What is CPI, WPI, IIP, Sensex, HDI & Exercises in Class 11 Statistics for Economics NCERT?

Interactive NCERT Class 11 Statistics for Economics lesson on CPI, WPI, IIP, Sensex, HDI & Exercises

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CPI, WPI, IIP, Sensex, HDI & Exercises

🎓 Class 11 Social Science CBSE Theory Ch 7 — Index Numbers ⏱ ~30 min

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Class 11 · Statistics for Economics · Chapter 7 · Part 2

Index Numbers in India — CPI, WPI, IIP, Sensex, HDI and Exercises

Part 1 built the toolkit; Part 2 puts it to work. The Indian economy publishes a small zoo of official index numbers — Consumer Price Index for Industrial Workers, Agricultural Labourers, Rural Labourers, the All-India CPI, the Wholesale Price Index, the Index of Industrial Production, the Sensex, the Human Development Index. Each answers a different policy question and uses different weights, baskets and bases. We unpack them one at a time, look at the practical pitfalls of constructing an index in the real world, and then walk through every NCERT end-of-chapter exercise with full model answers.

7.11 The Family of Indian Index Numbers

India's statistical system, run mainly by the Ministry of Statistics and Programme Implementation (MoSPI), the Labour Bureau and the Office of the Economic Adviser, publishes several index numbers every month. NCERT highlights five that matter most for an economics student: the CPI, the WPI, the IIP, the Sensex and the HDI. The Producer Price Index is a sixth member that is being readied for India.

🛒

CPI

Consumer Price Index — measures retail price change in a typical household basket. Used for cost-of-living, wage indexation, RBI inflation targeting.

🏭

WPI

Wholesale Price Index — tracks price at the wholesale stage. Used for "headline" inflation, deflating GDP, eliminating price effects from value aggregates.

⚙

IIP

Index of Industrial Production — a quantity index for mining, manufacturing & electricity. Reads the heartbeat of the industrial sector.

📈

Sensex / HDI

Sensex tracks the BSE 30-stock benchmark since 1978-79. HDI (UNDP) blends income, life expectancy and education into one human-development score.

7.12 Consumer Price Index (CPI) — The Cost-of-Living Index

The Consumer Price Index^?, also called the cost-of-living index^?, measures the average change in retail prices paid by a typical group of consumers. The basic interpretation is: "If a worker spent Rs 100 in the base year on a typical basket, how much does she need to spend today to buy the same basket?"

NCERT's example takes the CPI for Industrial Workers (2001=100) which stood at 277 in December 2014. Reading: a worker who could buy a typical basket for Rs 100 in 2001 needed Rs 277 to buy the same basket in December 2014. Equivalently, the cost of living rose by 177 per cent over those thirteen years.

7.12.1 NCERT Example 4 — Constructing a CPI

📝 NCERT Example 4 (Table 7.4) — Building the CPI

Five item-groups (Food, Fuel, Cloth, Rent, Misc.) with weights, base prices and current prices. Compute the cost-of-living index using the weighted average of price relatives method.

Table 7.4 — CPI computation by weighted price relatives
Item	Weight W (%)	Base price P₀ (Rs)	Current price P₁ (Rs)	R = (P₁/P₀)×100	WR
Food	35	150	145	96.67	3383.45
Fuel	10	25	23	92.00	920.00
Cloth	20	75	65	86.67	1733.40
Rent	15	30	30	100.00	1500.00
Misc.	20	40	45	112.50	2250.00
Total	100	—	—	—	9786.85

CPI = ΣWRΣW = 9786.85100 = 97.86

Reading: the cost of living has declined by 2.14 per cent from base to current period (because the index is below 100). This is unusual but possible when food, fuel and cloth all fall in price faster than miscellaneous items rise. An index above 100 (say 150) would indicate a 50 per cent rise in cost of living, demanding a 50 per cent upward adjustment in wages and salaries to keep workers as well off as before.

7.12.2 The Many CPIs of India

The Government of India publishes several CPI series for different population groups. NCERT lists the official series with the value as in May 2017:

Indian CPI series (May 2017 values)
Index	Base Year	Value (May 2017)	Target Group
CPI for Industrial Workers (CPI-IW)	2001 = 100	278	Factory workers in 78 industrially important centres
CPI for Agricultural Labourers (CPI-AL)	1986-87 = 100	872	Wage labour in agriculture
CPI for Rural Labourers (CPI-RL)	1986-87 = 100	878	Wage labour in rural areas
All-India Rural Consumer Index	2012 = 100	133.3	All rural population
All-India Urban Consumer Price Index	2012 = 100	129.3	All urban population
All-India Combined CPI	2012 = 100	131.4	RBI's headline inflation target measure

The Reserve Bank of India targets the All-India Combined CPI for its inflation-targeting framework (currently 4 per cent ± 2 per cent). The new 2012=100 series uses the Modified Mixed Reference Period (MMRP) data of the 68th Round of the National Sample Survey, with weights drawn from the Consumer Expenditure Survey (CES) 2011-12.

Major-group weights of the All-India CPI (Base 2012=100)
Major Group	Weight (%)
Food and beverages	45.86
Pan, tobacco and intoxicants	2.38
Clothing & footwear	6.53
Housing	10.07
Fuel & light	6.84
Miscellaneous	28.32
General	100.00

Within the food and beverages group sits the Consumer Food Price Index (CFPI), which excludes alcoholic beverages and prepared meals. CFPI is the figure quoted in news headlines whenever a vegetable price spike grabs attention.

Fig. 7.4 — All-India Combined CPI (Base 2012=100), illustrative annual averages 2013-2023. The slope of the line is exactly the year-on-year inflation rate. Source: derived from MoSPI press releases.

7.13 Wholesale Price Index (WPI) — The Inflation Barometer

The Wholesale Price Index^? tracks the change in the general price level at the wholesale stage. Unlike the CPI, the WPI has no reference consumer category and excludes services (no barber charges, no plumbing repairs). Only the prices of goods are included.

NCERT's reading example: "WPI with 2004-05 as base is 253 in October 2014" means the general wholesale price level has risen by 153 per cent over that decade. The current WPI series uses base 2011-12 = 100, and stood at 112.8 in May 2017 — a 12.8 per cent rise from the base.

Major-group weights of the WPI (Base 2011-12=100)
Major Group	Weight (%)
Primary Articles	22.62
Fuel and Power	13.15
Manufactured Products	64.23
All Commodities ("Headline Inflation")	100.00
WPI Food Index (sub-index)	24.23

The all-commodities inflation rate computed from the WPI is loosely called the headline inflation^?. The WPI Food Index (24.23 per cent of the total weight) combines food articles from Primary Articles with food products from Manufactured Products. Economists who want to strip out volatile food and fuel sometimes focus on core inflation, defined as the wholesale price change in manufactured non-food, non-fuel items, which makes up around 55 per cent of the WPI weight.

📖 Definition — Inflation^?

Inflation is a general and continuing increase in prices. If inflation becomes sufficiently large, money loses its traditional function as a medium of exchange and as a unit of account; its primary impact is to lower the value of money. The weekly inflation rate is given by the percentage change in the WPI: ((X_t − X_t-1) / X_t-1) × 100, where X_t and X_t-1 are the WPI values for the t-th and (t-1)-th week.

Fig. 7.5 — Annual inflation rate (Y-o-Y % change in WPI, illustrative). The bars cross zero in 2015-16, showing brief deflation, then climb sharply during 2021-22 commodity surge. Source: derived from Office of the Economic Adviser releases.

7.14 Index of Industrial Production (IIP) — A Quantity Index

Unlike the CPI and the WPI, the Index of Industrial Production^? measures quantities, not prices. With effect from April 2017, the IIP base year is 2011-12 = 100. The need for frequent base-year revision is acute for the IIP because each year a long list of items either stops being manufactured or becomes inconsequential, while many new items begin to be produced.

While the price indices are essentially weighted averages of price relatives, the IIP is a weighted arithmetic mean of quantity relatives, with weights allocated to items in proportion to their value added by manufacture in the base year — a Laspeyres construction in quantities:

IIP₀₁ = Σ q₁_i W_iΣ W_i × 100

where IIP₀₁ is the index for period 1 (current) with period 0 (base), q₁_i is the quantity relative for good i (current quantity divided by base quantity), and W_i is the value-added weight allotted to good i. The summation runs over all n goods in the production index.

7.14.1 Sectoral Weights of the IIP

Table 7.5 — Weightage Pattern of the IIP (Industrial Production Sectors)
Sector	Weight (%)
Mining	14.4
Manufacturing	77.6
Electricity	8.0
General Index	100.0

Within Mining and Manufacturing, particular focus is given to the Eight Core Industries — coal, crude oil, natural gas, refinery products, fertilisers, steel, cement and electricity — which together carry a combined weight of 40.27 per cent in the IIP. They are watched closely because they represent the upstream foundation of the rest of the economy.

7.14.2 Use-Based Classification

The IIP is also published according to the use of the product, throwing light on whether the economy's growth is being driven by capital investment, intermediate goods or consumer spending.

Table 7.6 — Weightage Pattern of the IIP (Use-based Groups)
Group	Weight (%)
Primary	34.1
Capital Goods	8.2
Intermediate Goods	17.2
Infrastructure / Construction Goods	12.3
Consumer Durables	12.8
Consumer Non-durables	15.3
General Index	100.0

Fig. 7.6 — Sectoral split of the IIP (Base 2011-12=100). Manufacturing dominates with over three-quarters of the weight, with mining and electricity making up the rest.

7.15 Sensex — The Stock-Market Pulse

The Sensex^? is the short form of "Bombay Stock Exchange Sensitive Index", with 1978-79 as base. It is the benchmark index for the Indian stock market and consists of 30 stocks drawn from 13 sectors of the economy; the listed companies are leaders in their respective industries.

If the Sensex rises, the market is said to be doing well — investors are optimistic about future earnings of the included companies. A falling Sensex, in NCERT's words, "erodes investor wealth"; the textbook example mentions a 600-point dip wiping out Rs 1,53,690 crore. Indeed the Sensex is "a useful guide for investors in the stock market" and is widely interpreted as a barometer of the basic health of the economy and of business confidence.

Fig. 7.7 — Sensex annual closing levels, illustrative 2010-2023. Notice the steep rise from below 21,000 in 2010 to above 70,000 by 2023 — a more than three-fold climb. Source: BSE.

7.16 Human Development Index (HDI) & Producer Price Index

The Human Development Index^?, prepared annually by the United Nations Development Programme (UNDP), is a composite index that you have already met in Class X. HDI is widely used to compare development across countries because it captures three dimensions: a long and healthy life (life expectancy at birth), knowledge (mean years of schooling and expected years of schooling) and a decent standard of living (gross national income per capita in PPP terms). Each dimension is normalised to a 0-1 scale and the three are combined as the geometric mean — a structure conceptually similar to Fisher's ideal index.

The Producer Price Index (PPI) is being prepared by the Office of the Economic Adviser as a future replacement for the WPI. It will track prices that producers receive for their output (rather than wholesale prices including taxes and transport), aligning India with international best practice followed by the US Bureau of Labor Statistics and the OECD.

7.17 Issues in the Construction of an Index Number

Six practical issues, all flagged by NCERT, make index-number construction a craft as much as a science:

Purpose of the index. A volume index will be inappropriate when one needs a value index. Get the question right before choosing the formula.
Selection of items. The items are not equally important for different consumer groups. A petrol price hike barely affects a poor agricultural labourer who walks to work; the same hike hurts an urban scooter-owner. Items must be selected to be representative of the target population.
Choice of base year. The base must be a "normal" year — no famine, no boom, no war. It also must not lie too far in the past. Comparing 1993 with 2005 is meaningful; comparing 1960 with 2005 is not (many 1960 items, like phonograph records or LP cassettes, have simply disappeared). Hence base years are routinely updated — CPI from 2001 to 2012, WPI from 2004-05 to 2011-12.
Choice of weights. Whether to use base-period (Laspeyres) or current-period (Paasche) quantities; whether to use expenditure shares or quantity shares.
Choice of formula. The only difference between the Laspeyres and Paasche indices lies in the weights used. The choice depends on the nature of the question to be studied.
Reliability of data. There are many sources of data with different degrees of reliability. Poor data give misleading results; due care must be taken in collection. If primary data are not available, the most reliable source of secondary data should be chosen.

7.18 Index Numbers in Economic Policy

Why bother with index numbers at all? NCERT lists a battery of policy uses:

CPI & Cost-of-Living

Wage negotiation between trade unions and employers
Formulation of income, price and rent-control policies
Calculation of dearness allowance for government employees
Computation of purchasing power of money = 1 / (Cost of living index)
Computation of real wage = (Money wage / Cost of living index) × 100

WPI

Eliminating price effects from aggregates such as national income and capital formation
Measuring the rate of inflation
Implicit deflator for sectoral GDP at current vs constant prices
Indexing financial contracts and bond payments

IIP & Agricultural Index

Quantitative reading of industrial-sector growth
Agricultural production index = ready reckoner of farm-sector performance
Tracking the Eight Core Industries

Sensex

Useful guide for investors
Rising Sensex = optimism about future economic performance, an appropriate time for investment
Indicator of business confidence and macroeconomic health

7.18.1 Worked Example — Purchasing Power and Real Wage

NCERT illustrates: if CPI (1982 = 100) is 526 in January 2005, the equivalent of a rupee in January 2005 in 1982 terms is 100/526 = Rs 0.19 — that is, a rupee in 2005 buys what 19 paise bought in 1982. If the money wage is Rs 10,000, the real wage is (10,000 / 526) × 100 = Rs 1,901. So Rs 10,000 in January 2005 has the same purchasing power as Rs 1,901 in 1982. If the worker was getting Rs 3,000 in 1982, he is worse off in 2005 because his real wage has fallen below his 1982 standard. To maintain the 1982 standard the salary should be (3,000 × 526) / 100 = Rs 15,780, obtained by multiplying the base-period salary by the factor 526/100.

NCERT Comment Rabi's father bought rice at Rs 4 a kilo in the 1970s; today it costs roughly Rs 50. Has the price risen 12.5 times? Yes nominally. But his salary has also risen, perhaps 8 to 10 times, and the consumption basket has changed entirely. Comparing 1970 prices with 2025 prices without an index that adjusts for changes in basket and base is meaningless — which is exactly why every economic series is published with an explicit base year.

EXPLORE — NCERT Activity (Daily Vegetable Price Index)

Bloom: L3 Apply

Collect data from the local vegetable market over a week for at least 10 items. Try to construct the daily price index for the week using both the simple aggregative and the simple average of price relatives method. What problems do you encounter in applying the two methods?

✅ Sample Observation

Common difficulties students encounter: (i) units differ — tomatoes are sold by the kilogram, lemons by the dozen, garlic by the pod; (ii) some items vanish on certain days (no leafy greens during heavy rain); (iii) prices vary across vendors, so the recorded price depends on whom one asks; (iv) seasonal items skew the relative method (mangoes triple in price during early summer). The simple aggregative is even more strongly distorted by units (Rs/kg added to Rs/dozen), while the simple relatives method side-steps that but still gives equal weight to a daily-bought essential like onion and a weekly-bought delicacy like mushroom. The exercise itself shows why a real CPI must use carefully chosen weights.

THINK — CPI Base Shift, 1982 to 2000

Bloom: L4 Analyse

What happens when the base of the consumer price index is shifted from 1982 to 2000? Will the inflation rate computed from the new series equal the inflation rate from the old series for the same period?

✅ Sample

Shifting the base resets the value 100 to a new year and rescales every other index value proportionally. The level of the index changes (an index of 526 with 1982=100 becomes 100 if 2005 is set as 100), but the percentage change between any two later years stays the same in principle. In practice the answer is "almost the same, not exactly". Because base-year revision is usually accompanied by a basket-revision (new items enter, dead items exit) and a weight revision, the two series can record slightly different inflation rates for the overlap years. That is why MoSPI publishes a "linking factor" to bridge old and new series.

DISCUSS — Should Sensex be Treated as the Health of the Economy?

Bloom: L5 Evaluate

Newspapers often equate "Sensex up" with "the economy is doing well". Discuss in pairs whether the Sensex really measures the health of the whole Indian economy, or only a slice of it.

✅ Sample

The Sensex covers only 30 large listed companies on the Bombay Stock Exchange — mostly big banks, IT firms, FMCG giants and energy majors. Together they represent perhaps a third of formal-sector market capitalisation but a far smaller slice of total economic activity, since vast swathes of agriculture, the unorganised sector, MSMEs and services remain unlisted. A rising Sensex therefore reflects the optimism of equity investors about large listed companies, not the full economy. It can rise during periods of agrarian distress or rising rural unemployment. The CPI, IIP and HDI together provide a much fuller picture; the Sensex is one useful indicator among many, not the whole story.

7.19 NCERT Exercises — Full Model Answers

Every numbered exercise from the NCERT chapter is solved below. Click "Show Answer" to reveal the model solution.

Q1An 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.

Answer: (i) weighted index. A weighted index allots a weight W to each commodity reflecting its share in expenditure or production, so important items count more. Both other options ignore relative importance entirely.

Q2In most of the weighted index numbers the weight pertains to: (i) base year (ii) current year (iii) both base and current year.

Answer: (i) base year. Most weighted indices use Laspeyres-type weights (base-period quantities or expenditure shares). Reason: base-period weights are surveyed once and stay fixed, making month-to-month comparisons feasible. Paasche (current weights) is theoretically valid but is impractical for routine official statistics.

Q3The impact of change in the price of a commodity with little weight in the index will be: (i) small (ii) large (iii) uncertain.

Answer: (i) small. A weighted index is ΣWR / ΣW. The contribution of any one commodity equals its weight times its price relative. A small weight automatically dampens that commodity's contribution to the overall index, however large the price change.

Q4A consumer price index measures changes in: (i) retail prices (ii) wholesale prices (iii) producers' prices.

Answer: (i) retail prices. The CPI tracks prices paid by the consumer at the retail counter. Wholesale prices are tracked by the WPI; producer prices (forthcoming in India) are tracked by the PPI.

Q5The item having the highest weight in consumer price index for industrial workers is: (i) Food (ii) Housing (iii) Clothing.

Answer: (i) Food. Food (with beverages) carries the largest weight in every Indian CPI series — about 45.86 per cent in the All-India CPI and a similar share in the CPI-IW. Indian households on average spend the largest single share of income on food, and the index design reflects that reality.

Q6In general, inflation is calculated by using: (i) wholesale price index (ii) consumer price index (iii) producers' price index.

Answer: (i) wholesale price index (NCERT's official answer, since the textbook's "headline inflation" is based on the WPI). Note: in current Indian policy, the Reserve Bank of India targets CPI inflation under the inflation-targeting framework adopted in 2016. So both WPI and CPI inflation rates are routinely reported, but the historic NCERT answer is WPI.

Q7Why do we need an index number?

Answer: An index number compresses the changes in many related variables (prices, quantities, costs of living) into a single number, making complex patterns easy to interpret. Specifically: (a) it summarises diverse percentage changes in one figure; (b) it allows comparison across periods or places; (c) it is used in policy — CPI for wage indexing and inflation targeting, WPI for deflating GDP, IIP for monitoring industrial performance, Sensex for stock-market trends, HDI for cross-country development comparisons. Without index numbers, economic policy would be effectively blind.

Q8What are the desirable properties of the base period?

Answer: A good base period should be (i) a "normal" year — no famine, war, drought or boom that distorts prices and quantities; (ii) not too far in the past — otherwise the consumption basket has changed beyond recognition; (iii) representative of the structure of the economy; and (iv) close enough to the period of comparison so that meaningful interpretation is possible. The base year is therefore routinely updated (Indian CPI moved from 2001 to 2012; WPI from 2004-05 to 2011-12).

Q9Why is it essential to have different CPI for different categories of consumers?

Answer: Different consumer groups have different consumption baskets. A factory worker in Mumbai spends a high share on food, transport and rented housing; an agricultural labourer spends more on food and fuel and less on housing; a rural household has very different patterns from an urban one. A single CPI cannot reflect every group's cost of living accurately. India therefore publishes CPI-IW (industrial workers), CPI-AL (agricultural labourers), CPI-RL (rural labourers), CPI-Rural and CPI-Urban — each tailored to a target population. Using the wrong CPI to index wages or pensions would systematically over- or under-compensate the target group.

Q10What does a consumer price index for industrial workers measure?

Answer: The CPI-IW measures the average change in the retail prices of a fixed basket of goods and services consumed by a typical industrial worker household. The value 278 in May 2017 (with 2001 = 100) means a worker who spent Rs 100 in 2001 needed Rs 278 in May 2017 to buy the same basket. It is used for indexing wages and dearness allowance of factory workers and central-government employees.

Q11What is the difference between a price index and a quantity index?

Answer: A price index measures the average change in prices of a fixed basket of goods over time, holding quantities constant (e.g. CPI, WPI). A quantity index measures the average change in quantities produced or consumed, holding prices (or value-weights) constant (e.g. IIP, agricultural production index). The two answer different questions: a price index tells us about inflation; a quantity index tells us about real output growth. Multiplying a price index by a quantity index gives a value index.

Q12Is the change in any price reflected in a price index number?

Answer: Not necessarily. A price index reflects only those items included in its basket. Items outside the basket — or services for the WPI, which excludes services entirely — have no impact, however much their prices change. Even within the basket, the impact depends on the weight: a doubling in the price of a low-weight item barely moves the index, while a small rise in a heavy-weight item shifts it sharply.

Q13Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?

Answer: No, it cannot. The CPI for urban non-manual employees is built on a basket representative of average urban white-collar households — food, rent, fuel, transport and so on. The President of India lives in Rashtrapati Bhavan with most expenses (housing, security, ceremonial expenditure) covered by the state, and spends on a wholly different basket of items. Applying a CPI built for urban clerical workers to the President's lifestyle would be meaningless. The principle generalises: an index designed for one group cannot be safely transplanted onto another group with a fundamentally different consumption pattern.

Q14The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on five items is given. Weights of the items are 75, 10, 5, 6, 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as base. Items: Food (Rs 100, Rs 200), Clothing (Rs 20, Rs 25), Fuel & lighting (Rs 15, Rs 20), House rent (Rs 30, Rs 40), Misc (Rs 35, Rs 65).

Answer: Compute price relatives R = (P₁/P₀) × 100 and the weighted sum ΣWR.
Food: R = (200/100)×100 = 200; W×R = 75 × 200 = 15000.
Clothing: R = (25/20)×100 = 125; W×R = 10 × 125 = 1250.
Fuel & lighting: R = (20/15)×100 = 133.33; W×R = 5 × 133.33 = 666.67.
House rent: R = (40/30)×100 = 133.33; W×R = 6 × 133.33 = 800.00.
Misc: R = (65/35)×100 = 185.71; W×R = 4 × 185.71 = 742.86.
ΣW = 75+10+5+6+4 = 100. ΣWR ≈ 15000 + 1250 + 666.67 + 800.00 + 742.86 = 18459.53.
Cost of living index = ΣWR / ΣW = 18459.53 / 100 = 184.6 (approximately 185).
Reading: cost of living rose by about 84.6 per cent from 1980 to 2005 for this group.

Q15Read the IIP table (Base 1993-94=100) and give your comments. General Index (Wt 100): 130.8 (1996-97), 189.0 (2003-04). Mining (10.73): 118.2, 146.9. Manufacturing (79.58): 133.6, 196.6. Electricity (10.69): 122.0, 172.6.

Answer: Several observations follow. (i) Industrial output grew strongly between 1993-94 and 2003-04: the General Index nearly doubled, from 100 to 189.0 — an 89 per cent rise over a decade, or roughly 6.6 per cent per annum on average. (ii) Manufacturing led the way — with the largest weight (79.58 per cent) and the highest end-of-period index (196.6, a 96.6 per cent rise), it pulled the General Index up. (iii) Electricity grew faster than mining: 72.6 per cent against 46.9 per cent, reflecting India's expansion of generation capacity and rural electrification. (iv) Mining lagged with only 46.9 per cent growth, indicating that domestic raw-material extraction did not keep pace with manufacturing demand — a precursor of the rising imports of coal and other minerals seen in later years. (v) Between 1996-97 and 2003-04 alone, the General Index jumped from 130.8 to 189.0, suggesting that the second half of the decade was particularly buoyant for Indian industry.

Q16Try to list the important items of consumption in your family.

Answer (sample): A typical Indian middle-class household spends on roughly these categories (illustrative weights): Food & beverages (35-45%), Housing/rent (10-15%), Fuel & light (5-7%), Transport (8-10%), Clothing & footwear (5-7%), Education (5-7%), Health (5-7%), Communication (3-4%), Recreation (2-3%), Personal care & miscellaneous (8-10%). The exact mix varies by income, family size and city. Listing one's own family's items and rough monthly spend is exactly how a household-budget survey is conducted, and is the raw material from which weights for the official CPI are derived.

Q17If 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: The CPI of 400 (with the base year = 100) means cost of living has risen 4-fold. To enjoy the same standard of living as in the base year, the worker needs base-year salary × (CPI / 100) = 4000 × (400/100) = Rs 16,000 per annum.
His current salary is only Rs 6,000.
Required additional rise = 16,000 − 6,000 = Rs 10,000 per annum.
So the salary must be raised by Rs 10,000 for him to be as well off as before.

Q18The 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: Let the weight of food be W_f and of "other items" be W_o, with W_f + W_o = 100.
The combined index is the weighted average: (W_f × 120 + W_o × 135) / 100 = 125.
120 W_f + 135 W_o = 12500.
Substituting W_o = 100 − W_f:
120 W_f + 135 (100 − W_f) = 12500
120 W_f + 13500 − 135 W_f = 12500
−15 W_f = −1000
W_f = 66.67%.
Approximately two-thirds of the total weight is given to food.

Q19An enquiry into the budgets of middle class families in a certain city gave the following information. Food (35%): Rs 1500 (2004), Rs 1400 (1995). Fuel (10%): Rs 250, Rs 200. Clothing (20%): Rs 750, Rs 500. Rent (15%): Rs 300, Rs 200. Misc. (20%): Rs 400, Rs 250. What is the cost of living index during the year 2004 as compared with 1995?

Answer: Treat 1995 as base period and 2004 as current period.
Food: R = (1500/1400)×100 = 107.14; W×R = 35 × 107.14 = 3750.0.
Fuel: R = (250/200)×100 = 125.00; W×R = 10 × 125 = 1250.0.
Clothing: R = (750/500)×100 = 150.00; W×R = 20 × 150 = 3000.0.
Rent: R = (300/200)×100 = 150.00; W×R = 15 × 150 = 2250.0.
Misc: R = (400/250)×100 = 160.00; W×R = 20 × 160 = 3200.0.
ΣW = 100. ΣWR = 3750 + 1250 + 3000 + 2250 + 3200 = 13450.
Cost of living index (2004 with 1995 as base) = ΣWR / ΣW = 13450 / 100 = 134.5.
The cost of living for these middle-class families rose by 34.5 per cent between 1995 and 2004.

Q20Record 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?

Answer (project guidance): Maintain a notebook for 14 days listing every purchase made by anyone in the household — vegetables, milk, bread, fuel, transport, recharge, soap, eggs — with quantity and price. At the end of two weeks: (i) total spending, (ii) compute price relatives for items bought in both weeks, (iii) compute a weighted price index using week-1 quantities as weights (a Laspeyres mini-CPI). If the index exceeds 100, the family's cost of living rose during week 2; if below, it fell. Compare with newspaper headlines on inflation. Typical observations: vegetable prices fluctuate sharply (10-20% in a fortnight), while staples (rice, oil) move slowly. The exercise demonstrates that even small statistical work can mirror what national agencies do on a vast scale.

Q21Given the table of CPI-IW (1982=100), CPI-AL (1986-87=100) and WPI (1993-94=100) from 1995-96 to 2003-04, comment on the relative values of the index numbers. Are they comparable?

Answer: (i) Relative values: CPI-IW rises from 313 (1995-96) to 500 (2003-04), an increase of about 60 per cent over eight years. CPI-AL rises from 234 to 331, about a 41 per cent rise. WPI rises from 121.6 (1995-96) to 175.9 (2002-03), about a 45 per cent rise over seven years. So CPI-IW shows the steepest rise, CPI-AL and WPI rise more modestly.
(ii) Are they comparable? No, they are not directly comparable for three reasons:
(a) Different base years — 1982, 1986-87 and 1993-94. An index of "300" with a 1982 base means much less of a price rise than "300" with a 1993-94 base because the latter accumulates from a more recent benchmark.
(b) Different baskets — CPI-IW reflects industrial workers' urban consumption, CPI-AL reflects agricultural labourers' rural consumption, WPI reflects wholesale goods (no services).
(c) Different weights — food share is much higher in CPI-AL than in WPI; manufactured goods dominate WPI.
To make them comparable one must rebase all three series to a common year (say 2001=100) and compare the year-on-year inflation rates rather than the absolute index levels.

Q22The monthly expenditure (Rs) of a family on items and the GST rates is given. Calculate the average tax rate as far as this family is concerned (using the weighted-average formula).

Answer (NCERT-style grouping): Group items by GST rate, find the total expenditure in each rate-bucket, multiply by the rate, and divide the total tax by total expenditure.
Category 1 (0% GST): Cereals (1500) + Eggs (250) + Fish, Meat (250) = Rs 2000. Tax = 2000 × 0 = 0.
Category 2 (5% GST): Medicines (50) + Biogas (50) + Transport (100) = Rs 200. Tax = 200 × 0.05 = 10.
Category 3 (12% GST): Butter (50) + Babool (10) + Tomato Ketchup (40) = Rs 100. Tax = 100 × 0.12 = 12.
Category 4 (18% GST): Biscuits (75) + Cakes/Pastries (25) + Branded Garments (100) = Rs 200. Tax = 200 × 0.18 = 36.
Category 5 (28% GST): Vacuum Cleaner, Car = Rs 1000. Tax = 1000 × 0.28 = 280.
Total expenditure = 2000 + 200 + 100 + 200 + 1000 = Rs 3500. Total tax = 0 + 10 + 12 + 36 + 280 = Rs 338.
Average tax rate = 338 / 3500 = 0.0966 = 9.66%.
Reading: although the family encounters GST rates ranging from 0% to 28%, its effective rate is just 9.66 per cent, because the largest single chunk of spending (Rs 2000 of food) is GST-exempt. This is precisely the logic behind any weighted average — the bigger the weight, the bigger the influence on the final figure.

7.20 Summary of the Chapter

📝 Recap — Index Numbers

An index number is a statistical device for measuring relative change in a large number of items between a base period and a current period, conventionally expressed as a percentage with the base set to 100.
There are two families of construction methods — the aggregative method (add up prices and take a ratio) and the method of averaging price relatives. Each can be unweighted or weighted.
The simple aggregative index P₀₁ = (ΣP₁ / ΣP₀) × 100 is easy but suffers from unit-mismatch and no weighting.
The weighted aggregative family includes Laspeyres (base-period quantity weights, tends to overstate), Paasche (current-period quantity weights, tends to understate) and Fisher's ideal (the geometric mean of the two, satisfying time- and factor-reversal tests).
The method of price relatives first standardises each price by computing R = (P₁/P₀) × 100 and then takes a (weighted or unweighted) average. It side-steps the units problem.
India's most-watched indices: CPI (cost of living, retail prices, RBI inflation target), WPI (wholesale prices, headline inflation, GDP deflator), IIP (quantity index, mining + manufacturing + electricity, base 2011-12=100), Sensex (BSE-30 stock benchmark, base 1978-79), and the HDI (UNDP composite of life, knowledge, income).
Several formulae exist; the choice depends on the question of interest. Issues in construction: purpose, item selection, base year, weights, formula and data reliability.
Index numbers are indispensable in economic policy — wage indexing, inflation targeting, GDP deflation, monitoring industrial growth, guiding investment.
Purchasing power of money = 1 / Cost of living index. Real wage = (Money wage / Cost of living index) × 100.

7.21 Key Terms & Definitions

Index Number

A specialised average measuring change in a variable or group of variables across two situations, expressed as percentage of a base.

Base Period

The reference period whose index value is fixed at 100; benchmark for comparison.

Current Period

The period whose index is being measured against the base.

Price Relative

The ratio (P₁/P₀) × 100 for a single commodity; the building block of relatives-method indices.

Simple Aggregative Index

P₀₁ = (ΣP₁/ΣP₀) × 100. Unweighted and unit-sensitive.

Laspeyres' Index

Weighted aggregative using base-period quantities q₀. Tends to overstate.

Paasche's Index

Weighted aggregative using current-period quantities q₁. Tends to understate.

Fisher's Ideal Index

Geometric mean √(L × P). Satisfies time- and factor-reversal tests.

Consumer Price Index (CPI)

Retail-price-based cost-of-living index. India publishes CPI-IW, CPI-AL, CPI-RL, CPI-Rural, CPI-Urban, All-India Combined.

Wholesale Price Index (WPI)

Wholesale-stage price index, no services. Base 2011-12=100. Used for headline inflation, deflating GDP.

Index of Industrial Production (IIP)

Quantity index for mining, manufacturing & electricity. Base 2011-12=100. Eight Core Industries combined weight 40.27%.

Sensex

BSE Sensitive Index, 30 stocks across 13 sectors, base 1978-79. Stock-market barometer.

Human Development Index (HDI)

UNDP composite of life expectancy, education and per-capita income; geometric mean of three normalised dimensions.

Inflation

A general and continuing increase in prices. Lowers the value of money.

Cost of Living Index

Synonym for CPI; measures average change in retail prices of a typical consumer basket.

Purchasing Power of Money

1 / (Cost of living index). Falls when cost of living rises.

Real Wage

Money wage adjusted for cost of living: (Money wage / Cost of living index) × 100.

7.22 A Worked Case-Based Question

📋 Case-Based Question — Reading the Indian Index Numbers, May 2017

In May 2017 the Labour Bureau and the Office of the Economic Adviser released the following figures: CPI-IW (2001=100) = 278; All-India Combined CPI (2012=100) = 131.4; WPI (2011-12=100) = 112.8; IIP General Index (2011-12=100) was about 119. The financial press reported "CPI inflation cools to 4.2 per cent year-on-year" and "WPI inflation at 2.2 per cent". A union leader wants a 12 per cent dearness allowance hike on the back of these numbers; the management resists.

Q1. State the meaning of the WPI value 112.8 and explain why it differs sharply from the CPI-IW value of 278.

L2 Understand

Answer: WPI = 112.8 means wholesale prices have risen by 12.8 per cent since the base year 2011-12. CPI-IW = 278 means retail prices for industrial workers have risen 178 per cent since the base year 2001. The gap is due to (a) different base years — CPI-IW is older, accumulating more inflation, and (b) different baskets — CPI includes services and food at retail, while WPI excludes services and uses wholesale prices.

Q2. The IIP General Index reached about 119 in May 2017. Compute the percentage change from the base year and identify which sector has the largest weight in this index.

L3 Apply

Answer: Percentage change = (119 − 100) / 100 × 100 = +19 per cent rise in industrial production from 2011-12 to May 2017 (about 3.4 per cent annualised). The largest-weight sector is Manufacturing, with 77.6 per cent of the IIP weight, followed by Mining (14.4%) and Electricity (8.0%).

Q3. The union leader's demand for a 12 per cent dearness allowance hike rests on which inflation figure, and is the figure justified?

L4 Analyse

Answer: Dearness allowance is meant to compensate workers for the rise in their cost of living, so the relevant index is CPI-IW (or now the All-India Combined CPI). The CPI inflation figure quoted (4.2%) is the Y-o-Y rate, far below the demanded 12%. The 12 per cent figure is not justified by current data. A defensible position is a hike close to 4-5 per cent (roughly the year's CPI inflation), with periodic adjustment if inflation accelerates. Quoting WPI (2.2%) would understate the workers' real squeeze because WPI excludes services.

Q4. Suppose the worker's money wage rises from Rs 30,000 to Rs 31,500 over the year. Compute his real wage growth using the CPI-IW change from 270 to 278 and evaluate whether he is better off.

L5 Evaluate

Answer: Real wage = (Money wage / CPI) × 100. Old real wage = (30000/270) × 100 = Rs 11,111. New real wage = (31500/278) × 100 = Rs 11,331. Real wage rise = (11331 − 11111) / 11111 × 100 = +1.98 per cent. The worker's nominal wage rose 5 per cent (1500/30000), but inflation (278/270 − 1 = 2.96 per cent) ate up most of it. He is better off, but only marginally — by about 2 per cent in real terms. Without indexing to CPI, even a "5 per cent raise" can fail to keep up with rising prices.

7.23 Assertion–Reason Questions

⚖ Assertion–Reason Questions (Class 11)

Choose: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true, R is false. (D) A is false, R is true.

Assertion (A): A consumer price index larger than 100 indicates that the cost of living has risen and the wages and salaries of workers must be adjusted upward by the amount the index exceeds 100.

Reason (R): The CPI is built as a weighted average of price relatives over a typical consumer basket, so its value above 100 reflects the rupee cost of buying that basket above the base-period level.

Correct: (A) — Both statements are true and R is the correct explanation of A. NCERT explicitly says: "If the index is 150, 50 per cent upward adjustment is required. The salaries of the employees have to be raised by 50 per cent." The cost-of-living interpretation flows directly from the weighted average construction.

Assertion (A): The Index of Industrial Production (IIP) is a price index that measures the change in the wholesale prices of industrial commodities.

Reason (R): Unlike the CPI and the WPI, the IIP measures changes in quantities of industrial output and is constructed as a weighted arithmetic mean of quantity relatives using value-added weights from the base year.

Correct: (D) — Assertion is false. The IIP is a quantity index, not a price index. NCERT is unambiguous: "Unlike the Consumer Price Index or the Wholesale Price Index, this is an index which tries to measure quantities." Reason is true and is precisely the construction that distinguishes IIP from CPI and WPI.

Assertion (A): The Sensex, with 1978-79 as base, is a complete and reliable measure of the health of the Indian economy.

Reason (R): The Sensex tracks 30 large-cap stocks listed on the Bombay Stock Exchange across 13 sectors and so reflects the performance of the entire Indian economy including agriculture, MSMEs and the unorganised sector.

Correct: (D) — Assertion is false. The Sensex is a useful guide for stock-market investors and signals confidence about large listed companies, but cannot represent agriculture, the unorganised sector, MSMEs and most rural activity. Reason is also partly false — the Sensex covers 30 stocks (true) but does not reflect the entire economy (false). On strict reading, A is false; the descriptive part of R is correct, the inferential part is not. The intended NCERT answer treating R as a true descriptive statement and A as false yields option (D); some teachers may grade as the answer with R also marked false. The safer pick aligned with standard practice is (D).

End of Chapter 7 — Index Numbers. You now command the full toolkit: simple and weighted aggregative methods, the price-relatives family, Laspeyres, Paasche and Fisher, and the family of Indian official indices — CPI, WPI, IIP, Sensex and HDI.

Frequently Asked Questions — Index Numbers in India — CPI, WPI, IIP, Sensex, HDI and Exercises

What is the difference between CPI and WPI in NCERT Class 11 Statistics?

The Consumer Price Index (CPI) measures the change in retail prices of a basket of goods and services typically consumed by households, while the Wholesale Price Index (WPI) measures price changes at the bulk or wholesale stage of transactions. NCERT Class 11 Statistics Chapter 7 Part 2 explains that CPI directly affects the cost of living, indexing of wages, dearness allowance and pensions, and is used by the RBI as the main inflation target. WPI tracks producer-level inflation and is more sensitive to global commodity prices. CPI in India is published by NSO (CSO), and WPI by the Office of Economic Adviser, Ministry of Commerce.

What is the Index of Industrial Production (IIP) in NCERT Class 11?

The Index of Industrial Production (IIP) is a composite index that measures the short-term changes in the volume of production of selected industrial sectors — mining, manufacturing and electricity — relative to a chosen base year. NCERT Class 11 Statistics Chapter 7 Part 2 explains that IIP is published monthly by the National Statistical Office and is used by policymakers, the RBI and analysts as an early indicator of industrial growth and the broader economic cycle. The current base year for IIP is 2011-12, and it covers around 800 manufactured items aggregated using value-added weights.

What is the Sensex in NCERT Class 11 Statistics Chapter 7?

The Sensex (Sensitive Index) is the Bombay Stock Exchange's benchmark stock market index, reflecting the weighted average of the share prices of 30 large, financially sound and actively traded companies on the BSE. NCERT Class 11 Statistics Chapter 7 Part 2 explains that the Sensex was launched with a base year of 1978-79 set to 100, and tracks daily movements that act as a barometer of investor sentiment and the broader Indian economy. A rise in the Sensex indicates rising market value of these 30 companies on average; it is sensitive to corporate earnings, interest rates, monsoon and global cues.

What is the Human Development Index (HDI) in NCERT Class 11 Statistics?

The Human Development Index (HDI) is a composite index published annually by the United Nations Development Programme (UNDP) that combines three dimensions of human development: a long and healthy life (life expectancy at birth), knowledge (mean years of schooling and expected years of schooling) and a decent standard of living (gross national income per capita). NCERT Class 11 Statistics Chapter 7 Part 2 explains that HDI ranges between 0 and 1, with higher values indicating better human development. India is in the medium human development category, and HDI is widely used to compare countries beyond income alone.

What are the main issues in the construction of index numbers in NCERT Class 11?

NCERT Class 11 Statistics Chapter 7 Part 2 lists six major issues in constructing reliable index numbers: (1) selection of items in the basket — must reflect typical consumption or production; (2) choice of base year — must be a normal year not too far from the present; (3) collection of price quotations — multiple sources, consistent methodology; (4) selection of weights — should reflect economic importance; (5) choice of formula — Laspeyres, Paasche or Fisher each have biases; and (6) coverage of regions and outlets. Poor decisions on any of these undermine the index's reliability for inflation measurement and policy use.

How is CPI used to measure inflation in India in Class 11 Statistics?

NCERT Class 11 Statistics Chapter 7 Part 2 explains that the Consumer Price Index (CPI) is used to measure retail inflation in India by computing the year-on-year percentage change in the index. The formula is Inflation rate = ((CPI_current − CPI_previous) / CPI_previous) × 100. The Reserve Bank of India targets CPI inflation at 4% with a tolerance band of ±2% under the flexible inflation targeting framework adopted in 2016. CPI is split into CPI-Combined (urban + rural), CPI-Urban and CPI-Rural, and is also used to revise dearness allowance for government employees and to index wages, pensions and welfare payments.

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