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EconomyNCERT Class 11 · Statistics for Economics

Index Numbers

Index numbers are statistical devices that compress the average change in a group of related variables (prices, output, cost of living) between a base period and a current period into a single comparable percentage figure.

⏱ 7 min readGS-III7 sections5 memory tricks
Why this matters for UPSC

Index numbers are the backbone of how India measures inflation (CPI, WPI), industrial output (IIP) and the stock market (SENSEX), making them recurring Prelims fodder on base years, nodal agencies and which index RBI targets. For GS-III they feed answers on inflation, monetary policy and cost-of-living adjustments. Classic exam traps include Laspeyre vs Paasche, Headline vs Core inflation and the Eight Core Industries.

Understand the chapter

What is an Index Number

An index number is a statistical device measuring the average change in the magnitude of a group of related variables across two situations, representing the general trend of diverging ratios. It is conventionally expressed as a percentage. The reference period is the base period, whose value is fixed at 100, and any later index is read in proportion to it.

  • Base period value = 100; an index of 250 means the value is 2.5 times the base period.
  • Price index measures change in prices; Quantity index measures change in physical volume of production, construction or employment.
  • Comparison can be across like categories (persons, schools, hospitals) or values (prices, output, cost of living).
  • Helps answer everyday questions: real change in living standards, what is SENSEX, how to measure inflation.

Aggregative Method: Simple, Laspeyre and Paasche

Under the aggregative method, prices of a basket of commodities are summed and compared. The simple aggregative index is unweighted and flawed because units differ and all items get equal importance. A weighted aggregative index fixes this by attaching quantity weights, so that a fixed basket's changing value reflects only price change.

  • Simple aggregative: P01 = (sum P1 / sum P0) x 100 — unweighted, ignores relative importance.
  • Laspeyre's index = (sum P1q0 / sum P0q0) x 100 — uses base-period quantities (q0) as weights.
  • Paasche's index = (sum P1q1 / sum P0q1) x 100 — uses current-period quantities (q1) as weights.
  • Laspeyre answers the cost of the base-year basket today; Paasche answers the cost of the current-year basket.

Method of Averaging Relatives

Here each commodity's price relative is computed first and then averaged. The simple price relative index is the arithmetic mean of the relatives; the weighted version is a weighted arithmetic mean using value-share weights. Base-period weights are generally preferred because recomputing weights every year is inconvenient and the changing baskets are not strictly comparable.

  • Price relative = (P1/P0) x 100 for a single commodity.
  • Simple index = (1/n) x sum of price relatives.
  • Weighted index = sum[Wi x (P1/P0)] / sum Wi; weights are value shares in total expenditure.
  • Weighted and unweighted values diverge sharply when a heavy-weight item's price jumps.

Consumer Price Index (CPI)

CPI, also called the cost-of-living index, measures the average change in retail prices of a fixed basket. An index above 100 signals a higher cost of living, and the exact excess over 100 is the upward wage adjustment needed (index 150 means 50% rise). The revised series uses base 2012=100, built from Modified Mixed Reference Period (MMRP) data of the Consumer Expenditure Survey 2011-12, 68th NSS Round.

  • CPI-IW (Industrial Workers, 2001=100) was 278 in May 2017; CPI-AL and CPI-RL use base 1986-87=100.
  • All-India Combined, Rural and Urban CPI use 2012=100; RBI uses the Combined CPI as its main inflation gauge.
  • Food and beverages carry the largest CPI weight (45.86%) in the 2012 series.
  • CFPI = CPI 'Food and Beverages' minus alcoholic beverages and prepared meals, snacks, sweets.

Wholesale Price Index (WPI)

WPI indicates the change in the general price level using wholesale prices, and unlike CPI it has no reference consumer category and excludes services — covering only the prices of goods. The revised series uses base 2011-12=100 (112.8 in May 2017). All-commodities inflation is termed Headline Inflation, while Core Inflation covers manufactured goods excluding food and fuel.

  • WPI major groups: Manufactured Products 64.23%, Primary Articles 22.62%, Fuel and Power 13.15%.
  • WPI Food Index weight = 24.23% (food articles from Primary + food products from Manufactured).
  • Headline Inflation = All Commodities; Core Inflation is about 55% of WPI weight (manufactured, ex food and fuel).
  • WPI excludes services; CPI includes them — a key WPI vs CPI distinction.

Index of Industrial Production (IIP)

Unlike CPI and WPI which track prices, IIP measures quantities of industrial output. It is a weighted arithmetic mean of quantity relatives using Laspeyre's formula, with weights equal to value added by manufacture in the base year (2011-12=100, with effect from April 2017). Its base year changes frequently because items continually enter and exit production.

  • IIP sectoral weights: Manufacturing 77.6%, Mining 14.4%, Electricity 8.0%.
  • Eight Core Industries: coal, crude oil, natural gas, refinery products, fertilisers, steel, cement, electricity — combined weight 40.27% in IIP.
  • Also classified by use: Primary, Capital, Intermediate, Infrastructure/Construction, Consumer Durables and Non-durables.
  • IIP is a quantity index even though it borrows the Laspeyre's weighting logic of price indices.

SENSEX, HDI and Limitations

Beyond prices and output, specialised indices track other domains. SENSEX (Bombay Stock Exchange Sensitive Index, base 1978-79) is the benchmark of the Indian stock market, built from 30 stocks representing 13 sectors. The Human Development Index gauges a country's development. Every index is bounded by its choice of base year, basket and weights, so it must be read with care.

  • SENSEX = 30 stocks across 13 sectors, base 1978-79; benchmark for Indian equities.
  • HDI measures the development of a country (introduced in Class X).
  • Limitations: base-year obsolescence, basket selection, weighting choices and changing consumption patterns.
  • Index numbers show average trends, not individual or distributional change.

Key terms

Index Number
A statistical device measuring average change in a group of related variables across two periods, expressed as a percentage.
Base Period
The reference period against which change is measured; its value is set at 100.
Price Index
An index measuring the change in the price level of a specified basket of commodities.
Quantity Index
An index measuring change in physical volume of production, construction or employment (e.g., IIP).
Laspeyre's Index
Weighted aggregative price index using base-period quantities (q0) as weights.
Paasche's Index
Weighted aggregative price index using current-period quantities (q1) as weights.
Price Relative
The ratio of current to base price multiplied by 100 for a single commodity.
Consumer Price Index (CPI)
Cost-of-living index measuring average change in retail prices of a fixed consumer basket.
Wholesale Price Index (WPI)
Index of the general price level based on wholesale prices of goods only, excluding services.
Headline vs Core Inflation
Headline = all-commodities WPI inflation; Core = manufactured goods excluding food and fuel (about 55% of WPI).

Must-know facts exam-ready

  • An index number of 250 means the value is 2.5 times the base-period value (base = 100).
  • Laspeyre's price index uses base-period quantities (q0); Paasche's uses current-period quantities (q1).
  • CPI (cost-of-living index) revised base = 2012=100, built from MMRP data of CES 2011-12, 68th NSS Round.
  • RBI uses the All-India Combined CPI (2012=100) as its main measure of consumer price change.
  • Food and beverages have the highest CPI weight in the 2012 series at 45.86%.
  • WPI revised base = 2011-12=100; it covers only goods, excludes services and has no reference consumer category.
  • WPI weights: Manufactured Products 64.23%, Primary Articles 22.62%, Fuel and Power 13.15%; WPI Food Index = 24.23%.
  • Headline Inflation = WPI All Commodities; Core Inflation is about 55% of WPI (manufactured, ex food and fuel).
  • IIP base = 2011-12=100 (w.e.f. April 2017); a quantity index via Laspeyre's formula; Manufacturing 77.6%, Mining 14.4%, Electricity 8.0%.
  • Eight Core Industries (coal, crude oil, natural gas, refinery products, fertilisers, steel, cement, electricity) = 40.27% of IIP.
  • SENSEX = Bombay Stock Exchange Sensitive Index, base 1978-79, 30 stocks representing 13 sectors.
  • Nodal agencies: WPI by Office of the Economic Adviser (Ministry of Commerce and Industry); CPI-Combined/Rural/Urban and IIP by NSO/CSO (MoSPI); CPI-IW, CPI-AL, CPI-RL by Labour Bureau (Ministry of Labour and Employment).

Memory tricks remember it for good

Laspeyre Looks Back, Paasche Points to Present
Laspeyre uses Base-period quantities (q0); Paasche uses Present/current-period quantities (q1)
💡 Distinguish the two weighted aggregative price indices and their weights.
Two Prices, One Quantity (C-W-I)
CPI = retail consumer prices; WPI = wholesale prices; IIP = quantity of industrial output
💡 Remember CPI and WPI are price indices but IIP is a quantity index.
Cool Crude Needs Refined Fertile Steel-Cement Energy
Coal, Crude oil, Natural gas, Refinery products, Fertilisers, Steel, Cement, Electricity
💡 Recall all Eight Core Industries (40.27% of IIP).
M-P-F = 64-22-13
Manufactured Products 64.23%, Primary Articles 22.62%, Fuel and Power 13.15%
💡 Recall WPI major-group weights (2011-12 base).
Manufacturing Mostly Moves IIP
Manufacturing 77.6% dominates; Mining 14.4%; Electricity 8.0%
💡 Recall IIP sectoral weights and that manufacturing dominates.

Traps to avoid

  • Laspeyre vs Paasche reversed: Laspeyre uses base-period quantities (q0), Paasche uses current-period quantities (q1) — students swap them.
  • CPI vs WPI: WPI is wholesale, excludes services and has no consumer category; CPI is retail, consumer-specific and includes services.
  • RBI's inflation anchor is CPI-Combined, NOT WPI — a very common Prelims trap.
  • IIP is a QUANTITY index of output, not a price index, even though it applies Laspeyre's weighting formula.
  • Base years differ: CPI = 2012=100, WPI = 2011-12=100, IIP = 2011-12=100, SENSEX = 1978-79 — easy to mix up.
  • Headline vs Core inflation: Headline = all commodities; Core excludes BOTH food and fuel, not just food.

Exam focus

🧠 Prelims angles

  • Match-the-following on base years: CPI 2012=100, WPI 2011-12=100, IIP 2011-12=100, SENSEX 1978-79.
  • Which index does RBI use for inflation targeting? CPI-Combined, under flexible inflation targeting (4% +/- 2%).
  • Eight Core Industries — identify members and their combined IIP weight (40.27%).
  • Laspeyre's vs Paasche's formula identification (which uses q0 versus q1).
  • CPI vs WPI distinctions (services, consumer category, retail vs wholesale).
  • Nodal agencies for WPI (Office of the Economic Adviser), CPI/IIP (NSO/CSO, MoSPI) and CPI-IW (Labour Bureau).

✍️ Mains angles GS-III

  • Is CPI or WPI the better measure of inflation faced by households, and why did RBI adopt CPI for inflation targeting?Contrast retail vs wholesale coverage, inclusion of services and consumer relevance; link to flexible inflation targeting.
  • Critically discuss the limitations of index numbers as measures of economic change.Cover base-year obsolescence, basket and weight selection, unweighted bias and changing consumption patterns.
  • How do CPI, WPI and IIP together signal the health of the economy?Map CPI to cost of living, WPI to general price level and Headline/Core inflation, IIP to industrial output and core-sector growth.
Practice Economy questions from this syllabus →

Last-minute revision tick as you recall

  • Index number = average change in related variables; base = 100, index 250 means 2.5x.
  • Laspeyre uses base quantities (q0); Paasche uses current quantities (q1).
  • CPI = retail cost-of-living, base 2012=100; RBI targets Combined CPI.
  • Food and beverages = top CPI weight (45.86%).
  • WPI = wholesale, goods only, no services, base 2011-12=100.
  • Headline = all commodities; Core = manufactured ex food and fuel (~55%).
  • IIP = quantity index, base 2011-12=100; Manufacturing 77.6%.
  • Eight Core Industries = 40.27% of IIP.
  • SENSEX = 30 stocks, 13 sectors, base 1978-79.

Distilled from NCERT Class 11 · Statistics for Economics for UPSC. Always cross-check facts with the original NCERT.