Important Questions and Answers for Class 11 Economics Chapter 7 Index Numbers 2025-26

Q1. Which of the following is a statistical measure that summarises the change in a group of related variables over time?

• (a) Mean
• (b) Index number
• (c) Mode
• (d) Median

Answer: (b) Index number. It measures relative change in a group of variables across time periods.

Q2. The base period in an index number calculation is given the value:

• (a) 0
• (b) 10
• (c) 100
• (d) 1000

Answer: (c) 100. The value for the base period is conventionally assigned 100 in index number calculations.

Q3. Which index number attempts to measure the changes in the quantity of production, not prices?

• (a) Consumer Price Index
• (b) Wholesale Price Index
• (c) Index of Industrial Production
• (d) Human Development Index

Answer: (c) Index of Industrial Production. It measures changes in the quantity of industrial output.

2. Very Short Answer (VSA).

Q4. What is an index number?

Answer: An index number is a statistical tool used to measure changes in the magnitude of a group of related variables over time, expressed relative to a base period.

Q5. State one use of the Consumer Price Index (CPI).

Answer: The CPI is used to measure inflation and helps in the formulation of wage policies for workers.

Q6. What does the base period represent in constructing an index number?

Answer: The base period is the reference period against which current values are compared and is given an index value of 100.

Q7. Name the index number used to indicate the retail price changes for industrial workers in India.

Answer: The Consumer Price Index (CPI) for industrial workers is used to indicate such retail price changes.

3. Short Answer Questions.

Q8. Explain the difference between price index numbers and quantity index numbers.

Answer: Price index numbers compare changes in the prices of selected goods over time, while quantity index numbers measure changes in the physical volume of goods produced, used, or consumed. Price indices reflect market trends; quantity indices show output or usage shifts.

Q9. State two desirable properties of a base period in constructing index numbers.

Answer: The base period should be a normal, representative period without abnormal events, and it should not be too far removed from the current period to ensure relevant comparisons.

Q10. Why is it necessary to assign weights in the construction of a weighted index number?

Answer: Assigning weights ensures that items of greater importance or higher consumption are given a proportionately higher impact on the index number, making results more accurate and representative of real-world significance.

Q11. What is the significance of the Sensex in the Indian economy?

Answer: The Sensex represents the overall performance of select major stocks on the Bombay Stock Exchange. It serves as a barometer for investor sentiment and overall economic trends in the country.

4. Long Answer Questions.

Q12. Discuss the steps involved in constructing a weighted aggregative price index. Illustrate with a brief example.

Answer: Constructing a weighted aggregative price index involves selecting commodities, assigning weights (usually base period quantities), collecting prices for the base and current periods, multiplying prices by their weights for both periods, and applying the formula: $P_{01} = \dfrac{\Sigma P_1 q_0}{\Sigma P_0 q_0} \times 100$ This index accurately represents importance by giving more weight to items with higher consumption.

1. Select commodities and assign appropriate weights (e.g., quantities consumed in the base year).
2. Collect base and current period prices for these items.
3. Calculate weighted totals for both periods: $\Sigma P_1 q_0$ and $\Sigma P_0 q_0$.
4. Apply the index formula and multiply the result by 100.

Q13. Explain the relevance and limitations of index numbers in economic analysis.

Answer: Index numbers are vital tools for summarizing large volumes of economic data, enabling policymakers to track price, quantity, or output changes. They are essential for analyzing inflation, wage adjustments, and living standards. However, limitations include selection of representative items, choice of base year, and sensitivity to changes in consumption patterns, which may affect accuracy. Changes in quality or new goods also pose challenges, requiring periodic review of items and weights used.

5. Assertion–Reason type questions.

Assertion (A): The Consumer Price Index helps in measuring the change in the cost of living.
Reason (R): CPI is based on the retail prices of goods bought by consumers.

• (a) A and R are true, and R is the correct explanation of A
• (b) A and R are true, but R is not the correct explanation of A
• (c) A is true, but R is false
• (d) A is false, but R is true

Answer: (a) Both statements are true, and R correctly explains why CPI measures the cost of living.

Assertion (A): The wholesale price index provides information about retail price movements.
Reason (R): WPI is calculated using wholesale prices of selected commodities.

• (a) A and R are true, and R is the correct explanation of A
• (b) A and R are true, but R is not the correct explanation of A
• (c) A is true, but R is false
• (d) A is false, but R is true

Answer: (d) The assertion is false; WPI tracks wholesale, not retail, price movements, while reason is true.

6. Case-based questions.

Ravi noticed that the price of food and fuel has changed over the last five years. The CPI shows a noticeable increase, while his family's monthly expenses have also gone up. He wonders how these changes affect his standard of living and if his salary rise matches the inflation measured by the CPI.

(i) What is the purpose of constructing the Consumer Price Index for families like Ravi's?

Answer: The CPI helps track changes in the cost of living and compare income increases with inflation for effective wage adjustments.

(ii) If Ravi’s salary increases by 10% but the CPI increases by 15% in the same period, what happens to his real wage?

Answer: His real wage declines because his salary rise is less than the increase in living costs as shown by CPI.

(iii) Name the formula used to calculate a weighted index number that considers both prices and quantities from the base year.

Answer: The Laspeyre’s Index formula is used: $P_{01} = \dfrac{\Sigma P_1 q_0}{\Sigma P_0 q_0} \times 100$.

(iv) State one limitation of using CPI in measuring standard of living.

Answer: CPI may not account for differences in consumption patterns among households or changes in quality of goods over time.

7. Match the following.

8. Numericals / Derivations.

Q14. Given the following data, calculate the Laspeyre’s Price Index:

Answer: Laspeyre’s Price Index is approximately 135.3.

1. Given: Base prices (P₀), Base quantity (q₀), Current prices (P₁).
2. Formula: $P_{01} = \dfrac{\Sigma P_1 q_0}{\Sigma P_0 q_0} \times 100$
3. Calculate: (4×10+6×12+5×20+3×15) = 257; (2×10+5×12+4×20+2×15) = 190
4. $P_{01} = \dfrac{257}{190} \times 100 \approx 135.3$

Q15. If the Consumer Price Index is 400 and a person’s salary in the base year was Rs 4,000 and current salary is Rs 6,000, by how much should his salary be raised to maintain the same standard of living?

Answer: The salary should be Rs 16,000 to maintain the same living standard.

1. Given: Base salary = Rs 4,000; Current CPI = 400; Base CPI = 100
2. Required salary = (Current CPI/Base CPI) × Base Salary = (400/100) × 4,000
3. Calculation: 4 × 4,000 = Rs 16,000
4. Final answer: Rs 16,000 per annum

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