NCERT Solutions for Class 11 Economics Chapter 7: Index Numbers (Statistics for Economics, 2026–27)
These Class 11 Economics Chapter 7 solutions cover Index Numbers from Statistics for Economics, the NCERT textbook for the 2026–27 session. An index number is a statistical device for measuring the average change in a group of related variables over two situations. This page reproduces every NCERT Exercises question verbatim and solves all of them — the multiple-choice items, the short theory questions, and every numerical (weighted cost-of-living index, Laspeyre’s and Paasche’s reasoning, CPI and weighted-average GST) worked out step by step in tables and verified. You also get key formulas, extra short and long questions, MCQs, Assertion–Reason practice, exam tips and FAQs.
Class 11 Economics Chapter 7 – Overview
Chapter 7, Index Numbers, teaches how a single figure can summarise change in many related variables at once. An index number measures the average change in the magnitude of a group of related variables (such as prices or quantities) between a base period (given the value 100) and a current period, expressed as a percentage. The chapter explains price index numbers and quantity (volume) index numbers, and two methods of construction — the aggregative method (simple and weighted) and the method of averaging relatives (simple and weighted). A weighted aggregative index using base-period quantities is Laspeyre’s index, while one using current-period quantities is Paasche’s index. It then describes important real-world indices — the Consumer Price Index (CPI / cost-of-living index), the Wholesale Price Index (WPI), the Index of Industrial Production (IIP), the Sensex and the Human Development Index — and shows how they are used in measuring inflation, calculating real wages and the purchasing power of money, and in economic policy making.
Key Concepts & Important Formulas
Index number: a statistical device for measuring the average relative change in a group of related variables between two situations; conventionally expressed as a percentage with the base period = 100.
Base period & current period: the base period is the reference against which comparison is made (value = 100); the current period is the period being compared. An index of 250 means the value is 2½ times the base.
Price vs quantity index: a price index measures and compares changes in prices of goods; a quantity (volume) index measures changes in the physical volume of production, construction or employment.
Weighted vs unweighted: an unweighted index treats all items as equally important; a weighted index reflects the relative importance (weight) of each item, e.g. food carrying a larger weight than a minor item.
Laspeyre’s index: a weighted aggregative price index using base-period quantities (q₀) as weights.
Paasche’s index: a weighted aggregative price index using current-period quantities (q₁) as weights.
Consumer Price Index (CPI): also called the cost-of-living index, it measures the average change in retail prices of a fixed basket of goods consumed by a defined group (e.g. industrial workers).
Simple aggregative price index: P₀₁ = (ΣP₁ / ΣP₀) × 100
Simple average of price relatives: P₀₁ = (1/n) × Σ(P₁/P₀) × 100
Laspeyre’s price index: P₀₁ = (ΣP₁q₀ / ΣP₀q₀) × 100
Paasche’s price index: P₀₁ = (ΣP₁q₁ / ΣP₀q₁) × 100
Weighted index of price relatives (CPI): P₀₁ = (ΣWR / ΣW), where R = (P₁/P₀) × 100 and W = weight
Purchasing power of money = 1 / cost-of-living index (per rupee = 100/CPI). Real wage = (Money wage / CPI) × 100. Inflation is generally measured using the WPI.
NCERT “Exercises” — Full Solutions
All questions below are reproduced verbatim from the NCERT textbook’s end-of-chapter Exercises. Answers are original; numericals are solved step by step and verified.
1. An index number which accounts for the relative importance of the items is known as (i) weighted index (ii) simple aggregative index (iii) simple average of relatives
2. In most of the weighted index numbers the weight pertains to (i) base year (ii) current year (iii) both base and current year
3. The impact of change in the price of a commodity with little weight in the index will be (i) small (ii) large (iii) uncertain
4. A consumer price index measures changes in (i) retail prices (ii) wholesale prices (iii) producers prices
5. The item having the highest weight in consumer price index for industrial workers is (i) Food (ii) Housing (iii) Clothing
6. In general, inflation is calculated by using (i) wholesale price index (ii) consumer price index (iii) producers’ price index
7. Why do we need an index number?
8. What are the desirable properties of the base period?
9. Why is it essential to have different CPI for different categories of consumers?
10. What does a consumer price index for industrial workers measure?
11. What is the difference between a price index and a quantity index?
12. Is the change in any price reflected in a price index number?
13. Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?
14. The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75, 10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as the base.
| Items | Price in 1980 | Price in 2005 |
|---|---|---|
| Food | 100 | 200 |
| Clothing | 20 | 25 |
| Fuel & lighting | 15 | 20 |
| House rent | 30 | 40 |
| Misc | 35 | 65 |
| Item | Weight W | P₀ (1980) | P₁ (2005) | R = (P₁/P₀)×100 | WR |
|---|---|---|---|---|---|
| Food | 75 | 100 | 200 | 200.00 | 15000.00 |
| Clothing | 10 | 20 | 25 | 125.00 | 1250.00 |
| Fuel & lighting | 5 | 15 | 20 | 133.33 | 666.67 |
| House rent | 6 | 30 | 40 | 133.33 | 800.00 |
| Misc | 4 | 35 | 65 | 185.71 | 742.86 |
| Total | 100 | 18459.53 |
15. Read the following table carefully and give your comments.
| Industry | Weight in % | 1996–97 | 2003–2004 |
|---|---|---|---|
| General index | 100 | 130.8 | 189.0 |
| Mining and quarrying | 10.73 | 118.2 | 146.9 |
| Manufacturing | 79.58 | 133.6 | 196.6 |
| Electricity | 10.69 | 122.0 | 172.6 |
16. Try to list the important items of consumption in your family.
17. If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 6,000, by how much should his salary be raised to maintain the same standard of living if the CPI is 400?
18. The consumer price index for June, 2005 was 125. The food index was 120 and that of other items 135. What is the percentage of the total weight given to food?
19. An enquiry into the budgets of the middle class families in a certain city gave the following information; What is the cost of living index during the year 2004 as compared with 1995?
| Expenses on items | Food | Fuel | Clothing | Rent | Misc. |
|---|---|---|---|---|---|
| 35% | 10% | 20% | 15% | 20% | |
| Price (in Rs) in 2004 | 1500 | 250 | 750 | 300 | 400 |
| Price (in Rs) in 1995 | 1400 | 200 | 500 | 200 | 250 |
| Item | Weight W (%) | P (1995) | P (2004) | R = (P₂₀₀₄/P₁₉₉₅)×100 | WR |
|---|---|---|---|---|---|
| Food | 35 | 1400 | 1500 | 107.14 | 3750.00 |
| Fuel | 10 | 200 | 250 | 125.00 | 1250.00 |
| Clothing | 20 | 500 | 750 | 150.00 | 3000.00 |
| Rent | 15 | 200 | 300 | 150.00 | 2250.00 |
| Misc. | 20 | 250 | 400 | 160.00 | 3200.00 |
| Total | 100 | 13450.00 |
20. Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks. How has the price change affected your family?
21. Given the following data—
| Year | CPI of industrial workers (1982 = 100) | CPI of agricultural labourers (1986–87 = 100) | WPI (1993–94 = 100) |
|---|---|---|---|
| 1995–96 | 313 | 234 | 121.6 |
| 1996–97 | 342 | 256 | 127.2 |
| 1997–98 | 366 | 264 | 132.8 |
| 1998–99 | 414 | 293 | 140.7 |
| 1999–00 | 428 | 306 | 145.3 |
| 2000–01 | 444 | 306 | 155.7 |
| 2001–02 | 463 | 309 | 161.3 |
| 2002–03 | 482 | 319 | 166.8 |
| 2003–04 | 500 | 331 | 175.9 |
(i) Comment on the relative values of the index numbers.
(ii) Are they comparable?
22. The monthly expenditure (Rs.) of a family on some important items and the Goods and Services Tax (GST) rates applicable to these items is as follows: Calculate the average tax rate as far as this family is concerned.
| Item | Monthly Expense (Rs) | GST Rate % |
|---|---|---|
| Cereals | 1500 | 0 |
| Eggs | 250 | 0 |
| Fish, Meat | 250 | 0 |
| Medicines | 50 | 5 |
| Biogas | 50 | 5 |
| Transport | 100 | 5 |
| Butter | 50 | 12 |
| Babool | 10 | 12 |
| Tomato Ketchup | 40 | 12 |
| Biscuits | 75 | 18 |
| Cakes, Pastries | 25 | 18 |
| Branded Garments | 100 | 18 |
| Vacuum Cleaner, Car | 1000 | 28 |
| Category (GST slab) | Expenditure / Weight (w) | GST Rate (x) | wx |
|---|---|---|---|
| Category 1 (0%): Cereals, Eggs, Fish & Meat | 2000 | 0.00 | 0 |
| Category 2 (5%): Medicines, Biogas, Transport | 200 | 0.05 | 10 |
| Category 3 (12%): Butter, Babool, Tomato Ketchup | 100 | 0.12 | 12 |
| Category 4 (18%): Biscuits, Cakes/Pastries, Branded Garments | 200 | 0.18 | 36 |
| Category 5 (28%): Vacuum Cleaner, Car | 1000 | 0.28 | 280 |
| Total | 3500 | 338 |
Extra Practice Questions
Short Answer Type Questions
Q1. Define an index number.
Q2. Distinguish between Laspeyre’s and Paasche’s price index.
Q3. If the cost-of-living index is 250, what is the purchasing power of a rupee?
Q4. What is meant by the ‘real wage’, and how is it calculated?
Q5. Why is the Wholesale Price Index used to measure inflation rather than the CPI?
Long Answer Type Questions
Q1. Explain the two methods of constructing a price index number.
Q2. Describe the important index numbers used in India and their uses.
Q3. Discuss the important issues that should be kept in mind while constructing an index number.
MCQs & Assertion–Reason
1. The value of an index number in the base period is always:
(a) 0 (b) 50 (c) 100 (d) 1000
2. A weighted aggregative price index using base-period quantities as weights is known as:
(a) Paasche’s index (b) Laspeyre’s index (c) Fisher’s index (d) simple aggregative index
3. Paasche’s price index uses as weights the:
(a) base-period quantities (b) current-period quantities (c) average of both quantities (d) no weights
4. The formula (P₁/P₀) × 100 gives the:
(a) price relative (b) quantity relative (c) weight (d) base value
5. The Consumer Price Index is also known as the:
(a) wholesale price index (b) cost-of-living index (c) production index (d) volume index
6. The Index of Industrial Production is a:
(a) price index (b) value index (c) quantity (volume) index (d) cost-of-living index
7. If the cost-of-living index is 200, the purchasing power of a rupee is:
(a) Re 1.00 (b) Re 0.50 (c) Re 0.20 (d) Rs 2.00
8. The Sensex is the sensitive index of the:
(a) National Stock Exchange (b) Bombay Stock Exchange (c) Reserve Bank of India (d) Ministry of Finance
9. In India, the rate of inflation is generally measured using the:
(a) CPI (b) WPI (c) IIP (d) Sensex
10. The simple aggregative price index has the limitation that it:
(a) needs too much data (b) is influenced by the units of measurement and ignores relative importance (c) cannot be calculated (d) uses weights
For each Assertion–Reason question, choose: (A) Both true and the Reason correctly explains the Assertion; (B) Both true but the Reason is not the correct explanation; (C) Assertion true, Reason false; (D) Assertion false, Reason true.
A-R 1. Assertion: The base period of an index number is given the value 100.
Reason: An index number expresses the value of any period in proportion to the base period, in percentage terms.
A-R 2. Assertion: Laspeyre’s and Paasche’s indices always give the same value.
Reason: Laspeyre’s index uses base-period quantities as weights while Paasche’s uses current-period quantities.
A-R 3. Assertion: Different consumer price indices are prepared for different categories of consumers.
Reason: Different groups have different consumption baskets and spending patterns.
A-R 4. Assertion: A price change in a low-weight item has a large impact on a weighted index.
Reason: In a weighted index, an item’s contribution is proportional to its weight.
A-R 5. Assertion: The base year of an index number should be a normal year.
Reason: A year with extreme values such as a famine or boom would distort the comparison.
Exam Tips & Common Mistakes
How to score full marks in this chapter
Memorise the formulas precisely and write the formula before substituting values — examiners give marks for the correct formula. In numericals, always set out a neat working table (item, weight, P₀, P₁, R, WR) and show every total; then state the final index and interpret it in words (e.g. “prices rose by 34.5%”). Remember the key distinctions: Laspeyre’s = base-period quantities, Paasche’s = current-period quantities; price index vs quantity index; CPI = retail/cost of living while WPI is used for inflation. Learn the standard relations — purchasing power = 100/CPI, real wage = (money wage/CPI)×100, and salary to maintain standard of living = base salary × CPI/100.
Common mistakes to avoid
- Confusing Laspeyre’s (base-year weights q₀) with Paasche’s (current-year weights q₁).
- Forgetting to multiply the price relative by 100 (R = (P₁/P₀)×100, not just P₁/P₀).
- In Q17, giving Rs 16,000 as the “rise” — the rise needed is 16,000 − 6,000 = Rs 10,000.
- Comparing indices with different base years directly (as in Q21) — they are not comparable without a common base.
- Treating a simple aggregative index as reliable — it ignores units and relative importance.
- Mixing up a price index (prices) with a quantity index like the IIP (physical volume).
- Leaving activity/project questions (Q16, Q20) blank instead of giving your own data.
Frequently Asked Questions
What is Chapter 7 of Class 11 Economics (Statistics for Economics) about?
Chapter 7, Index Numbers, explains how a single figure can measure the average change in a group of related variables between a base period and a current period. It covers price and quantity index numbers, the aggregative and averaging-of-relatives methods, Laspeyre’s and Paasche’s indices, and important indices like the CPI, WPI, IIP and Sensex.
What is the difference between Laspeyre’s and Paasche’s price index?
Both are weighted aggregative price indices; they differ only in the weights. Laspeyre’s index uses base-period quantities (q₀) as weights, while Paasche’s index uses current-period quantities (q₁) as weights. Because the baskets differ, the two usually give different values.
How is the Consumer Price Index (CPI) used to find the purchasing power of money and real wage?
The purchasing power of a rupee = 100 / CPI, so a higher CPI means lower purchasing power. The real wage = (money wage / CPI) × 100, which shows the actual value of income after adjusting for the change in the cost of living.
