Covers T.R. Jain & V.K. Ohri (2026-27) ch 2-3. Based on NCERT Statistics for Economics, Chapter 2 (Reprint 2026-27) and the CBSE curriculum 2026-27.
- Data, variables and observations; the two sources of data: primary and secondary
- The rules for a good questionnaire, with the book’s poor and good questions
- The three modes of data collection (personal interview, mail, telephone) and the pilot survey
- Census and sample surveys, population and sample, random and non-random sampling
- How to compute sampling error, the non-sampling errors, and the Census of India and the NSSO
1 Introduction: data, variables and observations
The purpose of collection of data is to show evidence for reaching a sound and clear solution to a problem. The book opens with a statement on food grain output:
- Food grain production in India was 108 million tonnes in 1970-71
- It rose to 132 million tonnes in 1978-79, but fell back to 108 million tonnes in 1979-80
- It then rose continuously to 252 million tonnes in 2015-16 and touched 272 million tonnes in 2016-17
- So output varies from year to year and from crop to crop
Economic facts expressed in terms of numbers are called data. The purpose of data collection is to understand, explain and analyse a problem and the causes behind it.
Values that vary are called variables. Variables are generally represented by the letters X, Y or Z.
Each value of a variable is an observation.
Table 2.1: Production of food grain in India (million tonnes)
| X (year) | Y (production) |
|---|---|
| 1970-71 | 108 |
| 1978-79 | 132 |
| 1990-91 | 176 |
| 1997-98 | 194 |
| 2001-02 | 212 |
| 2015-16 | 252 |
| 2016-17 | 272 |
- Years are the variable X and food grain production is the variable Y
- The values of X and Y are the data; from them we learn about the fluctuations in production
- ‘Data’ is a tool which helps in understanding problems by providing information
2 Sources of data: primary and secondary
Statistical data can be obtained from two sources. The person who collects the data is the enumerator (investigator).
Data collected by the researcher himself by conducting an enquiry are called primary data, as they are based on first-hand information.
Data that have been collected and processed (scrutinised and tabulated) by some other agency are called secondary data.
- Primary example: to know the popularity of a film star among school students, you ask a large number of students; the data you get are primary
- Sources of secondary data: government reports, documents, newspapers, books written by economists, or any other source, for example a website
- Data are primary to the source that collects and processes them for the first time and secondary for all sources that later use them
- You publish a report on the film star’s popularity; if somebody uses your data for a similar study, they become secondary data for that person
- Use of secondary data saves time and cost
Primary data
- Collected by the investigator, for the first time, through an enquiry
- First-hand information
- More time and money
- Example: asking students about a film star
Secondary data
- Already collected and processed by another agency
- From published sources or a website
- Saves time and cost
- Example: the same report used in another study
“The same data can be primary and secondary” is a correct statement: it depends on who is using them. Census data are primary for the Census office and secondary for a student who reads them.
3 Survey and questionnaire
A manufacturer decides about a product, or a political party about a candidate, by asking questions of a large group of people: a survey. For a product it describes price, quality and usefulness; for a candidate popularity, honesty and loyalty.
Survey is a method of gathering information from individuals. The purpose of a survey is to collect data.
3.1 Preparation of instrument
The most common instrument used in surveys is the questionnaire / interview schedule: a set list of questions. It is either self-administered by the respondent or administered by the researcher (enumerator) or a trained investigator.
Rules for a good questionnaire (with the book’s poor and good questions)
| Rule | Poor question | Good question |
|---|---|---|
| 1. Not too long; as few questions as possible | No example; rule only | |
| 2. Easy to understand; avoid ambiguous or difficult words | No example; rule only | |
| 3. Questions arranged so that the respondent feels comfortable | No example; rule only | |
| 4. Move from general to specific | (i) Is increase in electricity charges justified? (ii) Is the electricity supply in your locality regular? | First (ii) Is the supply regular? Then (i) Is the increase in charges justified? |
| 5. Precise and clear | What percentage of your income do you spend on clothing in order to look presentable? | What percentage of your income do you spend on clothing? |
| 6. Not ambiguous; respondents should answer quickly, correctly and clearly | Do you spend a lot of money on books in a month? | How much do you spend on books in a month? (i) Less than ₹200 (ii) ₹200 to ₹300 (iii) ₹300 to ₹400 (iv) More than ₹400 |
| 7. No double negatives; avoid starting with “Wouldn’t you” or “Don’t you” (biased responses) | Don’t you think smoking should be prohibited? | Do you think smoking should be prohibited? |
| 8. Not a leading question that gives a clue to the answer | How do you like the flavour of this high-quality tea? | How do you like the flavour of this tea? |
| 9. Should not indicate alternatives to the answer | Would you like to do a job after college or be a housewife? | What would you like to do after college? |
Nine rules in three groups: size (short, easy, comfortable order, general to specific), language (precise, not ambiguous, no double negatives) and fairness (not leading, no hint of alternatives).
3.2 Types of questions
Closed-ended or structured questions make the respondent choose from given options. They are either two-way questions or multiple-choice questions.
When there are only two possible answers, ‘yes’ or ‘no’, it is called a two-way question.
- When more than two answers are possible, multiple-choice questions are more appropriate
- The book’s example: Why did you sell your land? (i) To pay off the debts (ii) To finance children’s education (iii) To invest in another property (iv) Any other (please specify)
Open-ended or unstructured questions let the respondent answer in his own words, without options. Examples: “What is your view about globalisation?” and “What would you like to do after college?”
| Basis | Closed-ended (structured) | Open-ended (unstructured) |
|---|---|---|
| Form of answer | Chosen from given options (yes/no or multiple choice) | In the respondent’s own words |
| Merit | Easy to use, score and codify, as all respondents choose from the given options | Allows more individualised responses |
| Limits | Difficult to write, as the options must represent both sides of the issue; the true response may be missing (hence ‘Any Other’); they restrict the answers | Difficult to interpret and hard to score, as responses vary a lot |
| Example | Why did you sell your land? (four options) | What is your view about globalisation? |
4 Modes of data collection
Television reporters asking children, housewives or the general public about examination performance, a brand of soap or a political party are also doing a survey to collect data. There are three basic ways of collecting data:
Personal interviews
Face-to-face questions
Mailing surveys
Questionnaire sent by mail
Telephone interviews
Questions over the telephone
4.1 Personal interviews
In a personal interview the researcher (investigator) conducts face-to-face interviews with the respondents. It is used when the researcher has access to all the members.
- Merits: personal contact is made between the respondent and the interviewer
- The interviewer can explain the study and answer the respondent’s queries
- He can request the respondent to expand on answers that are particularly important
- Misinterpretation and misunderstanding can be avoided
- Watching the respondents’ reactions can provide supplementary information
- Demerits: it is expensive, as it requires trained interviewers
- It takes longer to complete the survey
- The presence of the researcher may inhibit respondents from saying what they really think
4.2 Mailing questionnaire
In a mail survey the questionnaire is sent to each individual by mail with a request to complete and return it by a given date.
- Merits: it is less expensive
- It gives access to people in remote areas who might be difficult to reach in person or by telephone
- It does not allow the interviewer to influence the respondents
- Respondents get sufficient time to give thoughtful answers
- These days online surveys and surveys through short messaging service (SMS) are popular
- Demerits: less opportunity to clarify instructions, so questions may be misunderstood
- Low response rates: questionnaires returned without completing, not returned at all, or lost in the mail
4.3 Telephone interviews
In a telephone interview the investigator asks the questions over the telephone.
- Merits: cheaper than personal interviews and can be conducted in a shorter time
- The researcher can assist the respondent by clarifying the questions
- Better where respondents are reluctant to answer certain questions in personal interviews
- Demerits: access is limited, as many people may not own telephones
- Reactions of respondents cannot be watched
Advantages and disadvantages of the three modes (the book’s table)
| Mode | Advantages | Disadvantages |
|---|---|---|
| Personal interview | Highest response rate; allows use of all types of questions; better for open-ended questions; allows clarification of ambiguous questions | Most expensive; possibility of influencing respondents; more time-taking |
| Mailed interview | Least expensive; only method to reach remote areas; no influence on respondents; maintains anonymity of respondents; best for sensitive questions | Cannot be used by illiterates; long response time; does not allow explanation of ambiguous questions; reactions cannot be watched |
| Telephonic interview | Relatively low cost; relatively less influence on respondents; relatively high response rate | Limited use; reactions cannot be watched; possibility of influencing respondents |
- A literate person in a remote village: mail (the only method to reach remote areas)
- An illiterate respondent: personal interview (a mailed questionnaire cannot be used by illiterates)
- Sensitive questions needing anonymity: mail
- Low cost and short time, but questions need clarifying: telephone
- The book’s activity: interviewing parents about the quality of teaching while the principal is present; the parents may be influenced and not say what they really think (a demerit of personal interviews)
4.4 Pilot survey
A try-out of the ready questionnaire with a small group is known as a pilot survey or pre-testing of the questionnaire.
A pilot survey helps in:
- providing a preliminary idea about the survey
- knowing the shortcomings and drawbacks of the questions
- assessing the suitability of questions and the clarity of instructions
- judging the performance of enumerators
- estimating the cost and time involved in the actual survey
5 Census and sample surveys
A survey which includes every element of the population is known as the census or the method of complete enumeration. Every unit of the population must be covered; you cannot pick some units and leave out others.
- The Census of India is carried out every ten years
- A house-to-house enquiry covers all households in India
- Demographic data on birth and death rates, literacy, employment, life expectancy, size and composition of population, etc. are collected
- They are published by the Registrar General of India
- The last Census of India was held in 2011
- In the 110 years from 1901 to 2011 the population increased by more than 97 crore (121.09 − 23.83 = 97.26 crore)
- The average annual growth rate of population was 2.2 per cent in 1971-81, came down to 1.97 per cent in 1991-2001 and 1.64 per cent in 2001-2011
5.1 Population and sample
Population or the universe in statistics means the totality of the items under study. It is the group to which the results of the study are intended to apply, all the individuals/items who possess certain characteristics according to the purpose of the survey.
A sample refers to a group or section of the population from which information is to be obtained. A good sample (representative sample) is generally smaller than the population and can give reasonably accurate information about the population at a much lower cost and shorter time.
- The first task in selecting a sample is to identify the population
- The researcher then selects a method; if a survey of the whole population is not possible, he selects a representative sample
- Average income example: the census method needs the income of every individual in the region, added up and divided by the number of individuals; a large number of enumerators is needed, so huge expenditure
- Alternatively, select a representative sample of a few individuals, find their average income and use it as an estimate of the average income of the whole region
- Research problem: to study the economic condition of agricultural labourers in Churachandpur district of Manipur
- Population: all agricultural labourers in Churachandpur district
- Sample: ten per cent of the agricultural labourers in Churachandpur district
Why are most surveys sample surveys?
- A sample can provide reasonably reliable and accurate information at a lower cost and in a shorter time
- Samples are smaller than the population, so more detailed information can be collected by intensive enquiries
- A smaller team of enumerators is needed, which is easier to train and to supervise effectively
| Basis | Census (complete enumeration) | Sample survey |
|---|---|---|
| Units covered | Every unit of the population | A representative part of it |
| Cost and time | Very high; a large number of enumerators | Lower cost, shorter time, small team |
| Depth of information | Limited information from each unit | Detailed information through intensive enquiry |
| Sampling error (Section 7) | None (everyone is counted) | Present; falls with a larger sample |
| Non-sampling error (Section 7) | Possible | Possible |
| Example | Census of India (every 10 years) | National Sample Survey (Section 8); 10% of labourers in Churachandpur |
- Students’ opinion about the new Class XI economics textbook: population = all Class XI students using the book; sample = some students selected from them (say, some students in some schools)
- Average yield of wheat in Punjab: population = all wheat-growing fields of Punjab; sample = some fields selected from them
- Next census in India and China: take this from that country’s official announcement; the book does not answer it
6 Sampling: random and non-random
There are two main types of sampling: random and non-random.
6.1 Random sampling
Random sampling is one where the individual units from the population (samples) are selected at random, so that every individual has an equal chance of being selected.
- The government wants to find the impact of the rise in petrol price on the household budget of a particular locality
- A representative (random) sample of 30 households has to be studied
- The names of all 300 households of the area are written on paper and mixed
- Then 30 names to be interviewed are selected one by one
- All 300 sampling units (also called the sampling frame) got an equal chance, so the sample is a random sample
Writing the names or numbers of all units on slips, mixing them and drawing the required number is the lottery method. Nowadays computer programmes are used to select random samples.
- When an election takes place, television networks provide election coverage and try to predict the results
- This is done through exit polls: a random sample of voters who exit the polling booths is asked whom they voted for
- The prediction is made from the data of this sample of voters
- Exit polls do not always predict correctly; the reasons are the errors of this chapter (Section 7): a small or unrepresentative sample (sampling error, sampling bias), voters who refuse to answer (non-response), or voters who do not answer truthfully (error in data acquisition)
- A random number table is a printed list of digits (0 to 9) in which each digit appears without any pattern, with equal chance
- Step 1: give every unit of the population a number (10 students: 1 to 9, and the tenth student 0)
- Step 2: start anywhere in the table and read in one direction (single digits for 10 units; pairs of digits for up to 100 units)
- Step 3: select the unit whose number appears; skip a number already drawn; continue until the sample is complete
- Example (illustrative row): reading single digits from the row 2952 6641 … gives 2, 9, 5, so students numbered 2, 9 and 5 are selected
- The food grain activity: number the last 50 years 01 to 50, read pairs of digits, and take the first 10 different numbers between 01 and 50
6.2 Non-random sampling
In a non-random sampling method all the units of the population do not have an equal chance of being selected, and the convenience or judgement of the investigator plays an important role. The units are mainly selected on the basis of judgement, purpose, convenience or quota.
- The book’s example: you have to select 10 out of 100 households in a locality
- You select the households conveniently situated, or those known to you or your friend
- You are using your judgement (bias) in selecting the 10 households, so this is not a random selection
| Basis | Random sampling | Non-random sampling |
|---|---|---|
| Chance of selection | Equal for every unit | Not equal for all |
| Role of the investigator | No judgement; slips or numbers decide | Judgement, convenience, purpose or quota |
| Bias | Free from the investigator’s personal bias | Bias may enter |
| Example | 30 of 300 households by slips; exit polls | 10 of 100 convenient or known households |
7 Sampling and non-sampling errors
A population of numerical values has two important characteristics: first, central tendency, measured by the mean, the median or the mode (Chapter 5); second, dispersion (how far the values are spread from the average), measured by the standard deviation, mean deviation, range, etc. In this chapter only their names are needed.
The actual value of a characteristic of the population (for example, average income) is a population parameter. The purpose of a sample is to get one or more estimates of the population parameters.
Sampling error refers to the difference between the sample estimate and the corresponding population parameter (the actual value). Its magnitude can be reduced by taking a larger sample.
Sampling error = population parameter (true value) − sample estimate
Population mean = sum of all values ÷ number of values
Given: incomes of 5 farmers (variable x): 500, 550, 600, 650, 700. Sample: 2 farmers with incomes 500 and 600.
Population average (parameter): (500 + 550 + 600 + 650 + 700) ÷ 5 = 3000 ÷ 5 = 600
Sample average (estimate): (500 + 600) ÷ 2 = 1100 ÷ 2 = 550
Sampling error: 600 (true value) − 550 (estimate) = 50
Meaning: a sample of only two farmers underestimated the average income by 50.
There are 10 possible samples of 2 out of the 5 farmers. Their means: 525, 550, 575, 600, 575, 600, 625, 625, 650, 675.
- The average of these 10 means = 6000 ÷ 10 = 600 = the population mean
- With samples of 2, the largest error is 75 (sample 500, 550 has mean 525; or 650, 700 has mean 675)
- With samples of 4 farmers, the largest error is only 25 (e.g. 500, 550, 600, 650 has mean 575)
- So a larger sample reduces sampling error, as the book says
- Use all the population values for the population mean, not only the sample values
- A census has no sampling error (everyone is counted), but it can have non-sampling errors
- “A larger sample reduces non-sampling errors” is false; a larger sample reduces only sampling error
7.1 Non-sampling errors
- Non-sampling errors are more serious than sampling errors
- Reason: a sampling error can be minimised by taking a larger sample, but a non-sampling error is difficult to minimise even with a large sample
- Even a census can contain non-sampling errors
Errors in data acquisition arise from the recording of incorrect responses.
- Table example: students asked to measure the teacher’s table get different lengths, due to differences in measuring tape, carelessness, etc.
- Orange example: prices of oranges vary from shop to shop, market to market and with quality, so only average prices can be considered
- Recording mistake: the enumerator or respondent may record 13 instead of 31
Non-response occurs if an interviewer is unable to contact a person listed in the sample or a person from the sample refuses to respond. The sample observation may then not be representative.
Sampling bias occurs when the sampling plan is such that some members of the target population could not possibly be included in the sample.
| Basis | Sampling error | Non-sampling error |
|---|---|---|
| Meaning | Gap between the sample estimate and the population parameter | Errors in collecting, recording or selecting data |
| Where | Only in sample surveys | In samples and in a census |
| Effect of a larger sample | Falls | Difficult to reduce |
| Seriousness | Less serious | More serious |
| Example | 600 − 550 = 50 | Recording 13 for 31; refusing to respond |
8 Census of India and NSSO
There are agencies both at the national and state level to collect, process and tabulate statistical data. Their data are our main sources of secondary data.
National-level agencies
- Census of India
- National Sample Survey (NSS)
- Central Statistics Office (CSO)
- Registrar General of India (RGI)
- Directorate General of Commercial Intelligence and Statistics (DGCIS)
- Labour Bureau
8.1 Census of India
- The Census of India provides the most complete and continuous demographic record of population
- It is being regularly conducted every ten years since 1881
- The first Census after Independence was conducted in 1951
- Census officials collect information on size, density, sex ratio, literacy, migration, rural-urban distribution, etc.
- Census data are interpreted and analysed to understand many economic and social issues in India
8.2 National Sample Survey Organisation (NSSO)
- The NSS was established by the Government of India to conduct nation-wide surveys on socio-economic issues
- It does continuous surveys in successive rounds
- Its data are released through reports and its quarterly journal Sarvekshana
- It provides periodic estimates of literacy, school enrolment, utilisation of educational services, employment, unemployment, manufacturing and service sector enterprises, morbidity, maternity, child care and utilisation of the public distribution system
- The NSS 60th round (January-June 2004) was on morbidity and healthcare
- The NSS 68th round (2011-12) was on consumer expenditure
- The NSS also collects details of industrial activities and retail prices for various goods, which the Government of India uses for planning purposes
| Basis | Census of India | National Sample Survey Organisation (NSSO) |
|---|---|---|
| Method | Complete enumeration (every household) | Sample survey |
| When | Every 10 years (since 1881) | Continuous, in successive rounds |
| Main topics | Size, density, sex ratio, literacy, migration, rural-urban distribution | Education, employment, unemployment, enterprises, health, consumer expenditure, PDS, retail prices |
| Publication | Census reports (Registrar General) | Reports and the quarterly journal Sarvekshana |
9 Differences the exam asks (summary)
| Pair | Key difference in one line |
|---|---|
| Primary vs secondary data | Collected first-hand for the first time vs already collected and processed by another agency |
| Census vs sample | Every unit of the population vs a representative part |
| Population vs sample | Totality of items under study vs the selected part of it |
| Random vs non-random sampling | Equal chance vs investigator’s judgement |
| Sampling vs non-sampling error | Gap between estimate and parameter (falls with a larger sample) vs mistakes in collection (more serious) |
| Closed-ended vs open-ended questions | Answer from given options vs answer in own words |
- Data = economic facts in numbers; a tool for reaching a sound conclusion on a problem
- Primary: first-hand, first time; secondary: from another agency, saves time and cost
- Questionnaire: short, easy, general to specific, precise, no double negatives or leading questions
- Three modes: personal (highest response, most expensive), mail (least expensive, remote areas, not for illiterates), telephone (cheap, limited access)
- Pilot survey = pre-testing of the questionnaire
- Census covers every unit; a sample is smaller, cheaper, quicker, more detailed
- Random: equal chance (lottery, random number tables); non-random: judgement, convenience, quota
- Sampling error = parameter − estimate (600 − 550 = 50); falls with a larger sample
- Non-sampling errors are more serious: data acquisition, non-response, sampling bias
- Census: every 10 years since 1881, first after Independence 1951, last 2011; NSSO: Sarvekshana, 60th round 2004, 68th 2011-12
- The choice of source of data and mode of collection depends on the objective of the study
- Can I write the difference between primary and secondary data with examples?
- Can I spot the fault in a poor question and rewrite it correctly?
- Can I choose the right mode of survey for a situation and give the reason?
- Can I compute the population mean, the sample mean and the sampling error from given values?
- Can I give examples of the three non-sampling errors and the facts about the Census and the NSSO?