2) Objective and Scope:  One should note the objective of collecting data as well as the scope of investigation. Data should be used only if the objective and scope of the study as undertaken earlier match with the objective and scope of the present study. (3) Method of Collection:  The method of collection of data by the original investigator should also be noted. The method adopted must match the nature of investigation. (4) Time and Conditions of Collection:  One should also make sure of the period of investigation as well as the conditions of investigations. For example, data collected during war times may not be suitable to generalise certain facts during peace times. (5) Definition of the Unit:  One should also make sure that the units of measurement used in the initial collection of data are the same as adopted in the present study. If the unit of measurement differs, data must be modified before use. (6) Accuracy:  Accuracy of the data should also be checked. If the available data do not conform to the required degree of accuracy, these should be discarded. In short, as stated by Bowley, “It is never safe to take published Statistics at their face value without knowing their meaning and limitations”

Two important Sources of Secondary Data :  ‘Census of India’ and Reports and Publications of National Sample Survey Office’ (1) Census of India:  Census of India is a decennial publication of the Government of India. It is published by Registrar General & Census Commissioner, India. It is a very comprehensive source of secondary data. It relates to population size and the various aspects of demographic changes in India. Broadly, it includes statistical information on the following parameters: (i) Size, growth rate and distribution of population in India. (ii) Population projections. (iii) Density of population. (iv) Sex composition of population. (v) State of literacy. Information on these parameters relates to country as a whole as well as different states and union territories of the country. As the name suggests, Census of India is a comprehensive enquiry on population size and the related parameters of change covering each and every household of the country.

(2) Reports and Publications of National Sample Survey Office (NSSO):  Reports and publications of NSSO is another important source of secondary data in India. NSSO is a government organisation under the Ministry of Statistics and Programme Implementation. This organisation conducts regular sample surveys to collect basic statistical information relating to a variety of economic activity in rural as well as urban parts of the country. For example, the 76th round of NSSO (July 2018- December 2018) was on “Persons with Disabilities, and Drinking Water, Sanitation, Hygiene and Housing Conditions”. Broadly, reports and publications of NSSO offers statistical information of the following parameters of economic change:

important The statistical data collected by NSSO are released through its quarterly journal, called SARVEKSHANA and its reports, popularly known as NSSO Reports. (i) Land and Livestock Holdings. (ii) Housing Conditions and Migration with special emphasis on slum dwellers. (iii) Employment and Unemployment status in India. (iv) Consumer Expenditure in India, including level and pattern of consumer expenditure of diverse categories of the people. (v) Sources of Household income in India. Unlike Census of India, Reports and Publications of National Sample Survey Office are based on ‘sample’ study of the population/universe.

There are 2,000 students in a college. An investigator wants to collect data regarding their family background. He has two possible choices. First, he collects information relating to all the 2.000 students. Second, he collects information relating to some of the students (sample of students) who would represent all the 2.000 students. In Statistics, the first approach for collecting data is called Census Method and the second approach is called Sample Method. The present chapter focuses on a comprehensive study of the census and sample methods of data collection. Beginning with the concepts of Census and Sample techniques the chapter offers a detailed discussion of the merits and demerits of the two techniques. Also, various techniques of ‘sampling’ are discussed with a comparative look at their merits and demerits.

1. CONCEPTS OF ‘CENSUS’ AND ‘SAMPLE’ Chapter 2 of the book introduces the concept of universe or population. It would be useful to recapitulate this concept for a comprehensive understanding of the concepts of ‘Census’ and ‘Sample’.

In Statistics, universe or population simply refers to an aggregate of items to be studied for an investigation. Ordinarily, the term population is used to mean total number of people living in a country. Population of India was approximately 121.02 crore in 2010- 11. But in Statistics, the term population is used differently. In Statistics, the term population means the aggregate of all items about which we want to obtain information. To illustrate, there are 2,000 students in a particular college. If an investigation relates to all the 2,000 students, then 2,000 would be taken as universe or population. Each unit of these 2,000 is called Item. To further illustrate, l sugar mill out of the 10 sugar mills we are studying, would be called an item. All the 10 sugar mills would constitute population or the universe. If a statistical inquiry is based on all items of the universe,

it is called a census inquiry. For example, if you want to know quality of life of the 25,000 households in your town and you decide to collect the relevant statistical data of all 25,000 households (that is, your statistical inquiry is covering all the items of the universe or is covering the entire universe) you are relying on census method of your statistical inquiry. Alternative is that you collect statistical data for every 5th or 10th household of your town, which you think should represent all the 25,000 households of the town. Now you are not covering each and every item of the universe; instead you are covering only a ‘sample’ of the universe. Characteristics of the ‘sample’ are supposed to represent characteristics of the entire

universe. Or, quality of life of a sample of (say) 2,500 families is supposed to represent quality of life of all the 25,000 families of your town. This is called a sample method of a statistical inquiry.

The concepts of ‘Sample’ and ‘Population’ are projected in Fig. 1. Bigger part of this picture is comprising the entire 27 items showing population or universe and the corresponding part comprising of 3 items shows sample.

Now you must be sure that Sample is only a part of the population or the universe. But it must be that part which, in terms of its characteristics, represents the entire population.

2. CENSUS METHOD Census method is that method in which data are collected covering every item of the universe or population relating to the problem under investigation.

To illustrate, you may be interested in the investigation of colour composition of the Maruti cars in India. According to the Census Method, you are required to collect data on the colour of each and every Maruti car sold in India.

Census method implies complete enumeration of the universe/ population. Census of population is the most suitable example of tbe census method of a statistical enquiry. For the estimation of the country’s population, house to house enquiry is conducted and even people living at the roadside are contacted in India, census of population is conducted every ten years, and the last census was conducted in February 2011.

Census of India 20V reveals that in terms of the size of population. India is the second largest country in the world next only to China. Suitability

Census method is suitable particularly for such statistical investigations which have (i) small size of population, (ii) widely diverse items in the population, (iii) requirement of intensive examination of different items, and (iv) high degree of accuracy and reliability.

Merits Principal merits of census method are as under: (1) Reliable and Accurate: Results based on census method are accurate and highly reliable. This is because each and every item of the population is studied.

(2) Less Biased: Results based on census method are less biased. It is because of the absence of investigator’s discretion regarding the selection of sample items.

(3) Extensive Information: Information collected through the census method is quite exhaustive and therefore, more meaningful because all the items of a universe are examined. For example, population census in India gives exhaustive information relating to the number of people in different parts of the country, their age and sex composition, education, status, occupation, and the like.

(4) Study of Diverse Characteristics: By using census method, one can study diverse characteristics of the universe.

(5) Study of Complex Investigation: When items in a universe are of complex nature and it is necessary to study each item, only census method can produce the desired results. Data on country’s population are collected by this method.

(6) Indirect Investigation: Census method can be successfully used in indirect investigations relating to unemployment, poverty, corruption, etc.

Demerits However, there are certain demerits of census method as under:

(1) Costly: Census method is very costly and is, therefore, generally not used for ordinary investigations. Only the Government or some big institutions can afford to use this method and that too for specific purposes only.

(2) Large Manpower: Census method requires large manpower (enumerators). Training of a large number of enumerators becomes essential, which is a very difficult process.

(3) Not Suitable for Large Investigations: If the universe comprises a large number of items, then it may not be possible to cover each and every item. Census method becomes practically inoperative in such situations.

3. SAMPLE METHOD Sample method is that method in which data is collected about the sample on a group of items taken from the population for examination and conclusions are drawn on their basis.

Sample method is widely used in our day-to-day life. A lady in the kitchen, for example, tests only a grain or two of the rice to know whether the rice is boiled or not. By examining only a few drops of blood, a doctor determines the blood group of a person.

Suitability Sample method is particularly suitable when: (i) the size of population is very large, (ii) very high degree of accuracy is not needed, (iii) intensive examination of diverse items is not required, and (iv) when different units of the universe are broadly similar to each other.

Merits Some of the principal merits of the sample method are as under: (1) Economical: Sample method of investigation is economical because only some units of the population are studied. (2) Time Saving: In this method, only limited number of the items are investigated. As such the process of investigation is time-saving, not time-consuming. (3) Identification of Error: Because only a limited number of items are covered, errors can be easily identified. To that extent sampling method shows better accuracy. (4) Large Investigations: Sample method is more feasible in situations of large investigations than the census method which generally involves unaffordable cost. (5) Administrative Convenience: There is an administrative convenience in handling a limited number of items. More capable and efficient investigators can be appointed. (6) More Scientific: According to R. Fisher, Sample Method is more scientific because the sample data can be conveniently- investigated from various angles.

Demerits Yet there are some demerits of the sample method as under: (1) Partial: It is only a partial investigation of the universe. The investigator’s bias in the selection of the sample is not ruled out. Accordingly, the results may be biased as well. (2) Wrong Conclusions: If the selected sample does not represent the characteristics of the universe, the study may end up with wrong conclusions. (3) Difficulty in Selecting Representative Sample: It is not very easy to select a sample which would represent the characteristics of the entire population. (4) Difficulty in Framing a Sample: Sometimes the universe may be so diverse that it becomes difficult to frame a sample. (5) Specialised Knowledge: Sampling involves a set of technical procedures. One must have the technical knowledge of choosing a representative sample from the universe. Persons who are well-versed with all the techniques of sampling are not easily available.

Two Basic Essentials of a Good Sample

(i) that the sample must represent characteristics of the entire universe/ population. (ii) that the sample must be adequate enough to offer reliable conclusions.

Essentials of a Sample In order to arrive at an unbiased and right conclusion, a sample must have the following qualities or essentials:

(1) Representative: A sample must represent all the characteristics of the universe. It is possible only when each unit of the universe stands equal chances of being selected in the sample.

(2) Independent: All units of a sample must be independent of each other. In other words, inclusion of one item in tire sample should not be dependent upon the inclusion of some other items of the universe.

(3) Homogeneity: If more than one sample are selected from a universe, these samples should be homogeneous (and not contradictory) to each other.

(4) Adequacy: The number of items in the sample should be fairly adequate so that some reliable conclusions are drawn covering the characteristics of the universe as a whole.

METHODS OF SAMPLING Following are the principal methods or techniques of sampling:

(1) Random Sampling Random sampling is that method of sampling in which each and every item of the universe has equal chance of being selected in the sample. In other words, there is an equal probability for every item of the universe being selected in the sample.

Which of the various items of the universe would get selected in the sample is beyond the control of the investigator. The selection is left entirely to the chance factors. This method is used particularly when various items of the universe are homogeneous or identical to each other. This method is impartial and economical. Random Sampling may be done in any of the following ways:

(i) Lottery Method: In this method, paper-slips are made for each item of the universe. These slips are shuffled in a box. Then, impartially, some of the slips are drawn to form a sample of the universe.

(ii) Tables of Random Numbers: Some statisticians have prepared a set of tables called Tables of Random Numbers. A sample is framed with reference to these tables. Of all these tables Tippet’s Table is most widely used. Using 41,600 figures, Tippet has involved 10,400 numbers comprising of four units each. For the use of this method, all items of the universe are first arranged in an order. Then using Tippet’s Table the required number of items are selected as are needed for a sample.

Merits Following points may be noted on the merits of random sampling: (i) This method is free from personal bias of the investigator. (ii) Each and every item of the universe stands equal chances of being selected. (iii) The universe gets fairly represented by the sample. (iv) This is a very simple and straightforward method. The Principal Merit of Random Sampling It is that each and every item of the universe has equal chance (or equal probability) of being selected.

Demerits However, there are two notable demerits of this method. These are as under: (i) This method does not guarantee proportionate representation of different items in the universe. (ii) Random sampling does not give weightage to certain important items in the universe.

Difference Between Random sampling and Haphazard sampling

Random Sampling and Exit Polls Exit polls is an interesting example of random sampling. What does it mean? It means a small percentage of the people exiting the poll booths are contacted and asked whom 

they voted for. From the sample of information thus collected, a prediction is made about the victory chances of different candidates contesting election.

(2) Purposive or Deliberate Sampling Purposive sampling is that method in which the investigator himself makes the choice of the sample items which in his opinion are the best representative of the universe. Thus, in this method of sampling, selection of the sample items is not left to the chance factors; it is simply made by choice. This method of sampling is specifically suitable when some of the items in the universe are of special significance and ought to be included in the sample. For example, if an investigation is to be made relating to the iron and steel industry in India, then the inclusion of such industries as the Tata Iron and Steel Company is obviously a purposive selection. However, there is a considerable possibility of personal bias in purposive sampling. As a result, it loses its credibility.

Merits (i) This method is flexible to allow the inclusion of those items in the sample which are of special significance. (ii) Selection of items can be deliberately tuned to the purpose of study. (iii) It is a very simple technique of selection of the sample items.

Demerits (i) There is a possibility of personal bias in the selection of items. (ii) Because of the possibilities of personal bias, reliability of the results becomes doubtful.

(3) Stratified or Mixed Sampling This method of sampling is generally adopted when population consists of different groups with different characteristics. According to this method of sampling, population is divided into different strata having different characteristics and some of the items are selected from each strata, so that the entire population gets represented. Each stratum should be represented in correct proportion in the sample. To illustrate, suppose there are 50 students in Class XL Out of them, 30 have studied Mathematics and 20 have studied Home Science in their Class X. Thus, the population of the 50 students gets divided into two strata consisting of 30 and 20 students respectively. From each of these strata, items would be selected proportionately such that the sample represents the characteristics of the entire population. If, of the total 50 students, only a sample of five is to be selected, then we shall randomly select three out of the first stratum (comprising 30 students) and two out of the second stratum (comprising 20 students). However, items may also be selected unproportionately from different strata.

An investigator may prefer to select four students from amongst those who studied Mathematics and only one from amongst those who studied Home Science. The choice will be governed by the nature of the enquiry and wisdom of the investigator.

Stratified Sampling is also called Mixed technique of sampling because this method involves the mixture of both purposive sampling and random sampling. The division of population into different strata is purposely done while selection of the items is done at random.

Merits (i) This method covers diverse characteristics of the population. (ii) On the basis of diverse characteristics of the population, a comparative analysis of the data becomes possible. (iii) This method of sampling offers reliable as well as meaningful results.

Demerits (i) This method is suitable only when there is a complete knowledge about the diverse characteristics of the population. Therefore, this has a limited scope. (ii) There is a possibility of bias at the time of classification of the population into different strata. (iii) When the size of population is already small, it may be difficult to further divide it into smaller parts/strata.

(4) Systematic Sampling According to this method, units of the population are numerically, geographically and alphabetically arranged. Every nth item of the numbered items is selected as a sample item. To illustrate, if 10 out of 100 students are to be selected for a sample, then 100 students would be numbered and systematically arranged. One item of the first 10 would be selected at random. Subsequently, every 10th item from the selected number will be selected to frame a sample. If the first selected number is 5th item, then the subsequent numbers would be 15th, 25th, 35th, 45th, 55th, 65th, 75th, 85th and 95th. This method of sampling is, in fact, a short-cut method of Random Sampling.

Merits (i) This is a very simple method. Sample is easily determined. (ii) There is hardly any possibility of personal bias in this method.

The Principal Merit of Stratified Sampling It allows selection of such items which represent diverse characteristics of the population. Principal Demerit of Systematic Sampling It does not allow every item of the universe equal chance (or equal probability) of being selected in the sample. Demerits

(i) Every item in the population does not get equal chance of being selected because only the first item is selected on the basis of random sampling.

(ii) If all the items in the population are homogeneous, this method of sampling serves no specific purpose.

(5) Quota Sampling In this method, the population is divided into different groups or classes according to different characteristics of the population. Some percentage of different groups in total population is fixed. Further, some quota of the items to be selected as sample-items is fixed for each group. The investigator selects the fixed number of items from each group to frame a sample. This method of sampling is not very expensive. But there is a high possibility of personal bias at the time of selection of the items by the investigator. Accordingly, the reliability of results becomes questionable.

(6) Convenience Sampling In this method, sampling is done by the. investigator in such a manner that suits his convenience. To illustrate, an investigator may select a sample of teachers merely by referring to the college prospectus. This method is the simplest and least expensive, but unscientific and unreliable. It depends too much on the whims of enumerators.

Reliability of Sampling Data The reliability of the sampling data means that the characteristics of the universe are fully represented by the sample. It depends mainly on the following factors:

(1) Size of the Sample: Reliability of sampling depends on the size of the sample. If its size is very small, it will fail to represent the population. Accordingly, the conclusions would lack reliability.

(2) Method of Sampling: If the method of sampling is not simple and exhaustive, it will not adequately represent the population. Consequently, the results will not be dependable.

(3) Bias of Correspondents and Enumerators: Personal bias of the correspondents and enumerators should be as less as possible. Otherwise, reliability of the sampling data is bound to suffer.

(4) Training of Enumerators: Reliability of sample also depends upon the training of the investigators. If they are not trained to make them expert in their field of investigation, the

sample will lack reliability . Census and Sampling Methods: A Comparative Look Some of the principal differences between census and sampling methods are as under:

(1) Coverage: In the census technique, an investigator collects information relating to all the items in the population. In sampling method, on the other hand, only some of the items which represent the population are covered for an investigation.

(2) Suitability: Census method is suitable when the area of investigation is relatively small. On the other hand, when the area of investigation is large, it is the sampling method which is generally used.

(3) Accuracy: There is generally a greater degree of accuracy in the results based on the census method than the sampling method. This is because in the census method each and every item of the population is studied. As against it, there is less accuracy and reliability in the sampling method because it studies only a few items of population. However, errors can be easily detected and removed in the sampling method because of the small number of items. To that extent sampling method shows greater accuracy than the census method.

(4) Cost: Sampling method is certainly much less expensive than the census method. Smaller the sample size out of the given population, lesser the cost of investigation.

(5) Time: Sample method is less time consuming than the census method.

(6) Nature of Items: Census method is particularly suitable when the items in the population have diverse characteristics. On the other hand, sample method is suitable when items in the population are homogeneous.

(7) Verification: Verification of the statistical information obtained through census method is generally not possible. It would involve huge expenses and the repetition of the whole process. Sample information, on the other hand, can be easily verified. In case of doubt, enumeration can be done again and facts verified accordingly. In short, sample method of statistical investigation is generally preferred to the census method because the former is less expensive in terms of the time, money and efforts involved. However, for the successful application of the sample method, it is very essential that the sample items represent the characteristics of population as a whole.

Statistical Errors: Sampling and Non-Sampling Errors Statistical errors are broadly classified as (i) sampling errors, and (ii) non-sampling errors. Following are the details:

(i) Sampling Errors: These are related to the size or nature of the sample selected for the study. Due to a very small size of the sample selected for study or due to nonrepresentative nature of the sample, the estimated value may differ from the actual value of a parameter. The error thus emerging, is called sampling error. For example, if the estimated value of a parameter is found to be 10 while the actual/true value is 20 then, the sampling error = estimated value of the parameter – true value of the parameter = 10-20 = -10.

(ii) Non-sampling Errors: These are errors related to the collection of data. These are of the following types:

Error of Measurement: Error of measurement may occur due to.- (a) difference in the scale of measurement, and (b) difference in the rounding off procedure adopted by different investigators.

Error of Non-response: This arises when the respondents do not offer the required information. Error of Misinterpretation: This arises when the respondent fails to interpret the questions in the questionnaire.

Error of Calculation or Arithmetical Error: It occurs in the course of addition, subtraction or multiplication of data.

Error of Sampling Bias: It occurs when, for some reason or the other, a part of target population, cannot be included in the choice of a sample.

Larger the field of investigation or larger the population size, greater is the possibility of errors related to the collection of data, or data acquisition. It must be noted here that a non-sampling error is more serious than a sampling error. Because a sampling error can be minimised by opting for a larger sample size. No such possibility exists in case of nonsampling errors.

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CBSE Class 11 Economics Revision Notes Chapter – 4 Presentation of Data class 11 Notes Economics

The presentation of data means exhibition of data in such a clear and attractive manner that these can be easily understood and analysed.

Forms of Presentation of data: 1. Textual/Descriptive Presentation 2. Tabular Presentation 3. Diagrammatic Presentation 4. Graphical Presentation

1. Textual/Descriptive Presentation of Data:- In this, data is presented in the form of text. This is suitable when quantity of data is not too large.

2. Tabulation – It is the process of presenting data in the form of a table. Parts or components of Table: 1. Table Number 2. Title 3. Caption Or Column Headings 4. Stubs Or Row Headings 5.  Body of the Table 6. Unit of Measurement 7. Source 8. Head Note 9. Foot Note

Features of a good table: (a) Compatible with the objective (b) Helpful in comparison (c) Ideal Size (d) Stubs (e) Headings (f) Percentage and ratio (g) Sources of Data (h) Simplicity

Kinds of Table: 1. According to Purpose 2. According to originality 3. According to construction

Classification of tabular presentation of data 1. Qualitative Classification:- When classification is done according to attributes such as social status, nationality, etc. It is called qualitative classification. 2. Quantitative Classification:- In this, the data are classified on the basis of characteristics which are quantitative in nature. e.g., age, height, income, etc. 3. Temporal classification:- In this, time becomes the becomes the classifying variable and data are categorised according to time. Time may be in hours, weeks, years, etc. 4. Spatial classification:- When classification is done on the basis of place, it is called spatial classification. The place may be village, town, state, country, etc.

Diagrammatic Presentation : When data is presented in a simple and attractive manner in the form of diagrams is called diagrammatic presentation of data.

Types of Diagrammatic Presentation : 1. Geometric Form a. Pie Diagram b. Bar Diagram i. Simple ii. Multiple iii. Sub Divided iv. Percentage

2. Frequency Diagram a. Histogram b. Frequency Polygon c. Frequency Curve d. Ogive curve

3. Arithmetic Line Graph or Time series graph 1. Bar diagram:-  Bar diagrams are those diagrams in which data are presented in the form of bars or rectangles. Simple bar diagram:- They are those diagrams which are based on a single set of numerical data. Different items are represented by different bars. Multiple bar diagram:- They are those diagrams which show two or more sets of data simultaneously. This type of diagram is, generally, used to make comparison between two sets of series. Sub divided bar diagram:- These are those diagrams which present simultaneously, total values and parts there in a set of a data. Percentage bar diagram:-  They are those diagram which show simultaneously different parts off the values of a sets of data in terms of percentage. Deviation bar diagram:-  These are used to compare the net deviation of related variables with respect to time and location. Bars which represent positive deviation and which represent negative deviation are drawn above and below the base line respectively. Pie or circular diagram is a circle divided into various segments showing the per cent values of a series. Histogram is graphical presentations of a frequency distribution of a continuous series.It can never be drawn for a discrete series. Frequency polygon is drawn by joining the mid points of the tops of rectangles in a histogram. It is constructed with the help of discrete as well as continuous series. Frequency curve is obtained by joining the points of a frequency polygon through free hand smooth curve not by straight lines. Cumulative frequency curves or ogive curve is the curve which is constructed by plotting cumulative frequency data on the graph paper in the form of a smooth curve. Arithmetic line Graphs or Time Series Graphs:-   In this graph, time(hour,day, date, week, month, year) is plotted along X-axis and the  corresponding value of variable along Y-axis.

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• Economics /

Class 11 Collection, Organisation and Presentation of Data

• Updated on  
• Jun 22, 2023

The collection of data aims to collect evidence for attaining a sound and comprehensible solution to a problem. To understand the inconsistencies in the output, we need the ‘data’ on the generation. It is a process which is conducted to measure and gather information. ‘Data’ is a device, which aids in the comprehension of problems by providing knowledge. Here is this blog, we will talk in detail about the Class 11 collection, organisation and presentation of data. 

Must Read: Business Services Class 11 Notes

This Blog Includes:

What are the sources of data, primary data, secondary data, preparation of instrument, mode of data collection, personal interviews, mailing questionnaire, telephone interviews, pilot survey, census and sample surveys, census , random sampling, non-random sampling, sampling errors, non-sampling errors, census of india and nsso.

To understand more about the chapter Class 11 collection, organisation and presentation of data, we fist need to know the sources of data. Statistical data can be obtained from two sources:

• Primary data

We further move on to the concept of primary data in class 11 collection, organisation and presentation of data. The important points of primary data are:

• The enumerator (person who assembles the data) may collect the data by administering an inquiry or research. Such data is called Primary Data , as it is formulated on first-hand information.
• Primary data are unique, do not require any modification, and are costly.

Next important form of data in class 11 collection, organisation and presentation of data is secondary data.

• If the data have been examined and analyzed by another agency, they are called Secondary Data . Usually, the issued data are secondary.
• They are already in the presence and therefore are not unique.
• It demands to be modified to satisfy the aim of the study at hand.
• Secondary data are low priced.

How do we collect Data?

Collection of data is important in class 11 collection, organisation and presentation of data. It is done by the following ways:

• The survey aims to describe characteristics like cost, worth, utility (in case of the product) and reputation, honesty, loyalty (in case of the nominee).
• The objective of the survey is to gather data and is a method of gathering information from individuals.

The most prevalent type of tool employed in surveys is a questionnaire/ interview schedule. The questionnaire is either self-directed by the interviewee or conducted by the enumerator or qualified investigator. While drawing-up the questionnaire/interview schedule, the following points should be kept in mind:

• The questionnaire should not be lengthy.
• The array of problems should move from indefinite to distinct.
• Questions should not be enigmatic.
• Questions should not use binary negatives. 
• Questions should not be leading.
• Questions should not indicate choices. 

Also Read: Emerging Modes of Business Class 11 Notes

The next important topic in class 11 collection, organisation and presentation of data is the mode of data collection. The aim of probing questions is to survey the acquisition of data. There are three ways of collecting data: 

• Mailing (questionnaire) Surveys

Personal interviews form an important part of the mode of data collection in class 11 collection, organisation and presentation of data. In this method, the researcher has the main role as he/she conducts the interviews face-to-face with the respondents. Personal interviews are preferred due to various reasons:

• Highest Response Rate 
• Allows use of all types of questions 
• Better for using open-ended questions 
• Allows clarification of ambiguous questions.

The personal interview has some demerits too:

• Most expensive 
• Possibility of influencing respondents 
• More time taking

Another important part of class 11 collection, organisation and presentation of data is the mailing questionnaire. In such a method, the data is collected through the mail. The questionnaire is mailed to each person and a  request is attached to complete and return it on time. 

The advantages of this method are:

• Least expensive 
• The only method to reach remote areas 
• No influence on respondents 
• Maintains anonymity of respondents 
• Best for sensitive questions

The disadvantages of mail surveys are:

• Cannot be used by illiterates 
• Long r esponse time  
• Does not allow an explanation of unambiguous questions  
• Reactions cannot be watched 

In telephone interviews, the investigator asks questions over the telephone. 

The advantages of telephone interviews are:

• Relatively low cost 
• Relatively less influence on respondents 
• Relatively high response rate.

The disadvantages of this method are:

• Limited use 
• Possibility of influencing respondents

Explore: Accountancy Class 11 NCERT Solutions

The pilot survey is another important tool in class 11 collection, organisation and presentation of data.

• After the questionnaire is ready, it is desirable to carry a try-out with a diminutive group, known as Pilot Survey or Pre-Testing of the questionnaire . 
• The pilot survey serves to give a preliminary impression of the survey. 
• It helps to pretest the questionnaire and know the lapses and drawbacks.
• It also aids to assess the appropriateness of questions, the accuracy of guidance, the administration of enumerators, and the expense and time required in the actual survey.

Census and sample surveys are an important tool in class 11 collection, organisation and presentation of data. 

• A survey, which encompasses every component of the population, is apprehended as Census or the Method of Complete Enumeration.
• The primary feature of this approach is that this comprises every individual unit in the whole population.

Sample Survey

• A sample refers to a section of the population from which information has to be taken. A good sample (representative sample) is usually short and competent in giving reasonably accurate information about the population at a lower cost and in less time.
• Most of the surveys are sample surveys and are preferable in statistics because of several reasons.
• A sample can give rationally secure and authentic information at a lower cost and in less time. 
• Now the question is how do you do the sampling? There are two main types of sampling:
• Non-random Sampling
• It is also known as the lottery method.
• Random sampling is where the specific units from the population (samples) are randomly selected. 
• In random sampling, each person has an equal possibility of being chosen, and the person who is selected is the same as the one who is not selected.
• Random number tables are generated to ensure an equal chance of selection of every single unit in the population.
• They are accessible either in an issued form or can be generated by employing relevant software packages.
• In this method, units of the population don’t have equal chances of being selected. 
• The convenience or interpretation of the investigator plays a crucial role in the adoption of the sample. 
• They are chiefly selected based on belief, purpose, ease, or quota and are non-random samples.

Sampling and Non-sampling Errors

While conducting surveys, in class 11 collection, organisation and presentation of data, sample and non-sampling errors find an important mention. 

• Sampling error applies to the variations between the sample estimate and the actual value.
• It is the error that transpires when you observe the sample taken from the population. 
• The point of differentiation between the actual parameter of the population and its estimate is known as sampling error. 

Non-sampling errors are more consequential than sampling errors. Sampling error can be minimized by taking a larger sample, on the other hand, it is difficult to minimize non-sampling error. Even a Census can carry non-sampling errors.

 Some of the non-sampling errors are:

• Errors in Data Acquisition: This type of error stems from recording inaccurate responses.
• Non-Response Errors: Non-response happens if an interviewer is incapable to contact a person listed in the sample or a person from the sample declined to respond. In this case, the sample research may not be representative.
• Sampling Bias: Sampling bias happens when the sampling plan is such that some portion of the target population could not possibly be incorporated into the sample.

Must Read: Class 11 Oscillations Notes

The census of India is a very important body of our country and is an important part in the chapter class 11 collection, organisation and presentation of data. 

• The Census of India and the National Sample Survey Organisation (NSSO), are two significant firms at the national level, which gather, manner, and tabulate data.
• The Census of India produces the most comprehensive and continuous demographic record of the population. 
• The NSSO was established by the Government of India to conduct nationwide surveys on socio-economic issues. 
• NSSO gives periodic measures of education, school enrolment, utilization of educational aids, employment, unemployment, manufacturing, and service sector enterprises, morbidity, maternity, child care, utilization of the public distribution system, etc.

Ans. Three methods exist for gathering data: Personal meetings. Telephonic Interviews, and mailing surveys with questions.

Ans. The term “presentation of data” refers to the display of data in a way that makes it easy for viewers to understand and examine it.

Ans. Based on the methods used to acquire them, data can be divided into four basic categories: observational, experimental, simulational, and generated. The kind of research data you gather may have an impact on how you manage that data.

Also Read: Class 11 Formation of a Company

We hope the Class 11- Collection of Data notes helped you understand the essential concepts covered in this chapter. Still unsure about which stream to choose after Class 12. Our Leverage Edu experts are here to guide you in selecting the right stream of study to make sure that you make an informed decision. Sign up for a free session with us now!

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• Commerce Important Questions
• Class 11 Statistics
• Chapter 2 Collection of Data

Important Questions for Collection of Data

Important questions with answers for Collection of Data which is drafted by expert commerce teachers from the latest version of CBSE (NCERT) books.

CBSE Class 11 Statistics Chapter 2 Important Questions

Define primary data.

Primary data is the collection of data collected by the investigator for his own purpose for the first time. These are collected from the source of origin.

Define secondary data.

According to Wessel, “Data collected by another person is known as secondary data”. It is known as secondary data as it has already been collected by somebody else. These data are accessible in the form of a published and unpublished report.

What are the two sources of data?

The two sources of data are:

• Primary source
• Secondary source

Mention two sources of secondary data.

The two sources of secondary data are:

• Government publication
• Semi-government publication

In what parameters is the statistical information published in the census of India?

The statistical information is published in the following parameters in the census of India[1] 

• Population projection
• Sex composition of a population
• Density of population
• Size, growth rate, and distribution of people in India

Mention two demerits of indirect oral investigation.

The two demerits of indirect oral investigation are:

• Less accurate
• Doubtful conclusion

The progress report of a railway published by the railway department is what kind of data?

The progress report of a railway published by the railway department is secondary data.

When is a direct personal investigation suitable for primary data collection?

The direct personal investigation method is suitable for collecting primary data only on the following situations:

• When the investigation is confined and less
• When an authentic and accurate information is required
• When the data is to be kept secret
• When the direct contact with information is needed

When are the qualities of a good questionnaire?

A good questionnaire should have the following qualities:

• Less number of questions
• Should be clear
• Proper order of question
• Non-controversial
• Questions related to the topic
• Request for return

Question 10

Why is a pilot survey important?

A pilot survey is essential because of the following:

• It helps in assessing the quality and suitability of questions.
• It evaluates the performance of enumerators.
• It helps in designing a set of rules for the investigator.
• It estimates the time and cost involved in the final survey.

Question 11

What is the universe in statistics?

In statistics, the term universe or population indicates an aggregate of items studied for investigators.

Question 12

Define sample.

Sample is a collection of an item from the population that represents the characteristics of the population.

Question 13

Define the census method.

It is a method of collecting data where each item related to the problem of the investigation is collected.

Question 14

Explain the sample method.

It is a process of collecting data in which the sample of a group of items are examined, and conclusions are drawn on their basis.

Question 15

What do you mean by random sampling?

In this method, every item of the universe has an equal chance of being selected in the sample.

Question 16

What is purposive or deliberate sampling?

It is a sampling method where the investor chooses the sampling items according to his opinion, and it is the best for the population.

Question 17

Define stratified and mixed sampling?

In this method, the universe is divided into two groups having different characteristics, and the items are selected for each group, hence the entire group is represented.

Question 18

Explain systematic sampling.

In systematic sampling, population units are arranged according to the alphabets, numbers, and geography. Here, every n th   numerical item is selected as a sample.

Question 19

What is quota sampling?

Here, the universe is divided into two sections or groups in terms of their characteristics.

Question 20

What is convenience sampling?

In this method, sampling is done according to the investigator’s convenience.

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