Q.What is a variable? Distinguish between a discrete and a continuous variable.
Concept understanding — Sampling And Variables
Sampling and Variables in Economics
You already do sampling without knowing it. When you taste one spoonful of dal to judge whether the whole pot needs salt, you are sampling. You assume that spoonful represents the entire pot. If you stirred well, it probably does. If you didn't, you might oversalt everything.
Economics faces the same problem — but with millions of households, firms, or prices. We cannot ask every single person in India how much they earn, or measure every single price in every single market. So we take a sample, and from that sample we try to learn about the whole population.
What is a Population? What is a Sample?
Population is the entire group you want to study. If you want to know the average monthly expenditure of households in Delhi, the population is all households in Delhi. If you want the average yield of wheat in Punjab, the population is every wheat field in Punjab.
Sample is a subset of that population — a few hundred households, or a few dozen fields — that you actually collect data from.
The goal of sampling is to estimate a characteristic of the population (called a parameter) using a statistic calculated from the sample. The sample must be representative — it should mirror the population in the ways that matter.
If your sample of Delhi households only includes people from South Delhi, it will overestimate average expenditure. That is sampling bias — the sample does not look like the population.
Why Sampling Matters in Economics
Governments and businesses make decisions worth crores based on sample data. The National Sample Survey Office (NSSO) does not interview every Indian household — it surveys a carefully chosen sample of about 1.2 lakh households. From that, it estimates national unemployment, consumption, and poverty rates.
A badly chosen sample gives wrong estimates. Wrong estimates lead to bad policy. That is why sampling design — how you pick your sample — is a serious subject.
Types of Sampling
1. Random Sampling (Simple Random Sampling)
Every member of the population has an equal chance of being selected. Like drawing names from a hat.
Advantage: Eliminates bias. The sample is likely to be representative.
Disadvantage: Hard to do in practice — you need a complete list of the population (a sampling frame), which often does not exist.
2. Stratified Sampling
Divide the population into groups (strata) that are internally similar but different from each other — for example, urban and rural households, or income brackets. Then take a random sample from each group.
Why use it? If you know that urban and rural spending patterns are very different, a simple random sample might accidentally get too many urban households. Stratified sampling ensures each group is represented in proportion to its size in the population.
3. Cluster Sampling
Divide the population into clusters (like villages or city blocks), randomly pick a few clusters, and then survey everyone in those clusters.
Why use it? Cheaper and easier — you only travel to a few locations. But less precise than stratified sampling because people within a cluster tend to be similar.
4. Convenience Sampling
You survey whoever is easiest to reach — people in a mall, students in your school.
This is almost always biased. The people easiest to reach are rarely representative of the whole population. Never trust conclusions from convenience samples in serious economics.
What is a Variable?
A variable is any characteristic that can take different values for different members of the population. Age, income, gender, education level, price of wheat — all are variables.
In any study, you have:
- Dependent variable: The outcome you are trying to explain or predict.
- Independent variable: The factor you think influences the dependent variable.
Example: You want to study how education affects income.
- Dependent variable: Income (what you want to explain)
- Independent variable: Education level (what you think causes the change)
Types of Variables
Quantitative Variables (Numeric)
Can be measured in numbers.
- Discrete: Can only take whole number values. Number of children in a family (0, 1, 2, ...). You cannot have 2.5 children.
- Continuous: Can take any value within a range. Height, weight, temperature, income in rupees (₹25,000.50 is possible).
Qualitative Variables (Categorical)
Cannot be measured numerically — they describe categories.
- Nominal: Categories with no natural order. Gender (male/female), religion, type of crop grown.
- Ordinal: Categories that can be ordered. Education level (primary, secondary, graduate, postgraduate). You know graduate is higher than secondary, but you cannot say by how much.
In economics, many variables that seem quantitative are treated as categorical for analysis. Income brackets (₹0–₹2.5 lakh, ₹2.5–₹5 lakh, etc.) are ordinal, not continuous, because you lose the exact value.
How Sampling and Variables Connect
When you design a sample, you must decide:
- Which variables to measure — what questions to ask.
- How to measure them — is income self-reported? Is it annual or monthly?
- Which sampling method will give you reliable data on those variables.
If your variable is "monthly household expenditure" and you only sample during Diwali week, your estimates will be too high — that is a measurement error caused by bad timing, not bad sampling.
A Simple Example
Suppose you want to estimate the average monthly pocket money of Class 12 students in your city.
- Population: All Class 12 students in the city.
- Sample: 200 students chosen randomly from 10 schools (stratified by school type: government, private, and Kendriya Vidyalaya).
- Variable: Monthly pocket money in rupees (continuous, quantitative).
- Dependent variable: Pocket money.
- Independent variable: Type of school (categorical, nominal).
You collect the data, calculate the sample average — say ₹1,200 — and use that as your estimate for the population average. The accuracy of that estimate depends entirely on how well your sample represents the population.
The key idea: A sample is only useful if it is representative. A representative sample requires careful design — random selection, proper stratification, and unbiased measurement of variables. Without that, your numbers are meaningless, no matter how many decimal places you report.
A variable is any characteristic that can take different values, and such variables fall into two kinds depending on whether they change in exact jumps or can take any value at all within a range.
A variable is a characteristic that can take different values (e.g., height, income, number of children). A discrete variable takes only exact, separate (usually whole-number) values with jumps between them — e.g., number of cars. A continuous variable can take any value within a range, including fractions — e.g., height or weight.
A variable is a quantity that varies from one item to another and can be measured or counted. Discrete variables jump from one exact value to the next (number of students), while continuous variables can assume every value in an interval, however small (height, weight, temperature).
What is a variable?
A variable is a characteristic or attribute that is capable of taking different values. In statistics it is the quantity whose values we collect and study — for example marks, age, income, or the number of members in a family. (A quantity that does not change is a constant.)
Discrete vs continuous
Variables that take numerical values are of two kinds:
| Basis | Discrete variable | Continuous variable |
|---|---|---|
| Values taken | Only exact, separate values (usually whole numbers) | Any value within a range, including fractions/decimals |
| Nature | Counted; jumps between values, no value in between | Measured; changes smoothly with no gaps |
| Examples | Number of students, number of cars, number of cell phones | Height, weight, age, temperature, distance |
Explanation
A discrete variable moves in jumps. The number of children in a family can be 1, 2 or 3 but never 2.5 — there is no observation possible between two consecutive values.
A continuous variable can assume any value in its range. A person's height can be 150 cm, 150.2 cm, 150.25 cm, and so on; between any two heights another height always exists. Such variables are measured rather than counted.
A variable is a characteristic that takes different values. A discrete variable takes only exact, separate values with gaps between them (e.g., number of cars), whereas a continuous variable can take any value in a range, including fractions (e.g., height or weight).
Showing the 12 most recent of 14 on this concept.
- CBSE 2026Set MARCH1 markQ.Write the meaning of "Census".
›Reveal solutionSolution
Census means the complete enumeration of every unit in the population.
In the Collection of Data chapter of the Karnataka 1st PUC course, the census method (also called the method of complete enumeration) refers to collecting information from each and every unit or item of the population under study, without leaving out any.
For example, the Population Census of India counts every person in the country. This method gives complete and accurate information but is time-consuming and expensive, which is why the sample method is often preferred for large populations.
✓Final answerCensus is the method of collecting data from every single unit of the entire population (complete enumeration).
- CBSE 2026Set ANNUAL1 markMCQQ.Secondary data are -(a) Published data(b) Data collected by investigator(c) Both of the above(d) None of the above
›Reveal solutionSolution
Secondary data are published data — option (a).
Secondary data are data that have already been collected and published by some agency or person and are used by someone else. Data collected first-hand by the investigator are primary data. Hence secondary data are 'published data' — option (a).
✓Final answerCorrect option: (a) Published data.
- CBSE 2026Set ANNUAL1 markMCQQ.When was first Census held in India?(a) 1900(b) 1881(c) 1942(d) 1950
›Reveal solutionSolution
The first census in India was held in 1881 — option (b).
Although an attempt was made in 1872, the first regular (synchronous) census of India was conducted in 1881, and a census has been held every ten years since then. Hence option (b).
✓Final answerCorrect option: (b) 1881.
- CBSE 2026Set ANNUAL1 markQ.Fill in the blank: Statistical data are collected by________ methods.
›Reveal solutionSolution
Data are collected by the census and sampling methods.
Statistical (primary) data can be collected by two methods:
- Census (complete enumeration) method – information is collected from every unit of the population.
- Sampling method – information is collected from a representative part (sample) of the population and conclusions are drawn for the whole.
Hence the blank is 'census and sampling'.
✓Final answerStatistical data are collected by the census (complete enumeration) method and the sampling method.
- CBSE 2026Set ANNUAL1 markMCQQ.Write True or False: The person who investigates is called publisher.(a) True(b) False
›Reveal solutionSolution
False — the person who investigates is the investigator/enumerator, not a publisher.
In a statistical enquiry, the person who plans and conducts the investigation and collects the data is called the investigator (and the field worker who records the answers is the enumerator). A publisher is one who publishes material. Therefore calling the investigator a 'publisher' is False.
✓Final answerFalse — the person who investigates is called an investigator (or enumerator), not a publisher.
- CBSE 2026Set ANNUAL1 markQ.Write the answer in one sentence: In which year the National Sample Survey Organization was established?
›Reveal solutionSolution
The NSSO was established in 1950.
The National Sample Survey Organization (NSSO) was set up by the Government of India in 1950 to conduct large-scale nationwide sample surveys on various socio-economic subjects. (It is now part of the National Statistical Office, NSO.) Hence the year is 1950.
✓Final answerThe National Sample Survey Organization was established in 1950.
- CBSE 2025Set MARCH1 markMCQQ.A source of secondary data is(a) Direct personal interview(b) Telephone interview(c) Investigation through mailed questionnaire(d) Census report
›Reveal solutionSolution
A source of secondary data is the Census report — option (d).
A data-collection fundamentals question in Kerala Plus One (DHSE) Economics. Primary data are collected first-hand by the investigator through direct personal interview, telephone interview, or a mailed questionnaire. Secondary data are collected by someone else and already exist in published form. A Census report is compiled and published by the government and reused by others, so it is a source of secondary data.
✓Final answer(d) Census report is a source of secondary data.
- CBSE 2025Set ANNUAL1 markMCQQ.In which year the first Census of independent India was conducted?(a) 1948(b) 1949(c) 1950(d) 1951
›Reveal solutionSolution
The first census of independent India was in 1951 — option (d).
The decennial Census of India had been held since 1881. After independence (1947), the first census of independent India was conducted in 1951, and every tenth year thereafter. Hence option (d).
✓Final answerCorrect option: (d) 1951.
- CBSE 2024Set ANNUAL1 markMCQQ.The source of secondary data is -(a) Census(b) Reserve Bank of India(c) N.S.O. report(d) All of the above
›Reveal solutionSolution
Sources of secondary data include all of the above — option (d).
Secondary data are data that have already been collected, processed and published by some agency and are used by someone else. Their sources include government and institutional publications such as the Census of India, the Reserve Bank of India bulletins, and National Statistical Office (N.S.O.) reports. Since all three are published sources, option (d) 'All of the above' is correct.
✓Final answerCorrect option: (d) All of the above.
- CBSE 2023Set MARCH1 markMCQQ.Population in statistics means :(a) Total number of people in the country(b) Total number of people in the world(c) Totality of the items under study area(d) Selected items in the study area
›Reveal solutionSolution
The correct option is (c) Totality of the items under study area, because in statistics 'population' (universe) means the complete set of all units under investigation, not just people.
In statistics, the population/universe is the whole collection of items (persons, objects, or observations) that a study covers. A sample is only a selected part of that population.
✓Final answer(c) Totality of the items under study area.
- (a) 'Total people in the country' and (b) 'total people in the world' are too narrow/literal — population need not be people.
- (d) 'Selected items' describes a sample, not the population.
- Only (c) captures the statistical meaning.
- CBSE 2023Set ANNUAL1 markMCQQ.Write True or False: The data collected by the researcher is called secondary data.(a) True(b) False
›Reveal solutionSolution
False — data collected by the researcher himself are primary data.
Primary data are data collected first-hand (originally) by the investigator/researcher for a specific purpose. Secondary data are data already collected and published by someone else and used by another person. Therefore data collected by the researcher himself are primary data, not secondary data — so the statement is False.
✓Final answerFalse — data collected first-hand by the researcher are primary data, not secondary data.
- CBSE 2022Set MARCH1 markMCQQ.A method of complete enumeration(a) Census method(b) Sample method(c) Pilot method(d) None of these
›Reveal solutionSolution
The census method is the method of complete enumeration.
In the Kerala Plus One (DHSE) economics chapter on Collection of Data, there are two broad approaches:
- Census (complete enumeration) — every unit/member of the population is studied. It is accurate but costly and time-consuming.
- Sample method — only a representative part of the population is studied, and results are generalised.
- A pilot survey is only a small trial run before the main survey.
Since the census covers each and every unit, it is the method of complete enumeration.
✓Final answer(a) Census method.
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