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Census vs Sampling, Errors, Secondary Sources & Exercises

🎓 Class 11 Social Science CBSE Theory Ch 2 — Collection of Data ⏱ ~25 min
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Class 11 · Statistics for Economics · Chapter 2

Census, Sampling, Errors and NCERT Exercises

Should the researcher count everyone in the population — or just a small, well-chosen group? In this part we contrast the Census with the Sample Survey, learn random and non-random sampling, distinguish sampling from non-sampling errors, meet the major Indian agencies that publish secondary data (Census of India, NSSO, RBI), and finish with worked answers to every NCERT exercise.

2.7 Census vs Sample Surveys

Once a researcher has chosen the survey method and the questionnaire, the next big decision is: how many people should I cover? The two extreme answers give us the two methods of enquiry — Census and Sample Survey.

2.7.1 The Census or Method of Complete Enumeration

A Census? is a survey that includes every single element of the population. If the population is "all households in India", a census collects information from every household — rural and urban — through a house-to-house enquiry. India's Census is conducted every ten years, and the Registrar General of India publishes demographic data on births, deaths, literacy, employment, life expectancy, size and composition of the population.

📊 India's Population in Census Numbers
Census 1901: population of India was 23.83 crore. Census 2001: 102.87 crore. Census 2011: 121.09 crore. In 110 years (1901–2011) India added more than 97 crore people. The annual growth rate of the population, which was 2.2% per year in 1971–81, fell to 1.97% in 1991–2001 and 1.64% in 2001–2011 — slow demographic transition visible in successive censuses. The last completed Census was held in 2011.

2.7.2 Population and Sample

In statistics, the Population (or Universe) is the totality of items under study — every individual or unit that possesses the characteristic the researcher is interested in. The first task of any survey is to define the population precisely. If the whole population cannot be studied, the researcher selects a representative sample? — a smaller group that mirrors the population.

📖 Definition — Population vs Sample
Population (Universe): all individuals/items possessing a given characteristic relevant to the study.
Sample: a subset of the population from which information is actually collected. A good sample is generally smaller than the population yet capable of providing reasonably accurate information about it at lower cost and shorter time.

2.7.3 NCERT Worked Example — Agricultural Labourers in Manipur

📜 Worked Example
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.
— NCERT Statistics for Economics, Ch. 2

Most surveys in modern statistics are sample surveys, not censuses. A sample provides reliable, accurate information at lower cost and in shorter time. Because samples are small, more detailed enquiries can be conducted; because the team of enumerators is small, training and supervision are easier and more effective.

2.8 Sampling Techniques — Random and Non-Random

How exactly does the researcher pick the sample from the population? There are two broad families.

2.8.1 Random Sampling

In a random sample?, every individual unit in the population has an equal chance of being selected. NCERT illustrates this with the petrol-price example: the government wants to study the impact of a petrol price rise on 300 households of a locality. The names of all 300 households (the sampling frame) are written on slips, mixed in a bowl, and 30 slips are drawn one by one. This is the lottery method. Today, computer programmes and Random Number Tables do the same job in milliseconds.

🗳️ Real-Life Example — Exit Polls
When elections take place, TV channels predict winners through exit polls: a random sample of voters leaving polling booths is asked who they voted for. From the sample replies, the result is forecast. Exit polls do not always predict correctly — partly because some voters lie, partly because the sample may not be perfectly representative.

2.8.2 Non-Random Sampling

Suppose you must select 10 households out of 100 in a locality. Instead of using the lottery method you pick the 10 most convenient — those near your house or known to your friends. In a non-random sample the units are chosen on the basis of judgement, purpose, convenience or quota; not every unit has an equal chance of being selected. The investigator's bias and convenience play an important role. Non-random samples are quicker and cheaper, but the results may not be safely generalised to the whole population.

A Population of 20 Kuchha + 20 Pucca Houses Representative Sample (Random) 4 Kuchha + 4 Pucca → mirrors the population Non-Representative Sample 7 Kuchha + 1 Pucca → biased A representative sample reflects the proportions in the population. A non-representative sample over- or under-counts certain groups. = Kuchha house = Pucca house
Fig 2.3 — A representative sample preserves the mix of the population; a non-representative one distorts it.
EXPLORE — Sampling Years for Foodgrain Trends
Bloom: L3 Apply

You have to analyse the trend of food-grain production in India over the last fifty years. Because collecting data for all fifty years is hard, you must select a sample of ten years. Using a Random Number Table (or computer randomiser), describe how you would draw the sample years and why this is preferred over picking ten "round" years like 1971, 1981, 1991, ...

✅ Sample
Number the 50 years 01–50 (where 01 = the earliest year). Open a Random Number Table and read two-digit pairs in any direction; pick the first 10 pairs in the range 01–50 (skipping out-of-range or repeated values). Those ten years are your sample. Picking only round years (1971, 1981, ...) would systematically over-represent boundary years and might miss the bumper or drought years that fall in between, so the trend would be smoothed unfairly. Random selection prevents this bias.

2.9 Sampling Errors and Non-Sampling Errors

Even a perfectly designed survey will not produce numbers exactly equal to the truth. Errors creep in. NCERT distinguishes two kinds — and surprisingly, the smaller one is the easier to control.

2.9.1 Sampling Error

Sampling error is the gap between the value calculated from the sample (the estimate) and the true value of the population parameter. Sampling errors arise because the sample, however carefully drawn, is only a part of the population. The good news: sampling error shrinks as the sample size grows. A larger sample is closer to the population on average.

Sampling Error = Population Parameter (true value) − Sample Estimate

2.9.2 NCERT Worked Example — Manipur Farmers' Income

📜 Worked Example — Income of 5 Farmers (₹)
Population values of variable X (income): 500, 550, 600, 650, 700.
Population mean = (500 + 550 + 600 + 650 + 700) ÷ 5 = 3000 ÷ 5 = 600.
Now suppose a sample of two individuals gives values 500 and 600.
Sample mean = (500 + 600) ÷ 2 = 1100 ÷ 2 = 550.
Sampling error = 600 (true value) − 550 (estimate) = 50.
— NCERT Statistics for Economics, Ch. 2

2.9.3 Non-Sampling Errors

Non-sampling errors are mistakes that have nothing to do with the sample size — and they are more serious than sampling errors because increasing the sample does not get rid of them. Even a Census can contain non-sampling errors. NCERT lists three sources.

🎯
Sampling Bias
The sampling plan systematically excludes a part of the target population — those excluded units have zero chance of selection. The estimate is then off-target however large the sample.
🤐
Non-Response Errors
A respondent in the sample cannot be contacted or refuses to reply. The remaining respondents may not represent the whole sample.
✏️
Errors in Data Acquisition
Wrong values get recorded. Students measuring a desk with different tapes; enumerators noting "13" when the answer was "31"; price recorded for one shop quoted as the market average. Recording & transcription mistakes.
⚠️ Why Non-Sampling Errors Are More Dangerous
Increasing the sample size cuts sampling error but does nothing for non-sampling errors — a poorly worded form, a biased enumerator or systematic exclusion of a community will distort even a 100% Census. That is why surveys spend so much energy on questionnaire design, enumerator training, and call-back procedures for non-respondents.

2.10 Census of India and NSSO — Major Sources of Secondary Data

India has a strong public statistical infrastructure. Several agencies — at the national and state level — collect, process and tabulate data and publish it for everyone to use. These agencies are the main sources of secondary data? for students, journalists, businesses and researchers.

Table 2.3 — Major National Agencies Producing Statistical Data in India
AgencyWhat it doesTypical data published
Census of IndiaConducted every 10 years since 1881; first post-Independence Census in 1951; last in 2011Population size, density, sex ratio, literacy, migration, rural-urban distribution
National Sample Survey (NSS / NSSO?)Continuous nation-wide socio-economic surveys in successive "rounds"; results released through reports and the journal SarvekshanaLiteracy, school enrolment, employment-unemployment, consumer expenditure, morbidity, healthcare, public distribution system, retail prices, industrial activity
Central Statistics Office (CSO)Co-ordinates national statistics; computes national income aggregatesNational Accounts, GDP, Index of Industrial Production, CPI
Registrar General of India (RGI)Conducts Census; maintains Civil Registration SystemBirth and death rates, life expectancy, demographic tables
Reserve Bank of India (RBI?)Central bank; collects and publishes financial & monetary statisticsMoney supply, interest rates, banking, balance of payments, inflation
DGCISDirectorate General of Commercial Intelligence and StatisticsForeign trade statistics — exports, imports
Labour BureauMinistry of Labour & EmploymentWage rates, CPI for industrial / agricultural workers, employment data
📚 Other Useful Sources
Beyond agencies, secondary data is published in the Statistical Abstract of India, RBI's Handbook of Statistics on the Indian Economy, the Economic Survey, state-government statistical handbooks, journals and reputable websites.

Some specific NSS rounds you should remember from NCERT: the NSS 60th round (Jan–June 2004) covered morbidity and healthcare; the NSS 68th round (2011–12) covered consumer expenditure. NSS data is widely used by the Government of India for planning purposes.

2.11 Conclusion

Economic facts expressed in numbers are called data. The point of collecting them is to understand, explain and analyse a problem and the causes behind it. Primary data are obtained by conducting a survey; surveys involve careful steps — defining the population, designing the questionnaire, running a pilot, picking a representative sample, choosing a mode and minimising both sampling and non-sampling errors. Where primary surveys are impractical, the researcher draws on the rich seam of secondary data published by the Census of India, NSSO, RBI and other agencies. The choice of source and mode always depends on the objective of the study.

REFLECT — Population, Sample and the Right Tool
Bloom: L4 Analyse
  1. If you study the opinion of students about the new Class XI Economics textbook, what is the population and what is a reasonable sample?
  2. If a researcher wants to estimate the average yield of wheat in Punjab, what will be her population and sample?
  3. In which year is the next decennial Census likely in India and China?
✅ Sample Answers
(1) Population = all Class XI students in India (or in your state) studying the new textbook. Sample = a few hundred students drawn at random from many schools across regions, urban + rural, government + private.
(2) Population = all wheat farms in Punjab. Sample = a randomly selected set of farms across the major wheat-growing districts (Ludhiana, Amritsar, Patiala, etc.) covering different farm sizes.
(3) India's last completed Census was 2011 and is decennial (next round was scheduled for 2021 and has been deferred). China's last decennial census was conducted in 2020 and is also held every 10 years.

📝 NCERT Exercises — Worked Solutions

Q1 Frame at least four appropriate multiple-choice options for the following questions: (i) Which of the following is the most important when you buy a new dress? (ii) How often do you use computers? (iii) Which newspapers do you read regularly? (iv) Rise in the price of petrol is justified. (v) What is the monthly income of your family?
(i) Most important when buying a dress: (a) Price (b) Brand (c) Fabric & comfort (d) Style/design (e) Any other (specify).

(ii) How often do you use computers? (a) Daily (b) 3–6 days a week (c) 1–2 days a week (d) Rarely (e) Never.

(iii) Which newspaper do you read regularly? (a) The Times of India (b) The Hindu (c) Hindustan Times (d) An Indian-language daily (specify) (e) Any other / online news portal.

(iv) Rise in petrol price is justified. (a) Strongly agree (b) Agree (c) Neither agree nor disagree (d) Disagree (e) Strongly disagree.

(v) Monthly family income (₹): (a) Below 25,000 (b) 25,000–50,000 (c) 50,000–1,00,000 (d) 1,00,000–2,00,000 (e) Above 2,00,000.
Q2 Frame five two-way questions (with `Yes' or `No').
(1) Do you own a mobile phone? Yes / No.
(2) Do you watch the news in English? Yes / No.
(3) Did you visit a doctor in the last 12 months? Yes / No.
(4) Do you live in a household connected to piped drinking water? Yes / No.
(5) Have you opened a bank account in your own name? Yes / No.
Q3 State whether the following statements are True or False. (i) There are many sources of data. (ii) Telephone survey is the most suitable method of collecting data when the population is literate and spread over a large area. (iii) Data collected by an investigator is called secondary data. (iv) There is a certain bias involved in non-random selection of samples. (v) Non-sampling errors can be minimised by taking large samples.
(i) True — primary surveys, government agencies, books, newspapers, websites, etc.
(ii) True — telephone surveys are quick and economical when respondents have phones and are spread out.
(iii) False — data collected first-hand by an investigator is primary data, not secondary.
(iv) True — judgement / convenience sampling carries the investigator's bias.
(v) False — non-sampling errors persist even in a Census; only sampling error shrinks with larger samples.
Q4 Diagnose the problems with the following questions: (i) How far do you live from the closest market? (ii) If plastic bags are only 5% of our garbage, should it be banned? (iii) Wouldn't you be opposed to an increase in price of petrol? (iv) Do you agree with the use of chemical fertilisers? (v) Do you use fertilisers in your fields? (vi) What is the yield per hectare in your field?
(i) Ambiguous — "far" needs a unit. Rewrite with options (less than 1 km / 1–3 km / more than 3 km).
(ii) Leading — the "only 5%" tilts the respondent against banning. Rewrite: "Should plastic bags be banned?"
(iii) Double negative ("Wouldn't you be opposed"). Rewrite: "Do you support / oppose an increase in petrol prices?"
(iv) Vague — "agree with" what aspect? Rewrite: "Do you support the use of chemical fertilisers in farming?"
(v) Acceptable, but should come after Q (vi) is reframed; better as part of a screening sequence.
(vi) Should specify crop and unit. Rewrite: "What is the average yield (in quintals per hectare) of wheat / rice on your land?"
Q5 Design a suitable questionnaire to research the popularity of Vegetable Atta Noodles among children.
A short eight-question schedule:
(1) Age: (a) 6–8 (b) 9–11 (c) 12–14.
(2) Gender: M / F / Prefer not to say.
(3) Have you eaten Vegetable Atta Noodles? Yes / No. (If "No", end survey.)
(4) How often do you eat them? (a) Daily (b) 2–3 times a week (c) Once a week (d) Rarely.
(5) Who normally cooks them? (a) Self (b) Parent (c) Sibling (d) Other.
(6) What do you like most? (a) Taste (b) Quick to make (c) Healthier than maida noodles (d) Pack design (e) Any other.
(7) On a scale of 1–5, how do you rate the taste?
(8) Would you recommend them to a friend? Yes / No / Maybe. Pre-test the form on 10 children before rolling out.
Q6 In a village of 200 farms, a study was conducted to find the cropping pattern. Out of the 50 farms surveyed, 50% grew only wheat. What is the population and the sample size?
Population: all 200 farms in the village.
Sample size: 50 farms (the ones surveyed).
The 25 farms (50% of 50) growing only wheat is a finding from the sample, not the sample itself.
Q7 Give two examples each of sample, population and variable.
Population: (i) all Class XI students in Delhi; (ii) all wheat farms in Punjab.
Sample: (i) 200 Class XI students drawn from 20 Delhi schools; (ii) 100 wheat farms drawn from 4 Punjab districts.
Variable: (i) monthly pocket money of a student (X); (ii) yield per hectare of wheat (Y).
Q8 Which of the following methods give better results and why? (a) Census (b) Sample.
Sample surveys generally give better practical results for most enquiries. They cost less, take less time, allow more detailed enquiry, need fewer (and better-trained) enumerators and are easier to supervise — so the data quality is often higher than a sprawling Census. A Census is preferable only when the population is small or the question demands complete coverage (e.g., national population count for parliamentary delimitation).
Q9 Which of the following errors is more serious and why? (a) Sampling error (b) Non-Sampling error.
Non-sampling error is more serious. Sampling error can be reduced simply by increasing the sample size, but non-sampling errors (sampling bias, non-response, recording mistakes) remain — and even a Census can suffer from them. Greater sample size cannot compensate for a biased questionnaire or a careless enumerator.
Q10 Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible?
The number of possible samples = 10C3 = (10 × 9 × 8) ÷ (3 × 2 × 1) = 720 ÷ 6 = 120 samples. (Order does not matter when picking a sample, so we use combinations.)
Q11 Discuss how you would use the lottery method to select 3 students out of 10 in your class.
Step 1: Write the names (or roll numbers 1–10) of all 10 students on identical slips. Step 2: Fold each slip the same way so that none can be distinguished by feel. Step 3: Mix all the slips thoroughly in a bowl. Step 4: Without looking, draw one slip — record the name and set it aside. Step 5: Draw a second slip and record. Step 6: Draw a third. The three names recorded form a random sample of size 3 from the population of 10. Every student had an equal chance of being selected.
Q12 Does the lottery method always give you a random sample? Explain.
The lottery method gives a random sample only if three conditions hold: (i) every member of the population has an entry in the lottery (the sampling frame is complete); (ii) all slips are physically identical so none can be picked deliberately; (iii) the slips are mixed thoroughly before each draw. If any condition fails — slips of different sizes, missing names, or sloppy mixing — selections become biased and the sample is no longer random.
Q13 Explain the procedure for selecting a random sample of 3 students out of 10 by using random number tables.
Step 1: Number the 10 students 0–9 (or 01–10). Step 2: Open the Random Number Table at any starting point and read in any consistent direction (left-to-right, row by row). Step 3: Read one digit at a time. The first digit you encounter that lies in 0–9 selects that student. Step 4: Continue until you have three different digits — repeats are skipped. Step 5: The three selected numbers identify the sample. This guarantees that each student had an equal chance of selection and avoids any human bias.
Q14 Do samples provide better results than surveys? Give reasons for your answer.
The question is best read as "do sample surveys give better results than complete surveys / Census?". For most studies the answer is yes — a well-drawn sample provides reasonably reliable information at lower cost and in shorter time. Smaller samples allow more detailed enquiry and easier supervision of enumerators, so quality of data is often better than in a sprawling Census. However, when the population is small or the question requires every unit (e.g., voter rolls, total head-count), a complete enumeration is necessary.

📋 Recap — Chapter 2 in One Page

Key Takeaways

  • Data are facts collected for analysis; they may be primary (first-hand) or secondary (re-used).
  • Primary data are gathered through surveys using personal interviews, mailed questionnaires or telephone interviews — each with its own pros and cons.
  • A questionnaire must be short, clear, well-ordered (general → specific), and free of leading or double-negative wording.
  • Closed-ended questions are easy to score; open-ended questions capture individuality.
  • A pilot survey tests the questionnaire before the main survey.
  • A Census covers every unit; a sample covers a representative subset and saves time and money.
  • Random sampling gives every unit an equal chance of selection (lottery method, random number tables); non-random sampling uses judgement or convenience.
  • Sampling error = true value − sample estimate; it shrinks as sample size grows.
  • Non-sampling errors (bias, non-response, recording mistakes) are more serious because they are not cured by a larger sample.
  • Census of India and NSSO are the two flagship national agencies for secondary data; RBI, CSO, RGI, DGCIS and the Labour Bureau also publish important series.

🔑 Key Terms

Variable
A quantity (X, Y, Z) that takes different values across observations or over time.
Observation
A single recorded value of a variable for a specific case.
Primary Data
First-hand data collected directly by the researcher for the question at hand.
Secondary Data
Data already collected and published by another agency, reused for a new study.
Questionnaire
A structured set of questions used to collect survey responses.
Pilot Survey
A small trial run of the questionnaire before the main survey, to test its design and cost.
Census
A survey covering every element of the population — complete enumeration.
Sample
A representative subset of the population selected for actual study.
Random Sampling
Each unit has an equal chance of selection (e.g., lottery method, random number tables).
Non-Random Sampling
Selection by judgement, convenience, purpose or quota — units do not have equal chance.
Sampling Error
Difference between sample estimate and the true population parameter; shrinks with larger samples.
Non-Sampling Error
Errors due to bias, non-response or wrong recording; not reduced by larger samples.
NSSO
National Sample Survey Office — conducts socio-economic surveys; publishes Sarvekshana.
RBI
Reserve Bank of India — central bank, source of monetary & financial data.
Statistical Abstract
An official compendium of statistical series on the Indian economy and society.
⚖️ Assertion–Reason Questions (Class 11)

Choose: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true, R is false. (D) A is false, R is true.

Assertion (A): A non-sampling error cannot be reduced merely by enlarging the sample.
Reason (R): Non-sampling errors arise from bias, non-response and recording mistakes, which can affect even a complete Census.
Correct: (A) — Both true; the reason explains why scaling up the sample does not eliminate these errors.
Assertion (A): Sample surveys are usually preferred to a Census for economic enquiries.
Reason (R): Samples are cheaper, faster, allow more detailed enquiry and require a smaller, better-supervised team of enumerators.
Correct: (A) — Both true and R correctly explains A.
Assertion (A): A non-random sample always gives unbiased estimates of the population parameter.
Reason (R): In non-random sampling not every unit of the population has an equal chance of being selected, so the investigator's judgement and convenience influence the outcome.
Correct: (D) — Assertion is false (non-random samples typically introduce bias). Reason is true and is, in fact, the precise reason why the assertion is false.

Frequently Asked Questions — Census, Sampling, Errors and NCERT Exercises

What is the difference between census and sample survey in Class 11 Statistics?

The census method, also called complete enumeration, collects information from every unit of the population, while a sample survey collects information from only a representative part of the population. NCERT Class 11 Statistics Chapter 2 Part 2 explains that the census gives complete coverage and is highly accurate but is expensive, slow and impractical for very large populations. A sample survey is fast and cost-effective and, when properly designed using random sampling, gives results that are statistically representative of the whole population. India conducts a population census every ten years and uses sample surveys (NSSO) for most economic indicators.

What is random sampling in NCERT Class 11 Statistics Chapter 2?

Random sampling is a method in which every unit in the population has an equal and known chance of being selected into the sample, with no investigator bias. NCERT Class 11 Statistics Chapter 2 lists three main random methods: simple random sampling using a lottery or random number table, stratified random sampling where the population is divided into groups (strata) and units are picked from each, and systematic sampling where every k-th unit is chosen after a random start. Random sampling is preferred because it makes the sample representative and allows the calculation of sampling error mathematically.

What are sampling errors and non-sampling errors in Class 11 Statistics?

Sampling error is the difference between the sample value and the true population value that arises only because the entire population was not surveyed; it can be measured and reduced by increasing sample size or improving design. Non-sampling error arises from mistakes during data collection, recording or processing — such as wrong responses, faulty questionnaire design, enumerator bias or computational mistakes — and these errors occur in both census and sample surveys. NCERT Class 11 Statistics Chapter 2 stresses that non-sampling errors are often larger than sampling errors and must be controlled through training, supervision and pilot testing.

What is the role of NSSO in collecting data in India?

The National Sample Survey Office (NSSO) is the largest organisation in India conducting nationwide household surveys on socio-economic topics such as employment, consumption expenditure, education and health. NCERT Class 11 Statistics Chapter 2 Part 2 explains that NSSO uses scientific stratified random sampling to produce official estimates that are used by the government, RBI, planners and researchers to design policies on poverty, food security and welfare. NSSO data is published as official secondary data and is one of the most authoritative sources of statistical information about Indian households.

When should an investigator use sample survey instead of census in Class 11 Statistics?

An investigator should use a sample survey instead of a census when the population is very large, when the data needs to be collected quickly, when the budget is limited, or when the test is destructive (for example testing the strength of bulbs destroys them). NCERT Class 11 Statistics Chapter 2 Part 2 also notes that a well-designed sample survey can sometimes be more accurate than a census because it allows tighter quality control over a smaller workforce. The census is preferred only when complete coverage is essential, as in the decennial Census of India.

What is stratified random sampling in NCERT Class 11 Chapter 2?

Stratified random sampling is a sampling method in which the population is first divided into homogeneous, non-overlapping subgroups called strata, and then a simple random sample is drawn from each stratum independently. NCERT Class 11 Statistics Chapter 2 Part 2 explains that the strata are formed on the basis of relevant characteristics like income, age, gender or geography. This method ensures that every important subgroup is represented in the final sample, reduces sampling error compared to simple random sampling, and is used widely in NSSO household surveys for accurate state-wise and rural/urban estimates.

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