Class | Subject | Book | Chapter | Session | Questions covered |
|---|---|---|---|---|---|
XI | Economics | Statistics for Economics (NCERT) | 7 – Index Numbers | 2026-27 | 22 of 22 |
Chapter at a glance
Topic | Key facts |
|---|---|
Index number | Statistical device for measuring relative changes in a group of related variables over time |
Methods | Aggregative () and average of relatives (, )    |
Weighted aggregative | Laspeyres (base-year weights); Paasche   |
Main indices | CPI (retail prices; for industrial workers, agricultural labourers, rural/urban), WPI, IIP, Sensex |
Uses | Measuring inflation, purchasing power (), real wages, wage indexation, policy  |
Base period | Normal, not too distant, with reliable data |
Exercise Questions
An index number which accounts for the relative importance of the items is known as
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- weighted index (ii) simple aggregative index (iii) simple average of relatives
Answer
- weighted index
In most of the weighted index numbers the weight pertains to
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- base year (ii) current year (iii) both base and current year
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Most indices (Laspeyres type, CPI, WPI) use base-year quantities as weights, because current weights are difficult to collect each period.
- base year
The impact of change in the price of a commodity with little weight in the index will be
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- small (ii) large (iii) uncertain
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- small
A consumer price index measures changes in
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- retail prices (ii) wholesale prices (iii) producers prices
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- retail prices
The item having the highest weight in consumer price index for industrial workers is
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- Food (ii) Housing (iii) Clothing
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- Food
In general, inflation is calculated by using
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- wholesale price index (ii) consumer price index (iii) producers’ price index
Answer
In the textbook’s framework, the general inflation rate is calculated from the wholesale price index. (Since 2014 the RBI targets inflation measured by the CPI (Combined), but the textbook answer is the WPI.)
- wholesale price index
Why do we need an index number?
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Answer
- To measure relative changes in a group of related variables (prices, production) that cannot be measured directly, in a single figure.
- To measure inflation and the change in the cost of living.
- To calculate purchasing power of money and real wages, and to fix dearness allowance.
- To guide policy: monetary, fiscal and wage policy.
- To compare industrial production (IIP), agricultural output, and share prices (Sensex).
To measure changes in prices, production or cost of living in one figure, compute real income and purchasing power, and guide policy.
What are the desirable properties of the base period?
Answer
Answer
- It should be a normal year, free from abnormal events such as war, drought, floods or booms.
- It should not be too distant in the past; habits and goods change over time.
- Reliable data for that period should be available.
- It should be comparable with the current period.
A normal year, not too far back, with reliable and comparable data.
Why is it essential to have different CPI for different categories of consumers?
Answer
Answer
Different groups of consumers (industrial workers, agricultural labourers, urban non-manual employees) have different consumption patterns: they buy different goods in different proportions. For example, food has a much larger weight for agricultural labourers than for urban salaried people. A price change therefore affects their cost of living differently. A single CPI cannot represent all groups, so separate indices are prepared.
Because different groups consume different goods in different proportions, a price change affects their cost of living differently.
What does a consumer price index for industrial workers measure?
Answer
Answer
The CPI for industrial workers measures the average change in the retail prices of a fixed basket of goods and services consumed by industrial workers, i.e. the change in their cost of living over time. It is used to fix their dearness allowance.
It measures the change in the cost of living of industrial workers through changes in retail prices of their consumption basket.
What is the difference between a price index and a quantity index?
Answer
Answer
Price index | Quantity index |
|---|---|
Measures changes in prices of a group of goods over time | Measures changes in the physical quantity of goods produced, consumed or sold |
Quantities are used as weights | Prices are used as weights |
Laspeyres: |  |
Examples: CPI, WPI | Example: Index of Industrial Production |
A price index measures changes in prices (with quantities as weights); a quantity index measures changes in physical volume (with prices as weights).
Is the change in any price reflected in a price index number?
Answer
Answer
No. Only changes in the prices of the items included in the index basket are reflected, and their effect depends on the weight of each item. Prices of goods not included do not affect the index, and changes in items with very small weights have little impact.
No; only prices of items in the basket affect it, in proportion to their weights.
Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?
Answer
Answer
No. The CPI for urban non-manual employees is based on the consumption pattern of that group. The President’s consumption basket, income level and lifestyle are very different. Most of the President’s expenses are also borne by the state. So that index cannot represent changes in the President’s cost of living.
No; the President’s consumption pattern differs greatly from that of urban non-manual employees.
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.
Answer
Items | Price in 1980 | Price in 2005 |
|---|---|---|
Food | 100 | 200 |
Clothing | 20 | 25 |
Fuel & lighting | 15 | 20 |
House rent | 30 | 40 |
Misc | 35 | 65 |
Answer
Formula: , where
Item |  |  | R | W | WR |
Food | 100 | 200 | 200.00 | 75 | 15,000.00 |
Clothing | 20 | 25 | 125.00 | 10 | 1,250.00 |
Fuel & lighting | 15 | 20 | 133.33 | 5 | 666.67 |
House rent | 30 | 40 | 133.33 | 6 | 800.00 |
Misc | 35 | 65 | 185.71 | 4 | 742.86 |
Total | 100 | 18,459.52 |
Cost of living index for 2005 (1980 = 100) ≈ 184.60
Read the following table carefully and give your comments.
Answer
Index of Industrial Production (Base 1993–94)
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 |
Answer
- Manufacturing has the largest weight (79.58 %), so it dominates the general index.
- Industrial production has risen steadily: the general index went up from 100 (1993–94) to 130.8 (1996–97) and 189.0 (2003–04), i.e. output nearly doubled in ten years.
- Manufacturing grew fastest (196.6), above the general index; electricity came next (172.6); mining and quarrying grew slowest (146.9).
- Since manufacturing grew faster than the general index, it pulled up overall industrial growth, while mining lagged.
Industrial output nearly doubled from 1993–94 to 2003–04; manufacturing (largest weight) grew fastest, electricity moderately, mining slowest.
Try to list the important items of consumption in your family.
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Answer
A typical family’s important items of consumption (each family’s list will differ):
- Food: cereals (rice, wheat), pulses, milk and milk products, vegetables, fruits, edible oil, sugar, spices, eggs/meat.
- Clothing and footwear.
- Housing: rent or home loan EMI, repairs.
- Fuel and light: LPG, electricity.
- Education: school fees, books, stationery.
- Health: medicines, doctor’s fees.
- Transport and communication: petrol, bus or metro fares, mobile and internet.
- Miscellaneous: personal care, recreation, household goods.
Food, clothing, housing, fuel and electricity, education, health, transport and communication, and miscellaneous items.
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?
Answer
Answer
Given: base salary = ₹4,000; current salary = ₹6,000; CPI = 400 (base = 100).
Formula: Required salary = base salary × CPI ÷ 100
Required salary
Raise needed
His salary should be raised by ₹10,000 (to ₹16,000 per annum).
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?
Answer
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Given: CPI = 125; food index = 120; other items index = 135. Let the weight of food be % and of other items %.
Formula:
Food has about 66.67 % (two-thirds) of the total weight.
An enquiry into the budgets of the middle class families in a certain city gave the following information:
Answer
Expenses on items | Food | Fuel | Clothing | Rent | Misc. |
|---|---|---|---|---|---|
Weight | 35% | 10% | 20% | 15% | 20% |
Price (₹) in 2004 | 1500 | 250 | 750 | 300 | 400 |
Price (₹) in 1995 | 1400 | 200 | 500 | 200 | 250 |
What is the cost of living index during the year 2004 as compared with 1995?
Answer
Formula: , where
Item | W |  |  | R | WR |
Food | 35 | 1400 | 1500 | 107.14 | 3,750 |
Fuel | 10 | 200 | 250 | 125.00 | 1,250 |
Clothing | 20 | 500 | 750 | 150.00 | 3,000 |
Rent | 15 | 200 | 300 | 150.00 | 2,250 |
Misc. | 20 | 250 | 400 | 160.00 | 3,200 |
Total | 100 | 13,450 |
The cost of living rose by 34.5 % between 1995 and 2004.
Cost of living index for 2004 (1995 = 100) = 134.5
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?
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Answer
This is a practical activity. Method:
- Make a table for each day: item, quantity bought, price per unit, and total expenditure.
- For each item, compare the average price in week 2 with that in week 1 and find the price relative .
- Use the week-1 expenditure shares as weights to compute a weighted index .
Illustration: if milk rose from ₹60 to ₹64 per litre (R = 106.7) and vegetables from ₹40 to ₹50 per kg (R = 125), while other prices stayed the same, the weighted index may come to about 105. It means the family needs about 5 % more money to buy the same basket. If income is unchanged, the family’s purchasing power falls, and it may have to cut quantities or switch to cheaper items.
Compute price relatives for week 2 over week 1 and a weighted index; an index above 100 shows the rise in cost and the fall in the family’s purchasing power.
Given the following data:
Answer
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 |
- Comment on the relative values of the index numbers.
- Are they comparable?
Answer
(i) Comments:
- All three indices rose steadily, showing continuous inflation.
- The CPI (IW) has the highest values because its base (1982) is the oldest; prices had more time to rise. The WPI has the lowest values because its base (1993–94) is the most recent.
- Over 1995–96 to 2003–04, CPI (IW) rose by about 60 % (313 → 500), CPI (AL) by about 41 % (234 → 331) and WPI by about 45 % (121.6 → 175.9). So retail prices for industrial workers rose fastest.
(ii) Comparability: the levels are not directly comparable, because the indices have different base years, different baskets of commodities and weights, and measure different prices (retail vs wholesale). Only their rates of change (percentage increases) can be compared, or they must first be shifted to a common base.
All three rose steadily; level differences come mainly from different base years. They are not directly comparable (different bases, baskets and price types); only their growth rates can be compared.
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:
Answer
Item | Monthly Expense (₹) | 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 |
Calculate the average tax rate as far as this family is concerned.
Answer
The average GST rate is a weighted average of the rates, with expenditure as weights.
Formula: Average rate
GST rate (X) | Expenditure (W) | WX |
|---|---|---|
0 % | 1500 + 250 + 250 = 2000 | 0 |
5 % | 50 + 50 + 100 = 200 | 10 |
12 % | 50 + 10 + 40 = 100 | 12 |
18 % | 75 + 25 + 100 = 200 | 36 |
28 % | 1000 | 280 |
Total | 3500 | 338 |
Average rate
Average GST rate for the family ≈ 9.66 %
Topic checklist
- Meaning and construction of index numbers
- Aggregative and average-of-relatives methods; Laspeyres and Paasche
- CPI, WPI, IIP, Sensex
- Issues: base year, weights, choice of items
- Uses: inflation, purchasing power, real wages, weighted average tax rate