6 Statistics: Data, Sampling & Presentation · 6.1 Data, sampling, probability and presentation
6.1.1 Statistics: meaning and scope; primary and secondary data; census and sample; schedule and questionnaire
Statistics is the science of collecting, presenting, analysing and interpreting numerical data; data are primary (collected first-hand for the purpose) or secondary (already collected by someone else), and may come from a census (every unit) or a sample (a part).
- APPSC Paper I
- Advanced level
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Core facts
- Plural sense: statistics = numerical facts (data), e.g. production figures, prices.
- Singular sense: statistics = the science (methods) of collection, presentation, analysis and interpretation of data (Croxton and Cowden).
- Statistics as data (Secrist's characteristics): aggregates of facts, affected by many causes, numerically expressed, estimated with reasonable accuracy, collected systematically for a predetermined purpose, placed in relation to each other (comparable).
- A single number (one person's height) is not statistics; only aggregates are.
- Stages of a statistical study: collection → organisation (classification) → presentation (tables, diagrams) → analysis → interpretation.
- Primary data: collected for the first time by the investigator for the inquiry in hand ("raw" and original).
- Secondary data: collected earlier by someone else, used again; published or unpublished.
- Methods of collecting primary data:
- Direct personal investigation
- Indirect oral investigation (questioning third parties / witnesses)
- Information through local agents or correspondents
- Mailed questionnaire (filled by the informant)
- Schedules filled by enumerators
- Questionnaire: list of questions filled in by the respondent himself; needs literate respondents.
- Schedule: list of questions filled in by the enumerator while asking the respondent face to face.
- Census (complete enumeration): every unit of the population is studied. Sample method: only a representative part is studied.
- Population (universe): the whole group under study; sample: the part actually examined.
- India's Census is held every 10 years (last completed: 2011); it is a census of population, not a sample.
- NSO (National Statistical Office), under the Ministry of Statistics and Programme Implementation (MoSPI), formed in 2019 by merging the CSO and NSSO.
Explained
1. Scope and functions. Statistics simplifies masses of figures, makes comparison possible, helps in forecasting, policy-making (planning, budgets, wage and price policy), business decisions (market research, quality control) and testing of theories in economics, biology and other sciences.
2. Limitations (classic textbook list).
- Studies aggregates, not individuals.
- Does not study qualitative phenomena directly (honesty, intelligence) unless converted to numbers (scores, ranks).
- Laws are true on average, not exactly.
- Data must be uniform and homogeneous to be compared.
- Can be misused by people who do not know the methods.
3. Primary versus secondary data.
| Point | Primary data | Secondary data |
|---|---|---|
| Collected by | the investigator | another agency, earlier |
| Originality | original | already used |
| Cost and time | high | low |
| Fit to purpose | exact | may need adjustment |
Sources of secondary data.
- Published: Census reports, NSS reports, RBI Bulletin and Handbook of Statistics on the Indian Economy, Economic Survey, Statistical Abstracts, reports of commissions, international bodies (UN, IMF, World Bank).
- Unpublished: records of offices, firms, research workers, kept but not printed.
Before using secondary data, check: reliability of the collecting agency, suitability (same definitions, units, area and period), and adequacy (coverage and accuracy).
4. The five methods of collecting primary data.
| Method | Suits | Main drawback |
|---|---|---|
| Direct personal investigation | small, intensive inquiries | costly, limited coverage, investigator bias |
| Indirect oral investigation | when informants are unwilling (e.g. addiction inquiries); used by inquiry committees | witnesses may be biased |
| Local correspondents | regular, wide-area estimates (crop reports, prices) | rough accuracy, personal bias |
| Mailed questionnaire | large, scattered, literate population | poor response; incomplete answers |
| Schedules through enumerators | large inquiries, illiterate respondents (Census) | costly; enumerators need training |
5. Questionnaire versus schedule.
| Point | Questionnaire | Schedule |
|---|---|---|
| Filled by | respondent | enumerator |
| Sent | by post / online | carried by enumerator |
| Respondents | must be literate | can be illiterate |
| Response rate | low | high |
6. A good questionnaire. Short; questions simple, clear and unambiguous; no leading questions; no personal or offending questions; questions in logical order; prefer closed (yes/no, multiple choice) questions that are easy to tabulate; cross-check questions for accuracy; covering letter explaining the purpose and promising secrecy; tested first by a pilot survey (a small trial run) to correct the form.
7. Census versus sample.
| Point | Census | Sample |
|---|---|---|
| Units studied | all | a part |
| Cost, time, labour | high | low |
| Detail per unit | less possible | more intensive |
| Sampling error | none | present (can be measured) |
- Census suits: small populations, heterogeneous units, when every unit's data are needed (population count, voters' list).
- Sample suits: large or infinite populations, destructive testing (testing bulbs, tasting food, crash tests), when time and money are limited.
- A census is free of sampling error but not of non-sampling errors (wrong answers, counting mistakes).
Deeper
Statistical units. Before collection, the unit must be defined clearly: e.g. "household" (people sharing a common kitchen), "worker", "factory". A unit should be clear, stable (same over time), homogeneous and suitable for the purpose. Vague units make data non-comparable.
Degree of accuracy. Complete accuracy is neither possible nor needed; the accepted level depends on purpose. Large totals are rounded (e.g. to lakhs); small measurements (medicine doses) need exactness. Approximation is part of statistics, but the rounding rule must be stated.
Indian statistical system (2026 position).
- MoSPI sets standards; NSO has the National Accounts and survey divisions (the old CSO and NSSO work).
- NSS rounds: household consumption expenditure survey, Periodic Labour Force Survey (PLFS; revamped from January 2025 to give monthly and quarterly estimates for rural and urban areas, plus an annual report), surveys of enterprises.
- Census 2027: India's next Census (delayed from 2021) is notified with reference date 1 March 2027, and 1 October 2026 for snow-bound areas; it will count caste (the first full caste count since 1931) and collect data digitally (2025 announcements). The house-listing phase runs before the population count.
- Registrar General and Census Commissioner of India (Ministry of Home Affairs) runs the Census and the Sample Registration System (SRS) for birth and death rates.
Example 1. Which of these is primary data for a researcher? (a) prices taken from an RBI bulletin (b) her own household survey of milk prices (c) Census 2011 tables (d) a ministry's annual report Solution. Only (b) is collected first-hand for her inquiry. Answer: (b)
Example 2. A firm wants the average life of the electric bulbs it produces. Why must it sample? Solution. Testing life means burning the bulb out: a census would destroy the whole output. Answer: destructive testing makes a census impossible
Example 3. A survey of a village where most adults cannot read. Questionnaire or schedule? Solution. A questionnaire needs the respondent to read and write; an enumerator with a schedule can ask orally. Answer: schedule
AP angle
- The Directorate of Economics and Statistics (DES), Andhra Pradesh, under the Planning Department, is the State's nodal statistical agency; Assistant Statistical Officers work in this system at district and mandal level.
- DES collects primary data by schedules: crop estimation surveys (crop-cutting experiments), agricultural and price statistics, and the State sample of NSS rounds; it also compiles secondary data for the State's Statistical Abstract and district hand books, and estimates of Gross State Domestic Product (GSDP).
- The Socio-Economic Survey of AP, released with the State Budget, is a standard secondary source for State data.
Common traps
- ✗ "A questionnaire is filled by the enumerator." ✓ A questionnaire is filled by the respondent; a schedule by the enumerator.
- ✗ "Census data are always secondary." ✓ For the Census office they are primary; for a later user of the published tables they are secondary. The same data change type with the user.
- ✗ "A census has no errors." ✓ It has no sampling error, but non-sampling errors remain.
- ✗ "One figure, such as Ravi's income, is a statistic." ✓ Statistics are aggregates of facts.
- ✗ "Statistics studies qualitative facts directly." ✓ Only after converting them to numbers (ranks, scores).
- ✗ "NSO was formed by merging CSO and RBI." ✓ CSO and NSSO merged into NSO (2019) under MoSPI.
- ✗ "Mailed questionnaires suit illiterate populations." ✓ They need literate respondents and get a low response rate.
Quick revision
- Statistics (plural) = data; (singular) = the science of methods.
- Stages: collection, organisation, presentation, analysis, interpretation.
- Primary = first-hand; secondary = collected by others earlier.
- Five primary methods: direct personal, indirect oral, local correspondents, mailed questionnaire, schedules by enumerators.
- Questionnaire: respondent fills; schedule: enumerator fills.
- Pilot survey = trial run to test the form.
- Census = all units; sample = part; destructive tests need samples.
- Census: no sampling error, still non-sampling errors.
- Check secondary data for reliability, suitability, adequacy.
- NSO (2019) = CSO + NSSO, under MoSPI; Census every 10 years, next reference date 1 March 2027.
Practise this topic. Questions on Data collection, census & sampling, with answers explained.
All Data, sampling, probability and presentation notes · APPSC Paper I syllabus · APPSC Paper I Mock 1 with answers · Start free
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