EconomicsCBSE Class 11 · Collection of Data

Census, Sampling Methods, Sampling Errors and Non-sampling Errors

Updated 17 October 2026 · Fact-checked

A census studies every unit of the population; a sample survey studies a part. Random sampling methods (lottery, random number tables) give every unit a known chance; non-random methods include judgement and convenience sampling. Sampling error is the difference between the sample statistic and the population value, and can be reduced by a larger sample; non-sampling errors arise from faulty collection or processing.

Notice that only random methods (green) give every unit a known chance; non-random ones (red) risk bias, and a larger sample cuts sampling error.

Illustration drawn for QuestionBuddy.

Understand Sampling Methods and Errors

Population and sample. The population (universe) is the complete group being studied; a sample is a part chosen to represent it. Each member is a unit.

Census (complete enumeration) studies every unit: accurate for small populations, costly, slow; example: the Census of India. Sample survey studies a part: cheaper, faster, can be more detailed; example: the National Sample Survey; but sampling error exists. A sample is chosen when the population is large, when testing destroys the unit (bulbs tested to failure), or when time and cost are limited.

Random (probability) sampling: every unit has a known chance of selection.

Simple random sampling: lottery method (units mixed and drawn blindly) or table of random numbers.
Systematic sampling: every k-th unit after a random start, with k = N ÷ n (N = population size, n = sample size).
Stratified sampling: population split into homogeneous strata and a random sample taken from each; with proportionate allocation, sample from a stratum = n × (stratum size ÷ N).

Non-random sampling: selection by the investigator's choice.

Judgement sampling: investigator picks units believed typical.
Convenience sampling: easily available units are chosen.
Chances of selection are not known, so bias is possible.

Sampling error. Difference between the sample estimate and the true population value; arises because the sample differs from the population. Sampling error = |sample statistic − population value|. Reduced by increasing sample size and by sound design.

Non-sampling errors. Not due to sampling but to faulty procedures, present in census as well: errors of measurement, wrong or misleading questions, interviewer bias, non-response, incomplete coverage, mistakes in recording, processing and tabulation. Reduced by careful design and training, not by increasing sample size.

Census of India and NSO are the standard sources: the Census counts the entire population periodically; National Sample Survey conducts large sample surveys on consumption, employment and others.

Table: random versus non-random. Chance known versus unknown; bias lower versus higher.

Sampling Methods and Errors: key facts

Systematic sampling: k = N / n; Interval
Proportionate stratified: n_h = n x (N_h / N); Allocation
Sampling error: |Sample estimate - Population value|; Absolute difference
Census vs sample: Census: all units | Sample: part of the units; Coverage

How to answer Sampling Methods and Errors questions

Questions ask for method names, intervals or errors.

1Identify the method from the selection rule: blind draw random; every k-th systematic; groups then draw stratified; own choice non-random.
2For systematic sampling compute k = N / n.
3For stratified sampling multiply n by each stratum's share.
4For error, take the absolute difference.
5Separate sampling errors (reduced by larger samples) from non-sampling errors.

Sampling Methods and Errors in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Selecting students for a quiz

Suppose a school has 600 students and 30 are to be chosen by listing all names and taking every 20th name after a random start.

Name the method and verify the interval.

Try it first, then show the solutionSolution

Every k-th unit after a random start is systematic sampling.
k = N / n = 600 / 30.
= 20, matching the rule.

Answer: Systematic sampling with k = 20.

Memory hook: Every 20th name.

Tricks to remember Sampling Methods and Errors

Short memory aids. Say each one aloud once, then use it on a question the same day.

Lottery = Random
Blind draw gives simple random sampling.
Use it when: Simple random
k = N/n
Population divided by sample.
Use it when: Systematic
Sampling shrinks with size
Increase sample size to cut sampling error; non-sampling error is not cured this way.
Use it when: Errors

Sampling Methods and Errors: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Census vs sample · 2 marks · Very short answerBoard level

State two differences between a census and a sample survey.

Try it first, then show the solutionSolution

Census covers every unit; sample covers a part (1 mark).
Census is costly and slow; sample is cheaper and quicker but has sampling error (1 mark).

Answer: Complete versus partial.

Example 2: Systematic sampling · 3 marks · Short answerBoard level

A list has 600 names and 30 are to be chosen systematically. Find the interval and, if the random start is 7, the first three selected positions.

Try it first, then show the solutionSolution

k = 600 / 30 = 20 (1 mark).
First is 7 (1 mark).
Next are 7 + 20 = 27 and 27 + 20 = 47 (1 mark).

Answer: k = 20; positions 7, 27, 47.

Example 3: Stratified sample · 4 marks · Short answerHarder board level

A population of 1000 has 400 in group A, 350 in group B and 250 in group C. Choose a proportionate stratified sample of 60 and verify the total.

Try it first, then show the solutionSolution

A: 60 x 400/1000 = 24 (1 mark).
B: 60 x 350/1000 = 21 (1 mark).
C: 60 x 250/1000 = 15 (1 mark).
Total 24 + 21 + 15 = 60 (1 mark).

Answer: 24, 21 and 15.

Example 4: Sampling error · 3 marks · Short answerHarder board level

The population values are 2, 4, 6, 8, 10. A sample of two values, 4 and 10, is drawn. Find the population mean, the sample mean and the sampling error. How could it be reduced?

Try it first, then show the solutionSolution

Population mean = (2+4+6+8+10) / 5 = 6 (1 mark).
Sample mean = (4+10) / 2 = 7; error = |7 - 6| = 1 (1 mark).
Increase the sample size or use a better design (1 mark).

Answer: Mean 6; sample mean 7; error 1.

Example 5: Error types · 5 marks · Long answerHOTS / competency

A survey asked leading questions and 20 per cent did not respond. Another had a sample of only 15 people. Classify the errors in each and say which is reduced by a larger sample.

Try it first, then show the solutionSolution

Leading questions cause non-sampling errors (1 mark).
Non-response is also a non-sampling error (1 mark).
A sample of 15 gives large sampling error (1 mark).
A larger sample reduces sampling error (1 mark).
Non-sampling errors need better design and training, not a bigger sample (1 mark).

Answer: Larger samples cut only sampling error.

Where students lose marks in Sampling Methods and Errors

The slips examiners see most often, and what to write instead.

Mistake: Sampling error equals blunder
Confusion with non-sampling.
Wrong working
Sampling error is a recording mistake.
Right working
It is the difference caused by studying only a sample.
Do this: Sample vs population.
Usually costs: 1 mark.
Mistake: Interval n/N
Ratio inverted.
Wrong working
k = n / N.
Right working
k = N / n.
Do this: Population over sample.
Usually costs: 1 mark.
Mistake: Census has no error
Non-sampling errors ignored.
Wrong working
A census has no errors.
Right working
A census has no sampling error but can have non-sampling errors.
Do this: Still errors.
Usually costs: 1 mark.

Exam tips

Show k = N/n and the arithmetic.
Verify that stratum shares add up to n.
Name both error types.
Mention randomness for probability methods.

Practice questions on Sampling Methods and Errors

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Selecting names by drawing slips blindly is
(a) systematic sampling (b) lottery method (c) judgement sampling (d) census
Hint
Blind draw.
Answer
(b).
Q2 · 1 mark · Assertion-reasonHarder board level
Assertion (A): A census can still contain errors.
Reason (R): Non-sampling errors such as wrong recording occur in complete enumeration too.
(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 but R is false.
(d) A is false but R is true.
Hint
More coverage.
Answer
(a).
Q3 · 2 marks · Very short answerBoard level
Find the interval for choosing 50 from 1000 systematically, and the 3rd selected unit if the start is 12.
Hint
k = N/n.
Answer
k = 1000 / 50 = 20; units are 12, 32, 52, so the 3rd is 52.
Q4 · 4 marks · Case-basedHarder board level
Read and answer.
Suppose a town of 2000 households is divided by income into low, middle and high in the ratio 5:3:2 (1000, 600, 400 households) and a 5 per cent sample is chosen proportionately.
(a) Find the sample size. (1)
(b) Find the number from each group. (1)
(c) Name the method. (2)
Hint
5 per cent.
Answer
(a) 5% of 2000 = 100. (b) Low 50, middle 30, high 20. (c) Proportionate stratified random sampling.
Q5 · 3 marks · Short answerHOTS / competency
Suppose a researcher interviews only people at a railway station to study the whole city's travel habits. Name the method, identify the likely error and suggest a remedy.
Hint
Convenience.
Answer
This is convenience (non-random) sampling; it is likely to be biased because it excludes people who do not use the railway. Use a random or stratified sample from all areas.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Whole population study?Show answer
Census.
2.k formula?Show answer
N / n.
3.Convenience sampling is?Show answer
Non-random.
4.Sampling error?Show answer
Sample estimate minus population value.
5.Which error remains in census?Show answer
Non-sampling.
6.Who runs NSS?Show answer
The National Statistical Office.

Sampling Methods and Errors: frequently asked questions

What is a sample?

A part of the population chosen for study.

Why sample?

Cost, time and destructive testing.

What is stratified sampling?

Random sampling within groups.

How to reduce sampling error?

Increase sample size.

What is non-response?

Failure to obtain data from selected units.