Dr. Anamika Shrivastava NCERT Economics · Class 11 & 12

Class 11 · Statistics for Economics · Chapter 7

Class 11 Economics Chapter 7: Index Numbers (NCERT Statistics for Economics)

Quick answerAn index number measures the average change in a group of related variables from a base period fixed at 100. This chapter covers the simple and weighted aggregative methods, Laspeyres and Paasche indices, price relatives, the CPI, WPI, IIP, Sensex and HDI, the issues in constructing an index, and its uses.

Reviewed and approved by Dr. Anamika ShrivastavaSyllabus year 2026-27Published Last updated

Key takeaways

  • An index number compares a period with a base period set at 100.
  • Laspeyres uses base-year quantities; Paasche uses current-year quantities.
  • The CPI is a weighted average of group indices; the WPI covers wholesale goods; the IIP is a quantity index.
  • Choose a normal, recent base year and reliable data.
  • Indices drive wage adjustment, inflation measurement and policy.

This is Chapter 7 of the Statistics for Economics chapter list for Class 11 Economics. It applies the weighted averages of Chapter 5 to prices and output.

7.1What is an Index Number?

An index number is a statistical device that measures the average change in a group of related variables between two periods. The earlier period is the base, set at 100, and the index for the later period shows the change as a percentage of it. Price, quantity and value indices are the main kinds.

A shopper sees some prices rise, some fall, and cannot tell how much costlier life has become. A single index summarises it. If the index for this year is 150 with last decade as base, prices are one and a half times the base level, a rise of 50 per cent. An index of 85 would mean a fall of 15 per cent.

Kinds of index numbers
KindMeasuresExample
Price indexChange in pricesConsumer Price Index, Wholesale Price Index
Quantity indexChange in physical volumeIndex of Industrial Production
Value indexChange in total value (price × quantity)Index of export value
A price index over six yearsA line rising from 100 in the base year Y0 to 104, 109, 113, 121 and 126 in Y5. The year-on-year inflation rates are 4.00, 4.81, 3.67, 7.08 and 4.13 per cent.Year (Y0 is the base year)Price index100104109113121126Y0Y1Y2Y3Y4Y5050100140Base year = 100
Figure 7.1: A price index and its inflation rateThe index (base Y0 = 100) is 126 in Y5, so prices are 26 per cent above the base year. The inflation rate between years is (indext − indext−1) ÷ indext−1 × 100.

7.2Construction of an Index Number

Price indices are built by the aggregative method, which compares the total cost of a set of goods, or by averaging price relatives. Unweighted versions treat all goods alike. Weighted versions give more importance to goods with larger shares of spending, as in Laspeyres’ index with base quantities and Paasche’s index with current quantities.

Prices and quantities of four goods (illustrative)
CommodityBase price p₀Base qty q₀Current price p₁Current qty q₁
Rice (kg)4010509
Pulses (kg)10041205
Milk (litre)50155516
Cooking oil (litre)12021502

Aggregative method

Aggregative indices

Simple: (Σp1 ÷ Σp0) × 100  ·  Laspeyres: (Σp1q0 ÷ Σp0q0) × 100  ·  Paasche: (Σp1q1 ÷ Σp0q1) × 100

Simple aggregative: Σp0 = 310 and Σp1 = 375, so the index is 120.97. It adds prices measured in different units and ignores how much of each good is bought, so it is of limited use.

Laspeyres: Σp1q0 = 2105 and Σp0q0 = 1790, giving 117.60. It asks: what does the base-year basket cost now compared with then?

Paasche: Σp1q1 = 2230 and Σp0q1 = 1900, giving 117.37. It asks the same question for the current basket.

Three price indices computed from the same dataThree horizontal bars measuring rise above 100: simple aggregative 120.97, Laspeyres 117.60 and Paasche 117.37. Weighted methods give lower figures than the unweighted index because milk, the item with the largest spending share, rose only 10 per cent.Simple aggregative120.97Laspeyres (base quantities)117.60Paasche (current quantities)117.37Axis starts at 100 (the base-year level)
Figure 7.2: The same data, three indicesWeighting changes the answer: unweighted 120.97, Laspeyres 117.60, Paasche 117.37.

Averaging price relatives

The price relative of a good is (p1 ÷ p0) × 100. Here they are 125, 120, 110 and 125. Their simple mean is 120. Weighting each relative by base-year expenditure (p0q0 = 400, 400, 750, 240) gives ΣWI ÷ ΣW = 2,10,500 ÷ 1,790 = 117.60, the same as Laspeyres.

Shifting the base of an index

Sometimes an index has to be moved to a new base year, for example to compare it with another series. The rule is to divide each value of the old series by the old-series value of the new base year, and multiply by 100. If the old index is 120 in year A, 150 in year B and 180 in year C, and year B is the new base, the new values are 80, 100 and 120.

Base shifting is only approximate when the weights of the series have changed, but it is widely used to put different indices on a common footing before comparing them.

7.3Some Important Index Numbers

India publishes the Consumer Price Index for retail prices, the Wholesale Price Index for goods traded in bulk, and the Index of Industrial Production for output. The Sensex tracks 30 large shares on the Bombay Stock Exchange, and the Human Development Index combines health, education and income into one score.

Consumer Price Index

The Consumer Price Index (CPI), or cost-of-living index, measures changes in the retail prices of a typical household basket. The weights come from a household consumption survey. An illustrative index:

CPI as a weighted average of group indices (illustrative)
GroupWeight (W)Index (I)W × I
Food451305850
Fuel and light101151150
Clothing121081296
Housing201202400
Miscellaneous131251625
Total10012,321

CPI = 12,321 ÷ 100 = 123.21. If a worker earns ₹30,000, the real wage in base-year rupees is 30,000 ÷ 1.2321 = about ₹24,349. To keep purchasing power, pay must rise by the same 23.21 per cent. India publishes CPI for industrial workers, agricultural and rural labourers, and an all-India combined series; the base year is revised every few years, so check the current base on the MoSPI site.

Wholesale Price Index

The WPI tracks prices of goods at the wholesale level. It has no services and no particular consumer group in mind. Its major groups are primary articles, fuel and power, and manufactured products. It is compiled by the Office of the Economic Adviser, Department for Promotion of Industry and Internal Trade.

Index of Industrial Production

The IIP is a quantity index: a weighted mean of quantity relatives, with weights based on value added in the base year (a Laspeyres form). With illustrative weights of 15, 75 and 10 and relatives of 108, 112 and 104 for mining, manufacturing and electricity, IIP = (1,620 + 8,400 + 1,040) ÷ 100 = 110.6.

Sensex and Human Development Index

The Sensex of the Bombay Stock Exchange tracks 30 large companies, with 1978–79 = 100. A rising Sensex signals rising confidence in listed companies. The HDI of the UNDP combines a health, an education and a standard-of-living index into one score between 0 and 1.

Reading index figures in the news

A report that says the CPI inflation rate was 5 per cent means that the index is 5 per cent higher than it was a year earlier, not that it stands at 5. A fall in the inflation rate does not mean that prices fell, only that they are rising more slowly. The same applies to the IIP growth rate, which compares output with the same month a year ago.

Check also the base year and the group covered, as the index for industrial workers differs from that for rural labourers, and the WPI differs from the CPI. A careful reader notes the month, the base, and whether the figure is provisional.

7.4Issues in Constructing an Index Number

Constructing an index needs choices that affect its meaning: the purpose of the index, which items to include, the base year, the formula and the reliability of data. The base year should be normal and not too distant, the items representative of the group measured, and prices collected from dependable sources.

  • Purpose. A cost-of-living index and a producer price index answer different questions.
  • Items and weights. A basket for rural labourers differs from one for urban professionals.
  • Base year. Choose a normal year; avoid years of drought, war or boom; update it regularly because consumption patterns change.
  • Formula. Laspeyres is easier to update; Paasche reflects current spending but needs fresh quantity data each year.
  • Data quality. Prices must come from a uniform, reliable source.

Uses in economics

The CPI is used to adjust wages and dearness allowance, to measure inflation and to set the inflation target for monetary policy. The WPI and GDP deflator help convert nominal values into real ones. The IIP signals industrial growth. Together, these indices turn many prices and quantities into signals that governments, firms and households can act on.

Weights in practice

Weights decide how much each item matters. In a consumer price index, a good that takes 40 per cent of household spending has twice the weight of one that takes 20 per cent, so a rise of 10 per cent in the first moves the index twice as much. Weights come from household expenditure surveys, so they need to be updated as spending patterns change.

A basket that matches a rural labourer’s spending differs from that of an urban professional, which is why separate indices exist for different groups. When using an index, check whose spending the weights describe.

Worked Examples

Example 1: Laspeyres and Paasche

Given
Prices and quantities of the four goods in the table above.
Formula
L = Σp1q0 ÷ Σp0q0 × 100; P = Σp1q1 ÷ Σp0q1 × 100
Steps
Σp1q0 = 2105; Σp0q0 = 1790; Σp1q1 = 2230; Σp0q1 = 1900.
Answer
Laspeyres = 117.60; Paasche = 117.37.

Example 2: Weighted CPI

Given
Group weights 45, 10, 12, 20, 13 and indices 130, 115, 108, 120, 125.
Formula
CPI = ΣWI ÷ ΣW
Steps
5,850 + 1,150 + 1,296 + 2,400 + 1,625 = 12,321; ΣW = 100.
Answer
CPI = 123.21: living costs are 23.21 per cent above the base.

Example 3: Inflation rate from an index

Given
A price index is 121 in Y4 and 126 in Y5.
Formula
Inflation rate = (It − It−1) ÷ It−1 × 100
Steps
(126 − 121) ÷ 121 × 100 = 4.13.
Answer
Inflation between Y4 and Y5 is 4.13 per cent.

Example 4: Real wage

Given
Monthly wage ₹30,000; CPI = 123.21 (base 100).
Formula
Real wage = money wage ÷ (CPI ÷ 100)
Steps
30,000 ÷ 1.2321 = 24,349.
Answer
The wage is worth about ₹24,349 in base-year prices.

Common Mistakes

  • Calling a rise from 100 to 126 “126 per cent”. The rise is 26 per cent.
  • Using the simple aggregative index when goods are measured in different units and bought in different amounts.
  • Mixing up the weights: Laspeyres uses base quantities, Paasche uses current quantities.
  • Comparing indices with different base years without converting them to a common base.

10 Important Questions for Class 11 Board and School Examinations

Questions are written in original words. Marks are shown beside each question.

Q1The base year of an index number is always given the value (a) 0 (b) 1 (c) 10 (d) 100 1 mark · MCQ

The correct option is (d) 100.

Q2Laspeyres’ price index uses as weights (a) base-year quantities (b) current-year quantities (c) average quantities (d) no weights 1 mark · MCQ

The correct option is (a) base-year quantities.

Q3Assertion (A): The Index of Industrial Production is a quantity index. Reason (R): It measures changes in the volume of output. Which is correct? 1 mark · Assertion-reason

Both A and R are true, and R explains A.

Q4What is an index number? Why is a base year needed? 3 marks

An index number measures the average change in a group of related variables over time, and the base year fixes the reference level of 100.

Without a base, a later value cannot be read as a percentage change. If this year’s index is 150 against a base of 100, the variable is 50 per cent higher. The base year should be a normal year without extreme values, and not too far in the past, so that the basket remains relevant.

Q5Distinguish between the CPI and the WPI. 3 marks

The CPI measures retail prices paid by consumers, and the WPI measures wholesale prices of goods.

The CPI includes services such as rent and education, while the WPI covers goods only. The CPI refers to a household basket and is the main measure of retail inflation, used to adjust wages. The WPI has no consumer group and tracks cost changes early. Different agencies compile them.

Q6Explain why a weighted index is better than a simple aggregative index. 4 marks

A weighted index is better than a simple aggregative index because it reflects the relative importance of each good.

  • A simple index adds prices measured in different units.
  • It gives all items equal importance, although families spend more on staples than on luxuries.
  • A weighted index uses quantities or expenditure shares as weights, so a rise in the price of an important item counts for more.
  • It therefore measures the true change in the cost of living or production.

Laspeyres uses base-year quantities and Paasche uses current-year quantities.

Q7Prices of two goods rise from 20 and 50 to 30 and 55. Find the simple average of price relatives. 4 marks

The simple average of the price relatives is 130.

  • Given: prices of good A rise from 20 to 30 and of good B from 50 to 55.
  • Formula: price relative = (p1 ÷ p0) × 100; the index is the mean of the relatives.
  • A: 30 ÷ 20 × 100 = 150. B: 55 ÷ 50 × 100 = 110.
  • Index = (150 + 110) ÷ 2 = 130.

Prices rose by an average of 30 per cent.

Q8List the issues to keep in mind when constructing an index number. 6 marks

Purpose, items, base year, formula and data reliability must be considered when constructing an index number.

  • Be clear about the purpose: a volume index is wrong when a value index is needed.
  • Select items that are representative of the group whose prices or output are measured.
  • Choose a normal base year, not one with extreme values, and not too far in the past; update it regularly.
  • Pick a formula suited to the question, such as Laspeyres or Paasche, which differ in their weights.
  • Use reliable data sources and check them, preferring official statistics when not collecting primary data.

A poorly built index gives a misleading picture of change.

A well-constructed index is useful only if these choices are made with care and explained.

Q9Describe the uses of index numbers in economics. 6 marks

Index numbers measure inflation, adjust wages and compare real values over time.

  • The CPI is used in wage negotiations, dearness allowance, price and income policy, and rent control.
  • The WPI and GDP deflator remove the effect of price changes from aggregates such as national income.
  • The WPI is widely used to measure inflation.
  • The IIP shows the growth of industrial output.
  • The Sensex indicates stock market sentiment and the Human Development Index compares development across countries.

Such indices turn many prices and quantities into signals for governments, firms and households.

Index numbers also make comparison possible across time and places by reducing many changes to one figure. They must be interpreted with their base year and coverage in mind, and different indices serve different users, so the right one should be chosen for each purpose.

Q10Using the data of the four-good table in this chapter, find the Laspeyres price index and interpret it. 4 marks · Numerical

The Laspeyres index is 117.60, meaning the base-year basket costs about 17.6 per cent more.

Formula: Σp1q0 ÷ Σp0q0 × 100.

Steps: 2,105 ÷ 1,790 × 100 = 117.60.

Final answer: 117.60; prices rose by about 17.6 per cent for the base basket.

10 Points for State PSC and UPSC Aspirants

  1. The CPI (Combined) is released monthly by the National Statistics Office, MoSPI; the base year is revised from time to time, so quote the current one.Why it matters: the main measure of retail inflation.Source: MoSPI
  2. Under the flexible inflation targeting framework, the RBI aims for CPI inflation of 4 per cent with a tolerance band of 2 per cent on either side.Why it matters: links index numbers to monetary policy.Source: Reserve Bank of India
  3. The WPI is compiled by the Office of the Economic Adviser, DPIIT, and covers goods only.Why it matters: know which agency publishes which index.Source: DPIIT
  4. The IIP is a monthly quantity index published by the National Statistics Office; the Eight Core Industries index is released by the Office of the Economic Adviser.Why it matters: frequently asked in current-affairs sections.Source: MoSPI; DPIIT
  5. The CPI for Industrial Workers, from the Labour Bureau, is used to set dearness allowance for many employees.Why it matters: an index with direct pay consequences.Source: Ministry of Labour and Employment
  6. CPI-AL and CPI-RL track prices for agricultural and rural labourers; wage revisions under some schemes refer to them.Why it matters: distinguish the CPI series by population group.Source: Ministry of Labour and Employment
  7. The Sensex (BSE, 30 stocks, base 1978–79 = 100) and the Nifty 50 (NSE) are India’s benchmark equity indices.Why it matters: frequent in economy and finance sections.Source: Bombay Stock Exchange; National Stock Exchange
  8. The HDI from UNDP combines life expectancy, schooling and gross national income per capita using a geometric mean.Why it matters: an index that mixes three dimensions.Source: UNDP Human Development Reports
  9. The GDP deflator is an index: nominal GDP divided by real GDP, times 100.Why it matters: used to separate price from output changes.Source: MoSPI
  10. Fisher’s ideal index is the geometric mean of Laspeyres and Paasche indices.Why it matters: a way to balance the two weighting biases.Source: Standard statistics textbooks

These are revision notes, not official predictions of exam content.

Quick Revision

  • Index = (current ÷ base) × 100; base = 100.
  • Laspeyres: base quantities; Paasche: current quantities.
  • Weighted relatives with base expenditure = Laspeyres.
  • CPI = ΣWI ÷ ΣW.
  • Inflation = (It − It−1) ÷ It−1 × 100.
  • IIP: quantity index; WPI: goods only.
  • Choose a normal, recent base year.

Glossary:

Index numberConsumer Price IndexWholesale Price IndexIndex of Industrial ProductionSensex

Related chapters: Measures of Central Tendency, since an index is a weighted average; Class 12 Introductory Macroeconomics, where inflation and the GDP deflator are explained.

Sources

  1. NCERT textbooks: Statistics for Economics, Class 11, National Council of Educational Research and Training. Syllabus reference. Accessed 23 October 2026.
  2. Ministry of Statistics and Programme Implementation (MoSPI), Government of India. Accessed 23 October 2026.
  3. Department for Promotion of Industry and Internal Trade, Government of India. Accessed 23 October 2026.
  4. Reserve Bank of India. Accessed 23 October 2026.
  5. Ministry of Labour and Employment, Government of India. Accessed 23 October 2026.
  6. Human Development Reports, United Nations Development Programme. Accessed 23 October 2026.

About this page

Drafted with AI assistance from the NCERT chapter structure, in original words. Content is checked and approved by Dr. Anamika Shrivastava, PhD Economics, before publication. Read how this site works or send a correction.

Syllabus year 2026-27 · Last updated