Census or sample: populations, samples and sampling methods

Detail

1. Population and census

• Population (also called the universe) means every unit that has the feature we want to study. A unit can be a person, a household, a farm or a firm.

• The purpose of the study decides the population. To study farm wages, the population is all agricultural labourers, not all people.

• Census (also called complete enumeration) means collecting data from every unit of the population. Nothing is left out.

• India's decennial census is held once every 10 years. It is a house-to-house count of all households. The Registrar General and Census Commissioner of India runs it.
• History:
• India's first population count took place between 1865 and 1872, but not at the same time in every region [2].
• The first synchronous census (held at the same time across the whole country) took place in 1881. Since then, the census has been held every 10 years [2].

• The census due in 2021 was not held on time because of COVID-19 [2].

• Legal and constitutional basis:

• The census is a Union subject. It is entry 69 of the Union List in the Seventh Schedule [2].
• It is run under the Census Act, 1948 and the Census Rules, 1990 [2].

• Section 15 of the Census Act keeps each person's answers confidential. They cannot be released under RTI, cannot be used as evidence in court, and cannot be shared with any institution [2].

• Census 2027 (the current round):

• It is the 16th Indian census overall and the 8th since Independence. It is also India's first digital census, with data collected on mobile apps [2].
• Phase I, Houselisting and Housing Census (HLO): April–September 2026. Each State/UT gets a 30-day window. Before that window, households have an optional 15-day self-enumeration period, when they can fill in their own details online in 16 languages [2].
• Phase II, Population Enumeration (PE): February 2027. Castes will also be counted in this phase [2].
• Reference date ("Census Moment"): 00:00 hours, 1 March 2027. For Ladakh and the snow-bound areas of J&K, Himachal Pradesh and Uttarakhand, it is 00:00 hours, 1 October 2026 [2].
• Caste enumeration: the Cabinet Committee on Political Affairs decided this on 30 April 2025. Until 2011, the census counted only SCs and STs in a systematic way [2].
• Scale: the outlay is ₹11,718.24 crore, and about 31 lakh enumerators and supervisors are involved [2].

2. Sample survey

• Sample: the part of the population from which data is actually collected.
• Sample survey: a study of a sample whose result is then applied to the whole population.
• Representative sample: a sample whose make-up matches the population, like a small copy of it. For example, if 60% of households in the population are rural, about 60% of the sample should be rural too.

• It gives fairly accurate results at lower cost and in less time.

• Parameter vs estimate:

• Population parameter: the true value in the whole population, for example the true average income of all households.

• Sample estimate (also called a statistic): the value worked out from the sample. It stands in for the parameter.

• Sampling error: the gap between the sample estimate and the population parameter.

• Worked example: 5 farmers earn ₹500, ₹550, ₹600, ₹650 and ₹700. The true mean is ₹600, and this is the parameter.
• A sample of 2 farmers (₹500 and ₹600) gives a mean of ₹550, and this is the estimate.

• Sampling error = 550 − 600 = −₹50. A larger, well-drawn sample usually makes this error smaller.

• Non-sampling errors can happen in a census as well as in a sample. Examples are wrong answers, non-response (people who do not reply), recording mistakes and a biased questionnaire.

• NCERT example (Churachandpur, Manipur):
• Population = all agricultural labourers in the district.
• Sample = 10% of them.

3. Why most surveys are samples

• Cheaper and quicker. Fewer units means fewer interviews and less data processing.
• More detail. With fewer respondents, each interview can go deeper (intensive enquiry).
• Smaller team. A small team is easier to train and supervise, so there are fewer non-sampling errors.
• Scale comparison:
• Census 2027 uses about 31 lakh field staff [2].
• The revamped PLFS covers about 2.72 lakh households a year [3].

4. Why a census is still needed

• Some tasks need data on every unit:
• electoral rolls and delimitation (redrawing constituency boundaries by population);
• small-area counts for a village or ward;

• caste counts, which need exact numbers for every locality.

• The census gives surveys their sampling frames.

• Sampling frame: the complete list of units from which a sample is drawn.
• PLFS picks its first-stage units from the list of Census 2011 villages and Urban Frame Survey (UFS) blocks [3].
• The number of census villages was 6,40,932 in 2011 and is 6,39,902 for Census 2027. Each new census refreshes this list [2].

• The census uses a frame of its own too. Phase I (HLO) builds the frame for Phase II [2]. Houselisting Blocks are marked digitally using satellite imagery, so that no area is left out or counted twice [2].

• Cost of an out-of-date frame:

• With no census since 2011, surveys in 2025 still draw from a 2011 list [3].
• New settlements and fast-growing towns may therefore be under-represented.

5. Random sampling

• Random sampling: every unit has an equal chance of being selected. The investigator's choice plays no part.

• "Random" does not mean "haphazard". It follows a strict, planned procedure.

• Step 1: build the sampling frame. NCERT example: all 300 households in a locality, studied to see how a petrol-price rise affects them.

• Step 2: draw the sample.
• Lottery method: write all 300 names on slips, mix them well and draw 30 one by one.

• Random number table: number the units 001–300, then read numbers from a table such as Tippett's. It is printed in Class 11, Use of Statistical Tools. Today, computers generate random numbers instead.

• Worked example (chance of selection):

• Each household's chance of being in the sample = n/N = 30/300 = 0.1 (10%).

• This is also the sampling fraction.

• NCERT exercise (counting possible samples):

• Choosing 3 of 10 students: ¹⁰C₃ = 10!/(3!·7!) = (10×9×8)/(3×2×1) = 120 possible samples.

• Each particular set of 3 has a 1/120 chance of being drawn. Each student has a 3/10 chance of being chosen.

• Stratified sampling (beyond NCERT):

• First divide the population into groups called strata, such as rural/urban or districts. Then sample randomly within each group.

• This makes sure every group is represented.

• Systematic sampling:

• Take every k-th unit from a list, where k = N/n.

• Worked example: N = 300, n = 30, so k = 10. Pick a random start between 1 and 10, say 4. Then take units 4, 14, 24 … 294.

• Multi-stage sampling:

• Sample in steps: first choose villages or blocks (first-stage units), then choose households inside them.
• This saves travel and does not need a list of every household in India.

6. Non-random sampling

• Non-random sampling: units do not have equal chances. The investigator picks them by:
• judgement (whom the investigator thinks is "typical");
• purpose;
• convenience (whoever is easy to reach);

• quota (a fixed number from each group, chosen by the investigator).

• Result: bias creeps in, and the sampling error cannot be measured properly.

• NCERT example: picking 10 of 100 households because they are nearby or known to you.
• Neighbours tend to have similar incomes, so the sample misses the variety in the population.

7. Exit polls

• Exit poll: a random sample of voters is asked, as they leave the polling booth, whom they voted for. The answers are used to predict the result.
• Why exit polls misfire:
• Non-response: some voters refuse to answer, and they may lean towards one party.
• Sampling bias: the booths or times chosen do not represent all voters.

• False answers: voters hide or change their real choice.

• Legal limit: Section 126A, Representation of the People Act, 1951. No one may conduct or publish an exit poll from the start of polling in the first phase until half an hour after polling closes in the last phase.

8. Beyond NCERT: how the NSS and PLFS sample

• National Sample Survey (NSS):
• Set up in 1950 on the advice of Prof. P. C. Mahalanobis, then Statistical Adviser to the Cabinet [4].
• The reason: the National Income Committee had found big gaps in data on the unorganised/household sector [4].
• NSS is now part of the National Statistics Office (NSO) under MoSPI, headed by a Director General [4].

• It completed 75 years in 2025, which was the theme of the 19th Statistics Day marking Mahalanobis's birth anniversary [5].

• NSS design: stratified multi-stage sampling.

• First-stage units (FSUs): census villages in rural areas and UFS blocks in urban areas.

• Households are selected at the second (final) stage [3].

• Periodic Labour Force Survey (PLFS):

• Launched in 2017. It gave quarterly data for urban areas only, and annual rural+urban data from July to June [3].
• Revamped from January 2025 [3]:
  • Sample size: 22,692 FSUs a year (12,504 rural and 10,188 urban), up from 12,800 FSUs before.
  • Households per FSU: 12, up from 8. The total is about 2,72,304 households, which is 2.65 times the earlier ~1,02,400.
  • Basic stratum: the district is now the main unit for selecting FSUs; in the remaining areas, the NSS region is used. So most districts now appear in the sample.
  • Rural strata: villages within 5 km of the district headquarters, or of a town with more than 5 lakh people, form a separate group. Urban strata: million-plus cities form their own group.
  • Rotational panel: each household is visited 4 times in 4 consecutive months.
  • New outputs: monthly all-India estimates (first bulletin for April 2025); quarterly rural+urban estimates; annual results on a calendar-year basis from 2025.
• Reference periods [3]:
  • Current Weekly Status (CWS): a person's activity in the last 7 days.
  • Usual Status (ps+ss): a person's activity in the last 365 days.
• Caution: results from 2025 onward should not be compared directly with results up to December 2024, because the sample design changed [3].

Prelims Hooks

• Census = every unit (complete enumeration). Sample survey = part of the population, used to estimate for the whole.
• Parameter = the true population value. Statistic/estimate = the value from the sample. Sampling error = estimate − parameter.
• In random sampling, every unit has an equal chance of selection. Random ≠ haphazard. Tippett's table is a random number table.
• ¹⁰C₃ = 120 possible samples. Systematic sampling interval k = N/n.
• First synchronous census: 1881. Census 2027 is the 16th overall and 8th since Independence. Its reference date is 1 March 2027 (snow-bound areas: 1 October 2026) [2].
• Census is entry 69, Union List. It is governed by the Census Act, 1948, and Section 15 guarantees confidentiality [2].
• NSS was set up in 1950 on Mahalanobis's advice. It now sits under NSO, MoSPI [4].
• PLFS (since 2017) uses a stratified multi-stage design. Its FSUs are Census 2011 villages / UFS blocks, and its final-stage units are households [3].
• Trap: PLFS CWS = last 7 days. Usual Status = last 365 days [3].
• Section 126A, RP Act 1951: the exit-poll ban runs from the start of the first phase until half an hour after polling closes in the last phase.

Mains Points

• A census and sample surveys work together; one does not replace the other.
• Surveys (NSS/PLFS) are cheaper, faster and more detailed.
• But their accuracy depends on an up-to-date census frame. PLFS 2025 still draws from 2011 villages [3].

• So the delay of Census 2021 also weakens the quality of survey data.

• The PLFS revamp trades cost for timeliness and detail.

• The sample grew 2.65 times, the district became the basic stratum, and monthly and rural quarterly data were added [3].
• Policy can now respond faster to changes in jobs.

• But the new series cannot be compared directly with the old one, and running it costs more.

• Caste enumeration shows why a census is still needed.

• Caste counts for each locality (for reservation, delimitation and targeting welfare) need every household, which a sample cannot give.

• The census also needs strong privacy protection, such as Section 15 and secure data centres [2].

• Exit polls show what happens when the sampling method is weak.

• Non-response, poorly chosen booths and false answers can make predictions wrong.
• Section 126A balances free speech against the fairness of elections.