Index Numbers Class 11: Meaning, WPI, CPI, IIP and Simple Aggregative Method

What Index Numbers is about

Weightage: This chapter is part of Unit 3, Statistical Tools and Interpretation, which carries 25 of the 80 theory marks in the school annual exam.Source: CBSE Economics (030) syllabus 2026-27, Class XI course structure, Unit 3 Statistical Tools and Interpretation

Key concepts

Meaning and features of an index number

NCERT section 2

An index number is a statistical measure of the average change in a group of related variables over two or more periods (or places). One period, the base period, is the reference; its index is taken as 100. The period being compared is the current period.

Features:

• It is a relative measure, expressed as a number (percentage of the base), not in rupees or tonnes.
• It measures change in a group of items, not one item.
• It is an average: some prices may rise more, some less, some may fall.
• It measures change over time (mostly) or across places.

An index of 135 means a 35% rise over the base; 92 means an 8% fall.

Price relative of one item = p₁ ÷ p₀ × 100. An index number combines many price relatives.

Worked example

The price of rice rose from ₹40/kg in 2024-25 to ₹46/kg in 2025-26. Find the price relative and interpret it.

Try it first, then show the solutionSolution

1. Price relative = 46 ÷ 40 × 100 = 115

Answer: 115: the price of rice rose by 15% over the base year.

Types of index numbers

NCERT section 2

• Price index: measures changes in prices (WPI, CPI). Most common.
• Quantity index: measures changes in physical quantity produced, sold or consumed (Index of Industrial Production, agricultural production index).
• Value index: measures changes in total value (price × quantity), such as the value of exports.

Other indices met in economics: the Sensex (share prices of 30 leading companies on the Bombay Stock Exchange, base 1978-79), the Human Development Index, and indices of agricultural production.

Worked example

Classify: (a) an index showing change in tonnes of steel produced; (b) an index showing change in retail prices paid by industrial workers; (c) an index of the rupee value of exports.

Try it first, then show the solutionSolution

1. (a) Physical output: quantity index
2. (b) Prices: price index (CPI)
3. (c) Price × quantity: value index

Answer: (a) Quantity; (b) price; (c) value index.

Simple aggregative method

NCERT section 3

In the simple aggregative method, the prices (or quantities) of all items in the current year are added and divided by the sum of base-year prices:

Price index: P₀₁ = Σp₁ ÷ Σp₀ × 100

Quantity index: Q₀₁ = Σq₁ ÷ Σq₀ × 100

where p₀ = base-year price and p₁ = current-year price.

Vegetable prices (₹ per kg) at a market:

Item	Price in 2024-25 (p₀)	Price in 2025-26 (p₁)
Potato	30	36
Onion	40	50
Tomato	25	35
Cabbage	20	22
Brinjal	35	42
Total	150	185

P₀₁ = 185 ÷ 150 × 100 = 123.33: on average vegetable prices rose by 23.33%.

Limitations: (1) it gives equal importance to all items, though a family spends much more on some (rice) than others (salt); (2) items with high prices dominate the index; (3) it is affected by the units in which prices are quoted (per kg, per quintal, per dozen). For these reasons official indices use weights, though the syllabus asks you to calculate only the simple aggregative index.

Worked example

Suppose the price of onions above were quoted per quintal (₹4,000 and ₹5,000) while others stay per kg. What happens to the simple aggregative index?

Try it first, then show the solutionSolution

1. Σp₀ = 30 + 4,000 + 25 + 20 + 35 = 4,110; Σp₁ = 36 + 5,000 + 35 + 22 + 42 = 5,135
2. Index = 5,135 ÷ 4,110 × 100 ≈ 124.9
3. Onion alone now decides the index, because of its unit

Answer: About 124.9 instead of 123.3: the result changes with the units, a key weakness of the method.

Consumer Price Index (CPI)

NCERT section 4

The Consumer Price Index (cost of living index) measures the average change in the retail prices of a basket of goods and services consumed by a particular group of people. It answers: how much more money does a household need to buy the same basket now?

A CPI of 277 for industrial workers (base 2001 = 100) means a basket that cost ₹100 in 2001 costs ₹277 now.

Indian CPIs (as described in NCERT): CPI for Industrial Workers, CPI for Agricultural Labourers and for Rural Labourers, and the All-India CPI (Rural, Urban and Combined) with base 2012 = 100, compiled by the government's statistics agencies. Base years are revised from time to time as consumption patterns change. The Consumer Food Price Index covers food items.

Official CPIs are weighted: each item's weight reflects its share in the household budget (from consumer expenditure surveys). The Reserve Bank of India uses CPI (Combined) inflation as the target for monetary policy.

Uses: wage negotiations and dearness allowance; income, price and rent-control policy; real wages; purchasing power of money.

Worked example

If the CPI rises from 100 to 160, what is the purchasing power of a rupee compared with the base year?

Try it first, then show the solutionSolution

1. Purchasing power = 100 ÷ CPI = 100 ÷ 160 = 0.625

Answer: ₹1 now buys what 62.5 paise bought in the base year.

Wholesale Price Index (WPI)

NCERT section 4

The Wholesale Price Index measures the average change in prices of goods traded in bulk at the wholesale level. It covers goods only, not services, and has no particular consumer group.

As described in NCERT, the WPI has base 2011-12 = 100, and its major groups and weights are primary articles (about 22.6), fuel and power (about 13.2) and manufactured products (about 64.2). The rate of change of the all-commodities index is often called headline inflation by WPI; focusing on manufactured goods excluding food and fuel gives core inflation.

Uses: measuring inflation in the economy; removing the effect of price changes from aggregates like national income and capital formation (deflating); price policy for industries.

CPI vs WPI:

Basis	CPI	WPI
Prices	Retail	Wholesale
Covers	Goods and services	Goods only
Group	A specific group of consumers	No particular group
Use	Cost of living, DA, real wages, RBI's inflation target	General price level, deflating aggregates

Worked example

The WPI rose from 154.2 last month to 158.9 this month. Find the rate of inflation for the month.

Try it first, then show the solutionSolution

1. Inflation = (X₁ − X₀) ÷ X₀ × 100
2. = (158.9 − 154.2) ÷ 154.2 × 100 = 3.05%

Answer: About 3.05% for the month.

Index of Industrial Production (IIP)

NCERT section 4

The IIP is a quantity index that measures changes in the volume of industrial output (not prices). As described in NCERT, its base is 2011-12 = 100 (with effect from April 2017), and items are weighted by their value added.

Sector-wise weights (NCERT): mining 14.4, manufacturing 77.6, electricity 8.0. It is also given by use-based groups: primary goods, capital goods, intermediate goods, infrastructure/construction goods, consumer durables and consumer non-durables. Eight core industries (coal, crude oil, natural gas, refinery products, fertilisers, steel, cement, electricity) have a combined weight of about 40% in the IIP.

The base year is revised often because some products stop being made and new ones appear.

Use: shows the growth of industry; guides industrial and economic policy; an early signal of the state of the economy.

Worked example

Suppose output of rice, wheat and pulses in a district changes from 400, 300 and 100 tonnes to 460, 330 and 90 tonnes. Find the simple aggregative quantity index.

Try it first, then show the solutionSolution

1. Σq₀ = 800; Σq₁ = 880
2. Q₀₁ = 880 ÷ 800 × 100 = 110

Answer: 110: total output of these crops rose about 10%.

Uses of index numbers, inflation and issues in construction

NCERT section 5 and 6

Uses:
1. Measuring inflation: inflation is a general and continuing rise in prices; its rate is the percentage change in a price index.
2. Real wages and DA: Real wage = Money wage ÷ CPI × 100. Dearness allowance is revised with the CPI so that real wages do not fall.
3. Purchasing power of money = 100 ÷ CPI (in base-year rupees).
4. Deflating national income and other aggregates to remove the effect of price changes.
5. Policy: price, wage, tax and industrial policies; business planning; the Sensex tracks the stock market and investor confidence.

Issues in constructing an index:

• Purpose must be clear (price, quantity or value index).
• Items must be representative of the group (petrol prices matter less to farm labourers).
• Base year should be a normal year (no war, famine or boom) and not too far in the past.
• Formula and weights must suit the purpose.
• Data must be reliable and comparable.

Worked example

A worker's money wage is ₹24,000 and the CPI is 160. Find the real wage.

Try it first, then show the solutionSolution

1. Real wage = 24,000 ÷ 160 × 100 = ₹15,000

Answer: ₹15,000 in base-year prices: the worker can buy what ₹15,000 bought in the base year.

Index Numbers 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

• Constructing Index Numbers
• CPI, WPI, IIP, Inflation and Real Wages

Index Numbers: key facts

Price relative

Price relative = \frac{p_1}{p_0} \times 100

For one item.

Simple aggregative price index

P_{01} = \frac{\sum p_1}{\sum p_0} \times 100

Base year index = 100.

Simple aggregative quantity index

Q_{01} = \frac{\sum q_1}{\sum q_0} \times 100

Measures change in physical volume.

Rate of inflation

\text{Inflation} = \frac{X_t - X_{t-1}}{X_{t-1}} \times 100

X = price index (WPI or CPI) in two periods.

Real wage

\text{Real wage} = \frac{\text{Money wage}}{\text{CPI}} \times 100

Wage in base-year prices.

Purchasing power of money

\text{Purchasing power} = \frac{100}{\text{CPI}}

Value of ₹1 in base-year rupees.

How the school exam asks Index Numbers

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

Tricks to remember Index Numbers

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

• Formula order

  "New over old, times a hundred": Σp₁ ÷ Σp₀ × 100.

  Use it when: Simple aggregative index.

• CPI vs WPI

  CPI: Consumer, Cost of living, goods + serviCes. WPI: Wholesale, goods Without services.

  Use it when: Distinctions.

• Issues: "PIBFD"

  Purpose, Items, Base year, Formula, Data.

  Use it when: Issues in construction.

Index Numbers: 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 Index Numbers

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

• ✗Mistake: Dividing Σp₀ by Σp₁

  Order mixed up.

  Wrong working

  Index = 150 ÷ 185 × 100 = 81.1

  Right working

  Index = 185 ÷ 150 × 100 = 123.3

  ✓Do this: Current year on top, base year below.

  Usually costs: The whole answer.

• ✗Mistake: Reading an index of 123 as "prices are ₹123"

  Index numbers look like prices.

  ✓Do this: An index is a relative number: 123 means 23% higher than the base.

  Usually costs: 1 mark in interpretation.

• ✗Mistake: Saying WPI includes services

  Confusing with CPI.

  ✓Do this: WPI covers goods only; CPI covers goods and services.

  Usually costs: 1 mark.

• ✗Mistake: Calculating inflation as the difference in index points

  Points look like percentages.

  Wrong working

  CPI 140 to 147: inflation = 7%

  Right working

  Inflation = 7 ÷ 140 × 100 = 5%

  ✓Do this: Divide the change by the earlier index.

  Usually costs: 1 mark.

• ✗Mistake: Ignoring the units problem

  Students add prices quoted in different units.

  ✓Do this: Make sure all prices are in comparable units before using the simple aggregative method, and mention this limitation.

  Usually costs: 1 mark in limitation questions.

NCERT exercise guide: Index Numbers

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 Index Numbers

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

   An index number measures:
   (a) the absolute change in one variable
   (b) the average change in a group of related variables
   (c) the total value of goods
   (d) the correlation between variables

   Hint

   Relative and average.

   Answer

   (b)

2. Q2 · 1 mark · MCQExam level

   The IIP is a:
   (a) price index
   (b) quantity index
   (c) value index
   (d) cost of living index

   Hint

   Industrial output volume.

   Answer

   (b) quantity index

3. Q3 · 1 mark · Very short answerExam level

   What is the Sensex?

   Hint

   Stock market.

   Answer

   The BSE Sensitive Index of 30 leading companies' share prices, base 1978-79; a benchmark of the Indian stock market.

4. Q4 · 3 marks · Short answerExam level

   Give three uses of index numbers.

   Hint

   Inflation, wages, policy.

   Answer

   (1) Measure inflation and the purchasing power of money. (2) Fix dearness allowance and find real wages. (3) Deflate national income and guide price and industrial policy.

5. Q5 · 3 marks · Short answerHarder exam level

   Compute the simple aggregative price index: base prices ₹50, 80, 20, 150; current prices ₹60, 92, 26, 162.

   Hint

   Add columns.

   Answer

   Σp₀ = 300; Σp₁ = 340; index = 113.33: prices rose about 13.3%.

6. Q6 · 3 marks · Short answerHarder exam level

   CPI rose from 140 to 147 in a year. Find the inflation rate. If a worker's wage rose from ₹28,000 to ₹29,000, did his real wage rise?

   Hint

   Compare percentages.

   Answer

   Inflation = 7 ÷ 140 × 100 = 5%. Wage rose 1,000 ÷ 28,000 × 100 ≈ 3.6%, less than 5%, so his real wage fell (from 20,000 to about 19,728 in base-year rupees).

7. Q7 · 4 marks · Long answerHarder exam level

   Distinguish between CPI and WPI on four bases.

   Hint

   Retail vs wholesale.

   Answer

   Prices: retail vs wholesale. Coverage: goods and services vs goods only. Group: a particular consumer group vs none. Use: cost of living, DA, RBI's inflation target vs general price level and deflating aggregates.

8. Q8 · 4 marks · Long answerHarder exam level

   What are the limitations of the simple aggregative method? Illustrate the unit problem with an example.

   Hint

   Equal weights, high prices, units.

   Answer

   It treats all items as equally important; high-priced items dominate; results depend on units. Example: if one item's price is quoted per quintal instead of per kg, its rupee figures become 100 times larger and that item alone decides the index.

9. Q9 · 4 marks · Long answerHarder exam level

   State four issues to keep in mind while constructing an index number.

   Hint

   Purpose, items, base, formula, data.

   Answer

   Clear purpose (price vs quantity); representative items; a normal and recent base year; a suitable formula and weights; reliable and comparable data.

10. Q10 · 1 mark · Very short answerHarder exam level

    If the CPI is 125, what is the purchasing power of ₹100 in base-year terms?

    Hint

    100 ÷ CPI.

    Answer

    ₹80 (₹100 × 100 ÷ 125).

11. Q11 · 3 marks · Short answerHarder exam level

    Suppose the Sensex rises from 78,000 to 81,900 in a month. Find the percentage change and say what it suggests.

    Hint

    Percentage change.

    Answer

    5% rise: share prices of leading companies went up, suggesting investors expect better earnings and are more confident about the economy.

12. Q12 · 4 marks · Long answerHOTS / competency

    Suppose the government says "inflation is only 2%", but a family finds its monthly spending rising 8%. Give three possible reasons, using ideas from this chapter.

    Hint

    Basket, weights, quantities.

    Answer

    (1) The official index basket and weights differ from the family's: if food, rent or school fees rose faster and form a bigger share of its budget, its own inflation is higher. (2) The family may be buying more or better goods (quantity change), not just facing higher prices. (3) The official figure may be for a different index (WPI, goods only) or period. A household-specific CPI would show the family's own cost-of-living change.

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 is the index of the base year?Show answer

   100.

2. 2.Formula of the simple aggregative price index?Show answer

   Σp₁ ÷ Σp₀ × 100.

3. 3.Which index covers services: CPI or WPI?Show answer

   CPI.

4. 4.Which index measures quantities?Show answer

   Index of Industrial Production (IIP).

5. 5.Formula for real wage?Show answer

   Money wage ÷ CPI × 100.

6. 6.Purchasing power of money?Show answer

   100 ÷ CPI (or 1 ÷ cost of living index).

7. 7.Base of the Sensex?Show answer

   1978-79.

Quick revision checklist

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

• ☐Can you define an index number and its base?
• ☐Can you name price, quantity and value indices with examples?
• ☐Can you compute a simple aggregative price index and interpret it?
• ☐Can you explain the units problem?
• ☐Can you distinguish CPI and WPI on four bases?
• ☐Can you say what the IIP measures and its sector weights?
• ☐Can you compute inflation from two index values?
• ☐Can you find real wages and purchasing power?
• ☐Can you list five issues in constructing an index?

Index Numbers: frequently asked questions