Q.Write down the main limitations of statistics.
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Statistics: The Science of Learning from Data
The Everyday Intuition
Imagine you're the captain of a school cricket team. You have to pick the best bowler for the final match. You've seen him bowl in practice — sometimes he's deadly, sometimes he gets smashed. How do you decide? You can't rely on just one memory. So you start counting: how many balls did he bowl in the last five matches? How many wickets did he take? What was his average runs per over?
That counting, that summarising, that making sense of numbers — that's what statistics is. It's the tool you use when you have too much information to hold in your head at once, and you need to find the pattern hidden inside the noise.
The Precise Meaning
Statistics is the science of collecting, organising, analysing, interpreting and presenting data to help make decisions under uncertainty.
Statistics does not deal with certainty. It deals with patterns in numbers that help us infer something about a larger reality. In economics, that "larger reality" is often the entire country's economy — and we can't possibly measure every single person or firm. So we use statistics to draw conclusions from a sample.
Why Economics Needs Statistics
Economics is a social science. Unlike physics, you can't put a country's economy in a lab and run controlled experiments. You can't say "let's double the money supply for one year and see what happens" — that would ruin lives. So economists rely on observed data — what actually happened — and use statistics to find relationships, test theories, and make forecasts.
Here's where statistics shows up in your Class 11/12 syllabus:
| Economic Problem | Statistical Tool Used |
|---|---|
| How much did the country produce last year? | National income accounting (summing data) |
| Are prices rising? | Index numbers (CPI, WPI) |
| Is unemployment increasing? | Time-series analysis of labour data |
| Does education affect income? | Correlation and regression |
| What is the "average" Indian's income? | Mean, median, mode |
The Two Branches of Statistics
1. Descriptive Statistics
This is what you do when you have a pile of data and you want to summarise it. You calculate averages, draw bar charts, find the range. You are describing what the data says, nothing more.
For example: "The average monthly expenditure of 100 households in Delhi is ₹18,500." That's descriptive statistics — you're not claiming anything about households outside those 100.
2. Inferential Statistics
This is the powerful part. You take data from a sample (say, 5,000 households) and use it to draw conclusions about the population (all 300 million Indian households). You are inferring something about the whole from a part.
Inferential statistics always comes with a margin of error. If a survey says "65% of Indians support policy X", the real number could be 63% or 67%. Never treat a sample statistic as an exact population truth.
The Core Vocabulary You Must Know
Population: The entire group you want to study (e.g., all students in India)
Sample: A subset you actually collect data from (e.g., 2,000 students across 10 schools)
Variable: A characteristic that varies (e.g., height, income, exam score)
Data: The actual values of variables collected (e.g., 165 cm, ₹25,000, 87 marks)
Parameter: A number that describes a population (e.g., the true average income of all Indians)
Statistic: A number that describes a sample (e.g., the average income of the 5,000 people surveyed)
The Statistical Cycle (How It Works in Practice)
- Pose a question: "Has poverty declined in India over the last decade?"
- Collect data: Government surveys like NSSO, Census, or your own questionnaire
- Organise the data: Tables, frequency distributions, spreadsheets
- Analyse the data: Calculate averages, percentages, growth rates
- Interpret the results: "Poverty headcount ratio fell from 37% to 22% between 2004 and 2012"
- Present the findings: Graphs, reports, policy recommendations
A Concrete Example: The Consumer Price Index (CPI)
This is where statistics meets a formula in your syllabus. The CPI measures how the average price of goods bought by households changes over time. …
Statistics has important limitations — it studies only numerical aggregates, not individuals or qualities, its results are true only on average, and it can be misused. …
Statistics is limited to numerical aggregates, true only on average, is a means not an end, and can be misused.
Main limitations of statistics:
- Studies only quantitative facts: statistics deals only with numerical data; qualities such as honesty, intelligence or beauty cannot be studied directly unless measured numerically.
- Studies aggregates, not individuals: it deals with groups/aggregates, not single, isolated items.
- Results true only on an average: statistical conclusions hold on an average and may not be true for every individual case.
- Can be misused: if collected or used by unskilled or dishonest persons, statistics can be manipulated to prove opposite conclusions ('figures can lie').
- Only a means, not an end: it is a tool to study problems, not a solution in itself. …
- CBSE 2026Set MARCH1 markMCQQ.The data collected by an investigator from a website(a) Primary data(b) Secondary data(c) Tertiary data(d) None of these
›Reveal solutionSolution
Data an investigator picks up from a website were originally collected by someone else, so they are secondary data — option (b).
In the Kerala Plus One (DHSE) Statistics for Economics chapter 'Collection of Data', data are classified by their source:
- Primary data are collected originally by the investigator for the first time, for a specific purpose (e.g. through a personal survey).
- Secondary data are already in existence — collected, processed and published by some other agency — and are simply used by the investigator. Figures taken from a website, a government report, or a newspaper fall in this category. …
- CBSE 2026Set MARCH1 markMCQQ.This subject is mainly around the study of mankind in the ordinary business of life.(a)(a) History(b)(b) Economics(c)(c) Political Science(d)(d) Sociology
›Reveal solutionSolution
The correct option is (b) Economics.
This is a definition-based MCQ from the very first chapter of Karnataka 1st PUC Economics. The phrase "the study of mankind in the ordinary business of life" is the well-known welfare definition given by Alfred Marshall. He viewed economics as the study of how ordinary people go about earning a living and spending their income to satisfy their wants.
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- CBSE 2024Set MARCH1 markQ.Fill in the blank by choosing correct answer from the bracket (agriculture, labour, statistics, sub-divided bar diagrams, consumer, project report): Data, numbers, equations are being used in __________
›Reveal solutionSolution
The correct word from the bracket is 'statistics'.
In the Introduction chapter of Karnataka 1st PUC Economics, statistics is described as dealing with the collection, presentation, analysis and interpretation of numerical data. Its whole working depends on quantitative material — figures, numbers and mathematical re …
- CBSE 2024Set ANNUAL1 markQ.Fill in the blank: Statistics is the science of ________ and probabilities.
›Reveal solutionSolution
Statistics is the science of estimates and probabilities.
Statistics, in its scientific sense, deals with the collection, analysis and interpretation of numerical data to make estimates about a population and to assess the probability (likelihood) of outcomes. Hence it is described (by Boddington) as 'the sci …
- CBSE 2023Set ANNUAL1 markMCQQ.Write True or False: Statistics studies only quantitative data.(a) True(b) False
›Reveal solutionSolution
True — statistics deals with numerically expressed (quantitative) data.
A defining characteristic of statistics is that statistics are numerically expressed — it deals with aggregates of facts that can be measured and expressed in numbers (quantitative data). Purely qualitative characteristics (like honesty, beauty, intelligence) are not statistics in themselves; they can be studied statistically only when they are converted into numbers (e.g., by scoring or ranking). In this sense, …
- CBSE 2021Set MARCH1 markMCQQ.Answer any 10 questions from 'a' to 'l' carries 1 score each.(a) Which of the following bank is known as 'World Bank'?(i) International Monetary Fund(ii) Asian Development Bank(iii) International Bank for Reconstruction and Development(iv) Reserve Bank of India(b) Data collected from a newspaper is an example of(i) Primary data(ii) Secondary data(iii) Un-published data(iv) Raw data(c) "Jail cost of living" as a measure of poverty line was used by(i) Dadabhai Naoroji(ii) VKRV Rao(iii) Findley Shiras(iv) Amartya Sen(d) Choose an example for commercial energy source(i) Fuel wood(ii) Agricultural waste(iii) Dried dung(iv) Electricity(e) Tally marks of a distribution represents(i) Class limit(ii) Class interval(iii) Class mid value(iv) Class frequency(f) The range of a series represents(i) Highest number in the series(ii) Lowest number in the series(iii) Middle number in the series(iv) Difference between highest number and lowest number in the series(g) Which of the following is an environmental issue?(i) Unemployment(ii) Inflation(iii) Land degradation(iv) Economic depression(h) Which of the following diagram helps to locate 'median'?(i) Histogram(ii) Ogives(iii) Frequency Polygon(iv) Frequency curve(i) Persons who own and operate an enterprise to earn their livelihood are known as(i) Self employed(ii) Casual wage labourers(iii) Regular salaried employees(iv) Government servants(j) Which index number indicate the changes in general price level?(i) Index for Industrial Production(ii) Consumer Price Index(iii) Wholesale Price Index(iv) Sensex (k) Which of the following is 'NOT' a Health indicator of a country?(i) Infant mortality rate(ii) Incidence of communicable and non communicable diseases(iii) Life expectancy(iv) Employment level (l) Population is statistics means(i) Totality of items under study(ii) A sample unit under study(iii) First 10 units under study(iv) Last 100 units under study
›Reveal solutionSolution
A mixed 12-part MCQ block from the Kerala Plus One (DHSE) Economics paper. Correct choices: (a) iii, (b) ii, (c) iii, (d) iv, (e) iv, (f) iv, (g) iii, (h) ii, (i) i, (j) iii, (k) iv, (l) i.
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- CBSE 2020Set ANNUAL1 markMCQQ.“Statistics is the science of counting”, who said this?(a) Johnson(b) King(c) A. L. Bowley(d) Marshall
›Reveal solutionSolution
'Statistics is the science of counting' was said by A. L. Bowley — option (c).
The statement 'Statistics is the science of counting' is a well-known definition given by A. L. Bowley (who also described i …
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