Collection of Data Class 11: Sources, Surveys, Sampling and Errors

What Collection of Data is about

Weightage: This chapter is part of Unit 2, Collection, Organisation and Presentation of Data. The syllabus groups Unit 2 with Unit 1, Introduction: together they carry 15 of the 80 theory marks in the school annual exam.Source: CBSE Economics (030) syllabus 2026-27, Class XI course structure, Unit 2 Collection, Organisation and Presentation of Data

Key concepts

Sources of data: primary and secondary

NCERT section 2

Primary data: collected by the investigator for the first time, directly from the source, for a specific purpose. Example: a student surveys 60 households in her locality on their electricity use.

Secondary data: data already collected by someone else, and used by the investigator from published or unpublished sources. Example: using the Census of India population figures or the RBI's data on bank deposits.

Basis	Primary data	Secondary data
Originality	Original, first-hand	Already collected; used again
Cost and time	Costly, time-consuming	Cheap, quick
Suitability	Fits the purpose exactly	May need adjusting; may not fit
Reliability	Known to the investigator	Must be checked before use
Collected by	The investigator	Some other agency or person

Before using secondary data, check: who collected them and why, the definitions and units used, the period covered, and whether they are accurate and suitable for your purpose.

Worked example

Classify: (a) a firm interviews 200 customers about its new soap; (b) a researcher uses NSS reports on household spending; (c) a student uses data from a newspaper article on crop output.

Try it first, then show the solutionSolution

1. (a) Collected first-hand for the purpose: primary
2. (b) and (c) Collected earlier by others: secondary

Answer: (a) Primary; (b) and (c) secondary.

Preparing a questionnaire

NCERT section 3

A questionnaire (filled in by the respondent) or interview schedule (filled in by the interviewer) is the main tool for collecting primary data. A good one:

1. Is short, with only the questions needed for the purpose.
2. Asks questions in a logical order, from general to specific.
3. Uses simple, clear words; avoids technical terms and ambiguity ("Do you eat often?" is vague).
4. Avoids leading questions ("Don't you think the new tax is unfair?") and questions with two ideas in one ("Do you like tea and coffee?").
5. Avoids questions that are personal or embarrassing, or that need calculations or long memory.
6. Uses mostly closed-ended questions (yes/no; multiple choice) which are easy to answer and tabulate, with some open-ended questions where opinions are wanted.
7. Begins with a short introduction stating the purpose, and promises confidentiality.

Worked example

Improve these questions: (a) "How much do you spend on food in a year?" (b) "Don't you agree that online shopping is better?" (c) "Do you own a car and a scooter?"

Try it first, then show the solutionSolution

1. (a) Needs calculation and memory: ask "How much did your family spend on food last month?" with ranges
2. (b) Leading: ask "Which do you prefer for buying clothes? (online / shop / both)"
3. (c) Two questions in one: split into "Do you own a car?" and "Do you own a scooter?"

Answer: Use recent periods and ranges, neutral wording, and one idea per question.

Modes of collecting data and the pilot survey

NCERT section 3

Mode	Advantages	Disadvantages
Personal interview	Highest response rate; doubts can be cleared; complex questions possible; interviewer can observe	Costly; needs trained interviewers; takes longer; respondent may be influenced by the interviewer
Mail (questionnaire) survey	Cheapest for a wide area; respondent answers at leisure; no interviewer influence	Needs literate respondents; low response rate; no chance to clarify doubts; slow
Telephone interview	Cheaper and quicker than personal visits; doubts can be cleared; covers a wide area	Only people with phones; no visual reactions; respondents may hang up

Online forms today work much like mail surveys (cheap and wide but with low response and limited to internet users).

Pilot survey (pre-testing): before the main survey, the questionnaire is tried on a small group. It shows which questions are unclear or unnecessary, how long the interview takes, what problems interviewers face, and roughly what the survey will cost, so the questionnaire can be improved.

Worked example

Suppose you want views of illiterate farmers in a district on a new irrigation scheme. Which mode will you use and why?

Try it first, then show the solutionSolution

1. Mail needs literate respondents: unsuitable
2. Telephone may miss farmers without phones and cannot show visuals
3. Personal interviews allow questions to be explained in the local language

Answer: Personal interviews.

Census and sample methods; population and sample

NCERT section 4

Population (universe): all the items or individuals about whom information is wanted (for example, all households in a town).

Census (complete enumeration): data are collected from every unit of the population. The Census of India is the best example.

• Merits: accurate and complete; covers every unit; suitable when the population is small or every unit must be known.
• Demerits: very costly and time-consuming; needs a large staff; impossible when units are destroyed by testing.

Sample method: data are collected from a sample, a part of the population chosen to represent it.

• Merits: less cost, time and labour; more detailed questions possible; the only method when testing destroys the item (testing bulbs); results can be fairly accurate if the sample is representative.
• Demerits: sampling error; a biased sample gives wrong results; needs skill to design.

A representative sample has the same broad characteristics as the population (for example, the same mix of kuchha and pucca houses as the whole village).

Worked example

Which method suits each: (a) checking the life of electric bulbs made in a factory; (b) finding the number of members in a club of 40 people; (c) estimating the average height of Class 11 students in India?

Try it first, then show the solutionSolution

1. (a) Testing destroys the bulbs: sample
2. (b) Small population: census
3. (c) Very large population: sample

Answer: (a) Sample; (b) census; (c) sample.

Random and non-random sampling

NCERT section 4

Random sampling: every unit of the population has an equal chance of being selected; the choice is not left to the investigator.

• Lottery method: write each unit's name or number on identical slips, mix them, and draw the required number.
• Random number tables (or computer-generated random numbers): number the units, then read numbers from the table and pick the units with those numbers.
• Free from personal bias; results can be judged for accuracy; suits fairly similar populations.

Non-random sampling: units do not have an equal chance; the investigator's judgement or convenience decides.

• Judgement (purposive): the investigator picks units he thinks are typical.
• Convenience: units easiest to reach are picked.
• Quota: the population is divided into groups and a quota is filled from each group by the investigator's choice.
• Quick and cheap, but open to bias; results cannot be checked for accuracy.

Worked example

Suppose a teacher wants 5 students out of 40 for a survey. She numbers them 01-40 and reads two-digit numbers from a random number table, skipping numbers above 40 and repeats. What method is this, and why is it fair?

Try it first, then show the solutionSolution

1. Selection is by random numbers, not by her choice
2. Each student has the same chance of selection

Answer: Random sampling with random number tables; fair because every student has an equal chance.

Sampling and non-sampling errors

NCERT section 5

Sampling error: the difference between the sample estimate and the actual population value (parameter), arising because only a part of the population is studied.

Sampling error = Population value − Sample estimate

It can be reduced by taking a larger sample and by random selection.

Non-sampling errors: errors that are not due to sampling and can occur even in a census. They are more serious, because a bigger sample does not cure them.

• Sampling bias: the sampling plan leaves out some members of the population (e.g. a phone survey misses people without phones).
• Non-response errors: selected people cannot be contacted or refuse to answer.
• Errors in data acquisition: wrong answers, measurement differences, or recording mistakes (writing 13 instead of 31).

Suppose the daily earnings of five fruit sellers are ₹320, ₹360, ₹410, ₹480 and ₹530; the population mean is 2,100 ÷ 5 = ₹420.

Worked example

For the five fruit sellers (mean ₹420), find the sampling error if the sample is (a) ₹320 and ₹410; (b) ₹360 and ₹480.

Try it first, then show the solutionSolution

1. (a) Sample mean = (320 + 410) ÷ 2 = ₹365; error = 420 − 365 = ₹55
2. (b) Sample mean = (360 + 480) ÷ 2 = ₹420; error = ₹0

Answer: (a) ₹55; (b) zero: a sample can by chance hit the true value, but we cannot rely on it.

Census of India and the National Sample Survey

NCERT section 6

India has national agencies that collect and publish data, among them the Census of India (under the Registrar General of India), the National Sample Survey (NSS), the Central Statistics Office (CSO), the Directorate General of Commercial Intelligence and Statistics (DGCIS) and the Labour Bureau. In 2019 the NSSO and CSO were merged into the National Statistical Office (NSO) under the Ministry of Statistics and Programme Implementation.

Census of India: the most complete and continuous record of India's population, conducted every ten years since 1881; the first after Independence was in 1951. It collects data on population size, density, sex ratio, literacy, migration and rural-urban distribution. As per the 2011 Census, India's population was 121.09 crore. The next Census, the first since 2011, has its reference date set as 1st March 2027.

National Sample Survey: set up by the Government of India to conduct nation-wide sample surveys on socio-economic issues in successive rounds: employment and unemployment, consumer expenditure, literacy and school enrolment, health and morbidity, use of the public distribution system, and enterprises. Results appear in reports and its journal Sarvekshana. These data are used for planning.

Worked example

Name the source you would use for: (a) the sex ratio of a state; (b) the share of household spending on food in rural India.

Try it first, then show the solutionSolution

1. (a) Complete count of population characteristics: Census of India
2. (b) Household consumer expenditure is surveyed in NSS rounds

Answer: (a) Census of India; (b) NSS (NSO) consumption expenditure survey.

Collection of Data in real life

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

Topics in this chapter

• Primary and Secondary Data and Questionnaire
• Sampling Methods and Errors

Collection of Data: key facts

Sampling error

Sampling error = Population parameter − Sample estimate

Falls as sample size rises.

Sample mean

Sample mean = Sum of sample values ÷ Number of sample values

An estimate of the population mean.

Sampling fraction

Sampling fraction = Sample size ÷ Population size

200 of 2,000 households = 10%.

Chance of selection in simple random sampling

Each unit has probability = n ÷ N of being selected

Equal for every unit.

Primary vs secondary

Primary = first-hand, for the purpose; Secondary = collected earlier by others

Same data can be primary for one user and secondary for another.

How the school exam asks Collection of Data

The question patterns to expect, and the method that works for each.

Tricks to remember Collection of Data

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

• Modes of survey: "PMT"

  Personal (best response), Mail (cheapest), Telephone (quickest).

  Use it when: Comparing survey modes.

• Non-sampling errors: "BNA"

  Bias in sampling, Non-response, Acquisition (recording) errors.

  Use it when: Types of non-sampling errors.

• Non-random types: "JCQ"

  Judgement, Convenience, Quota.

  Use it when: Kinds of non-random sampling.

Collection of Data: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section E style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 4-mark question split into 1 + 1 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Collection of Data

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

• ✗Mistake: Saying census data have no errors

  A census covers everyone.

  ✓Do this: A census has no sampling error but can still have non-sampling errors (wrong answers, recording mistakes).

  Usually costs: 1 mark.

• ✗Mistake: Calling convenience selection "random"

  In daily speech "random" means "any".

  Wrong working

  "I picked any 10 households near my house: random sampling."

  Right working

  Random means equal chance for all, by lottery or random numbers; picking nearby houses is convenience sampling.

  ✓Do this: Use the statistical meaning of random.

  Usually costs: 1 mark.

• ✗Mistake: Writing sampling error as sample value minus population value without a sign rule

  Order is forgotten.

  ✓Do this: Use Sampling error = Population value − Sample estimate, as NCERT does, and keep the sign.

  Usually costs: ½ mark.

• ✗Mistake: Listing questionnaire rules without examples

  Rules look self-explanatory.

  ✓Do this: Show a bad question and its corrected version for at least two rules.

  Usually costs: Half the marks in a 4-mark answer.

NCERT exercise guide: Collection of Data

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on Collection of Data

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

1. Q1 · 1 mark · MCQExam level

   Which of these is a source of secondary data?
   (a) Interviewing shopkeepers
   (b) Census of India reports
   (c) A pilot survey
   (d) Observing traffic at a junction

   Hint

   Already published.

   Answer

   (b)

2. Q2 · 1 mark · MCQExam level

   In random sampling:
   (a) the investigator chooses typical units
   (b) every unit has an equal chance of selection
   (c) only convenient units are chosen
   (d) quotas are filled

   Hint

   Equal chance.

   Answer

   (b)

3. Q3 · 1 mark · Very short answerExam level

   Since which year has the Census of India been conducted every ten years?

   Hint

   19th century.

   Answer

   1881.

4. Q4 · 3 marks · Short answerExam level

   State three precautions to be taken before using secondary data.

   Hint

   Who, why, how.

   Answer

   (1) Check who collected the data and whether they are reliable. (2) Check the purpose, definitions and units used. (3) Check the period covered and whether the data suit the present study.

5. Q5 · 3 marks · Short answerHarder exam level

   Give two merits and two demerits of the mail survey method.

   Hint

   Cheap but low response.

   Answer

   Merits: cheapest for a wide area; respondents answer at leisure without interviewer influence. Demerits: low response rate; needs literate respondents (and doubts cannot be cleared).

6. Q6 · 3 marks · Short answerHarder exam level

   Suppose the monthly incomes (₹ thousand) of six workers are 10, 12, 14, 16, 18 and 20. Find the sampling error for a sample of 12, 16 and 20.

   Hint

   Population mean 15.

   Answer

   Population mean = 90 ÷ 6 = 15; sample mean = 48 ÷ 3 = 16; sampling error = 15 − 16 = −1 thousand (−₹1,000).

7. Q7 · 3 marks · Short answerHarder exam level

   Distinguish between random and non-random sampling on three bases.

   Hint

   Chance, bias, accuracy.

   Answer

   Chance: equal for all vs not equal. Bias: free from investigator bias vs open to it. Accuracy: can be estimated vs cannot be judged (and random takes more effort, non-random is quick and cheap).

8. Q8 · 3 marks · Short answerHarder exam level

   What is a pilot survey? Give three uses.

   Hint

   Pre-testing.

   Answer

   A small trial survey before the main one. Uses: finds unclear or unnecessary questions; estimates time and cost; reveals problems the interviewers may face.

9. Q9 · 4 marks · Long answerHarder exam level

   Explain three types of non-sampling errors with examples.

   Hint

   Bias, non-response, acquisition.

   Answer

   Sampling bias: some members cannot be included (an online survey misses people without internet). Non-response: selected people are not found or refuse. Data acquisition errors: wrong measurement or recording (13 written as 31; different price quality). These occur even in a census.

10. Q10 · 4 marks · Long answerHarder exam level

    Why is the sample method preferred to the census method in most economic surveys? Give four reasons.

    Hint

    Cost, time, detail, destruction.

    Answer

    (1) Lower cost. (2) Less time, so results are timely. (3) Fewer people means more detailed questions and better-trained staff, sometimes reducing non-sampling errors. (4) The only possible method when testing destroys items or the population is very large.

11. Q11 · 4 marks · Long answerHarder exam level

    Suppose a newspaper runs an SMS poll asking "Should petrol prices be cut?" and reports that 92% said yes. Comment on the reliability of this result using the ideas of this chapter.

    Hint

    Who responds?

    Answer

    The sample is self-selected, not random: only people who read the paper, have phones and feel strongly reply (sampling bias, non-response of others). The question is leading in effect, since almost everyone wants lower prices without considering costs. The 92% cannot be generalised to all citizens.

12. Q12 · 4 marks · Long answerHOTS / competency

    Suppose a survey of 50 households finds an average family size of 4.6, while the Census of the same area gives 4.2. Give two possible reasons for the difference and say which kind of error each is.

    Hint

    Chance vs mistakes.

    Answer

    (1) Sampling error: by chance the 50 households include more large families; a bigger random sample would reduce it. (2) Non-sampling error: e.g. respondents counted guests or relatives living elsewhere, or households were chosen near a joint-family neighbourhood (bias). The Census can also have errors, and the dates differ, so families may have grown.

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. 1.What are primary data?Show answer

   Data collected first-hand by the investigator for a specific purpose.

2. 2.What is a pilot survey?Show answer

   A small trial survey to test the questionnaire before the main survey.

3. 3.Which survey mode has the highest response rate?Show answer

   Personal interview.

4. 4.Name two methods of random selection.Show answer

   Lottery method and random number tables.

5. 5.Formula for sampling error?Show answer

   Population parameter − sample estimate.

6. 6.Name NSS's journal.Show answer

   Sarvekshana.

7. 7.Since when has the Census been conducted every ten years?Show answer

   1881.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you distinguish primary and secondary data on three bases?
• ☐Can you list five qualities of a good questionnaire?
• ☐Can you choose a survey mode for a given situation?
• ☐Can you explain the use of a pilot survey?
• ☐Can you give merits and demerits of census and sample methods?
• ☐Can you explain the lottery method and random number tables?
• ☐Can you compute a sampling error?
• ☐Can you name three non-sampling errors?
• ☐Can you say what data the Census and NSS provide?

Collection of Data: frequently asked questions