Q.Explain two limitations of statistics.

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.

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:

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.

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)

1. Pose a question: "Has poverty declined in India over the last decade?"
2. Collect data: Government surveys like NSSO, Census, or your own questionnaire
3. Organise the data: Tables, frequency distributions, spreadsheets
4. Analyse the data: Calculate averages, percentages, growth rates
5. Interpret the results: "Poverty headcount ratio fell from 37% to 22% between 2004 and 2012"
6. 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. …