Class 11 Statistics Notes – Chapter 7: Index Numbers

1. Meaning of Index Number

An Index Number is a statistical measure used to show changes in a group of related variables over time.

Definition

It measures the average change in prices, quantities, values, or other economic variables compared to a base period.

Base Year

• The year chosen for comparison is called the Base Year.
• Base year index = 100
• All other years are compared with it.

Example

If the price index in 2025 is 150:

• Prices have increased by 50% compared to the base year.

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2. Importance of Index Numbers

Index numbers help to:

• Measure inflation
• Compare price changes
• Study production trends
• Measure cost of living
• Analyse economic growth
• Guide government policy decisions

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3. Types of Index Numbers

A. Price Index

Measures changes in prices.

Examples:

• Consumer Price Index (CPI)
• Wholesale Price Index (WPI)

B. Quantity Index

Measures changes in production or quantity.

Examples:

• Index of Industrial Production (IIP)
• Agricultural Production Index

C. Value Index

Measures changes in total value (Price × Quantity).

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4. Construction of Index Numbers

Method 1: Simple Aggregative Price Index

Formula

$$P_{01}=\frac{\Sigma P_1}{\Sigma P_0}\times100$$P01​=ΣP0​ΣP1​​×100

Where:

• $P_1$P1​ = Current year price
• $P_0$P0​ = Base year price

Features

• Easy to calculate
• No weights used
• Assumes all items are equally important

Limitation

Different commodities do not have equal importance in real life.

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Method 2: Weighted Aggregative Price Index

Weights are assigned according to the importance of commodities.

(A) Laspeyres Price Index

Uses base year quantities as weights.

Formula

$$P_{01}=\frac{\Sigma P_1Q_0}{\Sigma P_0Q_0}\times100$$P01​=ΣP0​Q0​ΣP1​Q0​​×100

Advantages

• Easy to calculate
• Widely used

Limitation

• Uses old consumption pattern

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(B) Paasche Price Index

Uses current year quantities as weights.

Formula

$$P_{01}=\frac{\Sigma P_1Q_1}{\Sigma P_0Q_1}\times100$$P01​=ΣP0​Q1​ΣP1​Q1​​×100

Advantage

Reflects current consumption habits.

Limitation

Requires current year quantity data.

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5. Method of Averaging Price Relatives

Price Relative Formula

$$R=\frac{P_1}{P_0}\times100$$R=P0​P1​​×100

Simple Average of Price Relatives

$$P_{01}=\frac{\Sigma R}{n}$$P01​=nΣR​

Where:

• R = Price Relative
• n = Number of commodities

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Weighted Price Relative Index

Formula

$$P_{01}=\frac{\Sigma WR}{\Sigma W}$$P01​=ΣWΣWR​

Where:

• W = Weight
• R = Price Relative

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6. Consumer Price Index (CPI)

Meaning

Consumer Price Index measures changes in retail prices paid by consumers.

Also Called

Cost of Living Index

Uses

• Measures inflation
• Wage revision
• Salary adjustments
• Government policy decisions

Interpretation

If:$$CPI = 150$$CPI=150

Then:

• Cost of living increased by 50%
• Salary should increase by 50% to maintain the same standard of living.

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7. Wholesale Price Index (WPI)

Meaning

Measures changes in prices at the wholesale level.

Characteristics

• Includes only goods
• Excludes services
• Used to estimate inflation

Importance

• Indicates general price level changes.
• Helps government monitor inflation.

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8. Index of Industrial Production (IIP)

Meaning

Measures changes in industrial production.

Major Sectors

Sector	Weight (%)
Mining	14.4
Manufacturing	77.6
Electricity	8.0

Uses

• Measures industrial growth
• Economic planning
• Policy formulation

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9. Sensex

Meaning

Sensex stands for:

Bombay Stock Exchange Sensitive Index

Features

• Represents stock market performance.
• Consists of 30 major companies.
• Indicates investor confidence.

Interpretation

• Rising Sensex → Positive economic outlook
• Falling Sensex → Negative market sentiment

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10. Human Development Index (HDI)

Meaning

Measures overall human development of a country.

Components

1. Health
2. Education
3. Standard of Living

Importance

Used to compare development among countries.

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11. Important Issues in Constructing Index Numbers

1. Purpose of Index

Clearly define what is being measured.

2. Selection of Items

Items should represent actual consumption or production patterns.

3. Choice of Base Year

A good base year should:

• Be normal
• Not be too old
• Be free from abnormal events

4. Choice of Formula

Depends on the objective of the study.

5. Reliable Data

Accurate data ensures accurate index numbers.

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12. Uses of Index Numbers in Economics

Consumer Price Index (CPI)

• Wage determination
• Rent control
• Tax policy
• Cost of living studies

Wholesale Price Index (WPI)

• Measures inflation
• Deflates national income data

Index of Industrial Production (IIP)

• Measures industrial growth

Agricultural Production Index

• Measures agricultural performance

Sensex

• Guides investment decisions

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13. Purchasing Power of Money

Formula

$$Purchasing\ Power = \frac{100}{CPI}$$Purchasing Power=CPI100​

Example

If CPI = 500$$Purchasing\ Power = \frac{100}{500}=0.20$$Purchasing Power=500100​=0.20

Meaning:
₹1 today has the purchasing power of only 20 paise of the base year.

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14. Real Wage

Formula

$$Real\ Wage=\frac{Money\ Wage}{CPI}\times100$$Real Wage=CPIMoney Wage​×100

Importance

Shows actual purchasing power of income after accounting for inflation.

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Quick Revision

✅ Index Number = Measure of change over time

✅ Base Year Index = 100

✅ Price Index → Measures price changes

✅ Quantity Index → Measures production changes

✅ CPI = Cost of Living Index

✅ WPI = Wholesale price changes

✅ IIP = Industrial production changes

✅ Sensex = Stock market indicator

✅ HDI = Human development measure

✅ Laspeyres → Base year weights

✅ Paasche → Current year weights

✅ Purchasing Power = 100 ÷ CPI

✅ Real Wage = (Money Wage ÷ CPI) × 100

Comprehensive Question Bank (MCQ, Fill in the Blanks, True/False, Match, Short Answer)

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A. Multiple Choice Questions (MCQs)

1. An index number is a statistical device used to measure:

a) Absolute values
b) Changes in a group of related variables
c) Population size
d) National income

Answer: b

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2. The period chosen for comparison is called:

a) Current year
b) Reference year
c) Base year
d) Census year

Answer: c

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3. The index number of the base year is generally:

a) 0
b) 1
c) 10
d) 100

Answer: d

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4. Which index measures changes in retail prices?

a) WPI
b) CPI
c) IIP
d) HDI

Answer: b

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5. CPI is also known as:

a) Wholesale Price Index
b) Cost of Living Index
c) Production Index
d) Sensex

Answer: b

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6. Which index measures changes in wholesale prices?

a) CPI
b) WPI
c) IIP
d) HDI

Answer: b

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7. Which index measures industrial output?

a) CPI
b) WPI
c) IIP
d) Sensex

Answer: c

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8. Laspeyres Index uses:

a) Current year quantities
b) Base year quantities
c) Current year prices
d) None of these

Answer: b

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9. Paasche Index uses:

a) Base year quantities
b) Current year quantities
c) Average quantities
d) None

Answer: b

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10. Sensex is related to:

a) Agriculture
b) Stock Market
c) Inflation
d) Population

Answer: b

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11. Sensex consists of:

a) 20 companies
b) 25 companies
c) 30 companies
d) 50 companies

Answer: c

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12. A weighted index takes into account:

a) Equal importance of all items
b) Relative importance of items
c) Population size
d) Time period

Answer: b

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13. Which index is commonly used to measure inflation?

a) CPI
b) WPI
c) Both
d) HDI

Answer: c

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14. HDI stands for:

a) Human Development Index
b) Human Data Index
c) Human Distribution Index
d) Human Demand Index

Answer: a

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15. Which sector has the highest weight in IIP?

a) Mining
b) Electricity
c) Manufacturing
d) Agriculture

Answer: c

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16. Which of the following is a Quantity Index?

a) CPI
b) WPI
c) IIP
d) Cost of Living Index

Answer: c

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17. If CPI = 150, cost of living has increased by:

a) 25%
b) 50%
c) 75%
d) 150%

Answer: b

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18. The simple aggregative index is:

a) Weighted
b) Unweighted
c) Relative
d) Quantity index

Answer: b

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19. Price Relative is:

a) P₀/P₁ ×100
b) P₁/P₀ ×100
c) P₀+P₁
d) P₁−P₀

Answer: b

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20. The Reserve Bank of India mainly uses:

a) WPI
b) Combined CPI
c) IIP
d) HDI

Answer: b

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B. Fill in the Blanks

1. An index number measures __________ in related variables.

Answer: changes

2. The base year index is always __________.

Answer: 100

3. CPI stands for __________.

Answer: Consumer Price Index

4. WPI stands for __________.

Answer: Wholesale Price Index

5. IIP stands for __________.

Answer: Index of Industrial Production

6. Sensex is related to the __________ market.

Answer: stock

7. Laspeyres index uses __________ year quantities.

Answer: base

8. Paasche index uses __________ year quantities.

Answer: current

9. CPI is also called the __________ Index.

Answer: Cost of Living

10. HDI stands for __________ Development Index.

Answer: Human

11. Inflation means a continuous rise in __________.

Answer: prices

12. Manufacturing has the highest weight in __________.

Answer: IIP

13. Weighted index considers the __________ importance of commodities.

Answer: relative

14. A quantity index measures changes in __________.

Answer: production

15. The value of Sensex is compared with its __________ year.

Answer: base

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C. True or False

1. An index number measures absolute values.

False

2. Base year index is taken as 100.

True

3. CPI measures wholesale prices.

False

4. WPI measures wholesale prices.

True

5. IIP measures industrial production.

True

6. Laspeyres index uses current year quantities.

False

7. Paasche index uses current year quantities.

True

8. Sensex is a stock market index.

True

9. HDI measures human development.

True

10. Inflation reduces purchasing power.

True

11. Weighted index gives equal importance to all items.

False

12. CPI is useful in wage negotiations.

True

13. A base year should be abnormal.

False

14. WPI includes only goods.

True

15. Manufacturing sector has maximum weight in IIP.

True

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D. Match the Following

Column A	Column B
CPI	Cost of Living Index
WPI	Wholesale Prices
IIP	Industrial Production
Sensex	Stock Market
HDI	Human Development

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Column A	Column B
Laspeyres	Base Year Quantity
Paasche	Current Year Quantity
Base Year	Index 100
Inflation	Rise in Prices
Purchasing Power	Inverse of CPI

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E. One Word Answers

1. Index of stock market in India.
   Sensex
2. Index measuring cost of living.
   CPI
3. Index measuring industrial production.
   IIP
4. Index measuring wholesale prices.
   WPI
5. Year used for comparison.
   Base Year
6. Continuous rise in prices.
   Inflation
7. Human development indicator.
   HDI
8. Quantity-based industrial index.
   IIP
9. Statistical measure of change.
   Index Number
10. Base year index value.
    100

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F. Very Short Answer Questions (1 Mark)

1. What is an index number?
2. What is a base year?
3. What is CPI?
4. What is WPI?
5. What is IIP?
6. What is inflation?
7. What is Sensex?
8. What is HDI?
9. What is a weighted index?
10. What is a price relative?

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G. Short Answer Questions (3 Marks)

1. Define index number with example.
2. Differentiate between CPI and WPI.
3. Explain Laspeyres Price Index.
4. Explain Paasche Price Index.
5. What are weighted index numbers?
6. State three uses of CPI.
7. State three uses of WPI.
8. Explain the importance of IIP.
9. What is inflation?
10. Why should a base year be normal?

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H. Long Answer Questions (5 Marks)

1. Explain the meaning and importance of index numbers.
2. Describe the methods of constructing index numbers.
3. Explain Consumer Price Index and its uses.
4. Explain Wholesale Price Index and its significance.
5. Discuss Index of Industrial Production and its uses.
6. Explain the issues involved in constructing an index number.
7. Discuss the role of index numbers in economic policy.
8. Explain Sensex and its importance.
9. Explain purchasing power of money with formula.
10. Explain real wage and its significance.

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Important Numericals

1. Calculate Simple Aggregative Price Index.
2. Calculate Laspeyres Price Index.
3. Calculate Paasche Price Index.
4. Calculate Weighted Price Relative Index.
5. Calculate Consumer Price Index.
6. Calculate Purchasing Power of Money.
7. Calculate Real Wage.
8. Calculate Average GST Rate (Weighted Average Method).