Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Chapter Introduction
Data is the raw material of statistics. Before you can organise, present, or analyse data, you must first collect it. This chapter focuses on how data is collected — the sources it comes from, the methods used to gather it, and the critical decisions investigators must make between census and sampling approaches. Understanding data collection is essential because the quality of your statistical analysis depends entirely on the quality of the data you start with.
The chapter also introduces the important distinction between sampling and non-sampling errors, and the roles of key Indian statistical organisations (NSSO and CSO). These concepts are frequently tested in CBSE exams.
Key Definitions
| Term | Definition |
|---|---|
| Population | The complete set of all units (individuals, items, or events) that the investigator wants to study |
| Sample | A subset of the population selected for study |
| Census | Method of collecting data from every unit in the population (complete enumeration) |
| Sampling | Method of collecting data from a representative subset of the population |
| Sampling frame | A complete list of all units in the population from which a sample is drawn |
| Questionnaire | A set of questions designed to collect data from respondents in a structured way |
| Schedule | A questionnaire filled by the enumerator (not the respondent); used in personal interviews |
| Enumerator | A person appointed to collect data from respondents through personal interview |
| Respondent | A person who provides data by answering the questions asked |
| Sampling error | The difference between the sample result and the true population value, arising because only a part is studied |
| Non-sampling error | Errors that occur in both census and sampling due to factors other than sampling — response errors, non-response, processing mistakes, etc. |
| NSSO | National Sample Survey Organisation — conducts large-scale sample surveys in India on socio-economic issues |
| CSO | Central Statistical Organisation — coordinates statistical activities in India and publishes national accounts |
Detailed Concepts
Sources of Data
| Source | Description | Examples |
|---|---|---|
| Primary | Data collected firsthand by the investigator | Door-to-door survey, field experiment, telephone survey |
| Secondary | Data already collected by another agency | Census reports, RBI bulletins, NSSO surveys, published journals |
The choice between primary and secondary data depends on: purpose of study, available resources (time, money, personnel), degree of accuracy required, and availability of secondary data.
Methods of Collecting Primary Data
| Method | How it works | Advantages | Disadvantages |
|---|---|---|---|
| Personal interview | Enumerator visits respondent face-to-face and asks questions | High response rate; can clarify doubts; non-response is low; information is reliable; can observe body language | Expensive; time-consuming; requires trained enumerators; interviewer bias possible; limited geographical reach |
| Mailing questionnaire | Questionnaire sent by post/email to respondents | Cheap; covers wide area; no interviewer bias; respondents have time to think | Low response rate (often below 40%); cannot clarify doubts; only literate respondents can answer; delayed responses; no control over who fills it |
| Telephone interview | Questions asked over the phone by the enumerator | Quick; moderate cost; wider reach than personal interview; can clarify doubts | Limited to phone owners; short interviews only; cannot show visual aids; response may be incomplete; call reluctance growing |
Choosing the right method:
- Small population, need for accuracy: personal interview
- Large, literate population, limited budget: mailing questionnaire
- Quick results, moderate accuracy: telephone interview
- Sensitive topics requiring trust: personal interview
Preparation of Questionnaire
A good questionnaire is the backbone of primary data collection. Poorly designed questions lead to unreliable data.
Essential features of a good questionnaire:
1. Short and simple — Avoid lengthy questions; respondents lose interest 2. Clear and unambiguous — Every question must have only one interpretation 3. Logical sequence — Start with simple questions, move to complex ones 4. No leading questions — Do not suggest the answer (e.g., "Don't you think inflation is bad?") 5. No personal/sensitive questions unless absolutely necessary 6. Close-ended and open-ended balance — Use close-ended for easy tabulation, open-ended for depth 7. Pre-test (pilot study) — Test the questionnaire on a small group before the main survey 8. Covering letter — Explain the purpose and assure confidentiality 9. Instructions — Clear instructions on how to answer each question 10. Avoid double-barrelled questions — One question should ask only one thing
Difference between questionnaire and schedule:
| Feature | Questionnaire | Schedule |
|---|---|---|
| Filled by | Respondent | Enumerator |
| Cost | Lower | Higher (needs trained enumerator) |
| Response rate | Lower | Higher |
| Clarification | Not possible | Possible (enumerator explains) |
| Best for | Literate respondents | Illiterate or busy respondents |
Census vs Sampling
| Feature | Census | Sampling |
|---|---|---|
| Coverage | Every unit of the population | Only a subset of the population |
| Accuracy | More accurate (no sampling error) | Less accurate (subject to sampling error) |
| Cost | Very expensive | Relatively cheap |
| Time | Very time-consuming | Quick |
| Suitability | Small population; need for high accuracy | Large population; limited resources |
| Organisation | Requires large team, complex logistics | Smaller team, simpler logistics |
| Verification | Difficult to verify due to scale | Easier to verify results |
| Errors | Only non-sampling errors | Both sampling and non-sampling errors |
| Example | Population Census of India | NSSO surveys, exit polls, market research |
| Intensity of study | Limited depth (too many units) | Greater depth possible (fewer units) |
Methods of Sampling
Random Sampling (Probability Sampling)
Every unit in the population has an equal and known chance of being selected.
| Method | How it works | Advantages | Disadvantages |
|---|---|---|---|
| Lottery method | Write each unit's name on a slip, put in a box, draw randomly | Simple; no bias | Impractical for large populations |
| Random number tables | Use published tables of random numbers to select units | Scientific; suitable for large populations | Requires a sampling frame |
| Systematic sampling | Select every k-th unit after a random start (k = N/n) | Simple; evenly spread | If population has periodic pattern, results may be biased |
Non-Random Sampling (Non-Probability Sampling)
Selection depends on the investigator's judgement or convenience; not every unit has an equal chance.
| Method | How it works | Advantage | Disadvantage |
|---|---|---|---|
| Judgement (Purposive) sampling | Investigator selects units considered most representative | Useful when specific expertise or characteristics are needed | Highly subjective; prone to investigator bias |
| Convenience sampling | Select units that are easiest to reach | Quick and cheap | May not represent the population; high bias risk |
| Quota sampling | Investigator selects units to match known population proportions in quotas | Ensures representation of subgroups | Still non-random within each quota; interviewer bias possible |
Random vs Non-Random Sampling Comparison
| Feature | Random Sampling | Non-Random Sampling |
|---|---|---|
| Selection basis | Chance (equal probability) | Investigator's judgement or convenience |
| Bias | Minimal sampling bias | High risk of selection bias |
| Representativeness | More likely to represent the population | May not represent the population |
| Statistical inference | Results can be generalised to the population | Generalisation is unreliable |
| Complexity | Requires sampling frame (list of all units) | No sampling frame needed |
| Cost | Relatively higher | Relatively lower |
| Example | Lottery method, random number tables | Judgement, convenience, quota sampling |
Sampling Errors and Non-Sampling Errors
| Feature | Sampling Error | Non-Sampling Error |
|---|---|---|
| Cause | Studying only a part of the population | Factors other than sampling — response, non-response, processing |
| Occurs in | Only sampling | Both census and sampling |
| Increases with | Smaller sample size | Poor training, faulty design, careless work |
| Decreases with | Larger sample size | Better training, good questionnaire, careful supervision |
| Types | Only one type | Multiple types — response error, non-response, measurement error, processing error, bias |
| Detectability | Can be estimated mathematically | Hard to detect and measure |
| Prevention | Increase sample size; use random sampling | Train enumerators; pre-test questionnaire; supervise fieldwork; follow up non-responses |
Types of non-sampling errors in detail:
1. Response error — Respondent gives incorrect or misleading answers (intentional or unintentional). Example: under-reporting alcohol consumption. 2. Non-response error — Some selected units do not respond at all. Creates bias if non-respondents differ systematically from respondents. 3. Measurement error — Faulty instrument or method leads to wrong measurement. Example: a defective weighing scale. 4. Processing error — Mistakes in coding, tabulating, or computing data. Example: entering 100 instead of 10. 5. Sampling bias — Non-random selection introduces systematic error. Example: surveying only urban households to estimate national income. 6. Interviewer bias — The enumerator's personal views influence responses. Example: leading tone or body language that suggests a "correct" answer.
NSSO and CSO
| Body | Full form | Role |
|---|---|---|
| NSSO | National Sample Survey Organisation | Conducts large-scale sample surveys on employment, consumption, health, etc. Established in 1950. Surveys are conducted in "rounds" (e.g., 75th round on household consumer expenditure). |
| CSO | Central Statistical Organisation | Coordinates statistical activities across India; publishes national accounts data, GDP estimates, Index of Industrial Production (IIP). |
| MoSPI | Ministry of Statistics and Programme Implementation | Parent ministry overseeing both NSSO and CSO since 1999. |
Choosing Between Census and Sampling
The choice depends on several factors:
| Factor | Favour census | Favour sampling |
|---|---|---|
| Population size | Small | Large |
| Resources available | Adequate budget and time | Limited budget or time |
| Accuracy needed | Very high (e.g., defence equipment) | Moderate (e.g., market research) |
| Nature of study | Complete enumeration required | General trends sufficient |
| Destruction testing | Not applicable (every unit tested) | When testing destroys the item (e.g., bulb testing) |
| Legal requirement | When law demands (e.g., Population Census) | When no legal mandate exists |
Example where census is necessary: Population Census — the Constitution requires it for seat allocation and policy. Example where sampling is better: Testing bulb life — every bulb tested would leave nothing to sell.
Worked Example: Choosing the Right Method
| Situation | Best method of primary data collection | Reason |
|---|---|---|
| Survey of farmer opinions in a village | Personal interview | Farmers may be illiterate; need rapport and clarification |
| Survey of IT professionals' job satisfaction across India | Mailing questionnaire (online) | Literate, tech-savvy, geographically spread |
| Quick opinion poll before an election | Telephone interview | Need fast results, moderate accuracy acceptable |
| Study of sensitive health issues | Personal interview with trained enumerator | Trust needed; confidentiality assurance |
| Survey of book-reading habits of college students | Mailing or online questionnaire | Literate population, large sample, limited budget |
Important Points for Exams
1. Primary data is collected firsthand by the investigator; secondary data is already available from other sources. 2. Personal interview method has the highest response rate but is the most expensive. 3. Mailing questionnaire is cheap but has a very low response rate. 4. Census covers every unit and is more accurate but very costly; sampling covers only a subset. 5. In random sampling, every unit has an equal chance of selection; in non-random sampling, it does not. 6. The lottery method and random number tables are the two main methods of random sampling. 7. Judgement, convenience, and quota sampling are non-random methods. 8. Sampling error occurs only in sampling; non-sampling errors occur in both census and sampling. 9. Increasing sample size reduces sampling error but does not affect non-sampling errors. 10. NSSO conducts sample surveys; CSO coordinates statistical activities and publishes national accounts.
Common Mistakes
| Mistake | Why it is wrong | Correct approach |
|---|---|---|
| Saying sampling error occurs in census | Sampling error is caused by studying only a part of the population | Census studies every unit, so there is no sampling error |
| Confusing random and non-random methods | Lottery method and random numbers are random; judgement and convenience are non-random | Check whether every unit has an equal chance of selection |
| Thinking larger sample eliminates all errors | Larger sample reduces sampling error but not non-sampling errors | Address non-sampling errors through better design and training |
| Believing census has no errors at all | Census has no sampling error but still has non-sampling errors | Both methods can have non-sampling errors |
| Using convenience sampling and calling it representative | Convenience sampling is biased and non-random | For representativeness, use random sampling methods |
| Not pre-testing the questionnaire | Pilot study catches ambiguous or leading questions before the main survey | Always conduct a pilot study on a small group first |
| Confusing questionnaire with schedule | Questionnaire is filled by respondent; schedule is filled by enumerator | Choose based on literacy level and sensitivity of topic |
NCERT Exercise Focus
Focus on these NCERT exercise questions while preparing:
1. "Distinguish between census and sampling" — Prepare a 6-8 point comparison table. Most frequently asked. 2. "Explain methods of random sampling" — Describe lottery method and random number tables with examples. 3. "What are sampling and non-sampling errors?" — Distinguish clearly; emphasise that sampling error occurs only in sampling. 4. "What are the features of a good questionnaire?" — List at least 6 features with reasons. 5. "Distinguish between questionnaire and schedule" — Prepare a comparison table.
Exam Tips
1. Census vs Sampling comparison — This is the most frequently asked distinction question. Prepare a table with at least 6 points of difference. 2. "Explain the methods of random sampling" — Describe lottery method and random number tables with examples. A typical 3-mark question. 3. Sampling vs non-sampling errors — Very common 3-5 mark question. Emphasise: sampling error occurs only in sampling, non-sampling error occurs in both. 4. Questionnaire design — List 5-6 features of a good questionnaire. Use keywords: short, clear, logical sequence, no leading questions, pre-test. 5. Methods of primary data collection — Compare all three methods (personal interview, mailing, telephone) with advantages and disadvantages. 6. For 1-mark questions — Know exact definitions: sample, census, sampling error, NSSO, CSO. 7. Real-world examples score marks — Mention NSSO rounds, Population Census, exit polls as examples. 8. Questionnaire vs Schedule — Know the difference; it has appeared in previous years' papers.
Practice Questions for Self-Test
1. Distinguish between census and sampling methods of data collection. (3 marks) 2. What are the methods of random sampling? Explain any two with examples. (3 marks) 3. Differentiate between sampling error and non-sampling error. (3 marks) 4. What are the features of a good questionnaire? List any five. (3 marks) 5. Compare personal interview, mailing questionnaire, and telephone interview as methods of data collection. (5 marks) 6. What is the difference between questionnaire and schedule? (2 marks) 7. What are non-sampling errors? Explain any three types. (3 marks) 8. What is the role of NSSO and CSO in India? (2 marks) 9. "Larger sample size reduces sampling error but not non-sampling error." Explain. (3 marks) 10. What is convenience sampling? Why is it considered unreliable? (2 marks)
Key Statistics and Facts for Quick Reference
| Fact | Detail |
|---|---|
| Census example | Population Census of India |
| Sampling example | NSSO surveys, exit polls |
| Best response rate method | Personal interview |
| Cheapest method | Mailing questionnaire |
| Quick method | Telephone interview |
| Random sampling methods | Lottery, Random number tables, Systematic |
| Non-random methods | Judgement, Convenience, Quota |
| NSSO established | 1950 |
| MoSPI oversees | Both NSSO and CSO |
| Error that decreases with larger sample | Sampling error |
| Error in both census and sampling | Non-sampling error |
Quick Revision Notes
- Primary data: collected firsthand; Secondary data: already available.
- Three methods of primary data: personal interview (best response, most expensive), mailing (cheapest, lowest response), telephone (moderate).
- Good questionnaire: short, clear, logical order, no leading questions, pre-tested, covering letter.
- Questionnaire: filled by respondent. Schedule: filled by enumerator.
- Census: every unit, accurate, expensive, time-consuming. Sampling: subset, less accurate, cheap, quick.
- Random sampling: equal chance — lottery, random number tables, systematic.
- Non-random sampling: judgement, convenience, quota — faster but biased.
- Sampling error: only in sampling, decreases with larger sample.
- Non-sampling error: in both census and sampling — response, non-response, measurement, processing errors.
- NSSO: conducts sample surveys. CSO: coordinates statistics, publishes national accounts.
- Both NSSO and CSO come under MoSPI.