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Simple Index Numbers and Price Relatives, ISC 11

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EconomicsISC Class 11 · Index Numbers

Simple Index Numbers: Price Relatives, Base Shifting and Real Wages (ISC Class 11)

Updated 17 October 2026 · Fact-checked

An index number is a statistical measure showing the average change in a group of related variables over time, expressed in relation to a base period taken as 100. In the simple aggregative method the price index = Sum P1 / Sum P0 x 100; in the average of price relatives method it is the mean of (P1/P0 x 100). Index numbers are used to deflate money values to real values, for example real wage = money wage / price index x 100.

Line graph of annual real food price indices from 1990 to 2014 with 2002–2004 as base equal to 100, showing food, meat, dairy, cereals, oils

Notice the base period (2002–2004) is set at 100, so values above 100 show prices higher than the base and values below 100 show prices lower.

Picture: Nigelj · CC BY-SA 3.0 · Wikimedia Commons

When prices rise to 125 against a base of 100, the same money wage buys less, so real wage = money wage ÷ index × 100.

Illustration drawn for QuestionBuddy.

Understand Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages

Meaning and features. An index number measures relative change. It is a special type of average, expressed as a percentage (base = 100), is used to compare over time, and measures changes that cannot be measured directly (the general price level).

Types. *Price index* (WPI, CPI), *quantity index* (IIP), *value index*.

Simple (unweighted) methods.
1. *Simple aggregative:* P01 = (Sum P1 / Sum P0) x 100, where P0 is the base-year price and P1 the current-year price.
2. *Average of price relatives:* price relative = P1 / P0 x 100; P01 = Sum of relatives / n.

Quantity index (simple): Q01 = Sum Q1 / Sum Q0 x 100.

Base shifting. To change the base to another year: New index = Old index of the year / Old index of the new base year x 100.

Deflating. Real wage = (Money wage / Price index) x 100. Real income similarly. This removes the effect of price changes.

Uses. Measure inflation; adjust wages (dearness allowance); compare cost of living; deflate national income (GDP deflator); policy.

Limitations of simple methods. They give equal importance to all items (no weights), and the aggregative method depends on the units of the items. Weighted indices (Laspeyres, Paasche, Fisher) are better.

Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages: key facts

Simple aggregative
P01 = Sum P1 / Sum P0 x 100 | P0 base price, P1 current price
Depends on units.
Average of price relatives
P01 = Sum (P1/P0 x 100) / n | Mean of price relatives
Unit free.
Real wage
Real wage = Money wage / Price index x 100 | Deflating
Price index with base 100.

How to answer Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages questions

Decide the method, set out P0 and P1 and compute.

  1. 1Write P0 and P1 for each item in columns.
  2. 2Aggregative: total the columns and divide; relatives: compute each ratio first.
  3. 3Check that the base year has an index of 100.
  4. 4For wages, divide by the index and multiply by 100.

Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Real wage

Suppose a worker's salary rises from Rs 20,000 to Rs 24,000 while the consumer price index rises from 100 to 130.

Has her real wage risen?

Try it first, then show the solutionSolution
  1. Real wage now = 24,000 / 130 x 100 ≈ Rs 18,462.
  2. Her real wage has fallen from Rs 20,000.

Answer: No; real wage fell to about Rs 18,462 despite the higher money wage.

Memory hook: Money wage rose, but prices rose faster.

Tricks to remember Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • Base is 100

    The base year index is always 100.

    Use it when: Check.

  • Aggregate adds first, relatives divide first

    Two orders of operation.

    Use it when: Methods.

  • Divide by index, times 100

    Deflating money to real.

    Use it when: Real wage.

Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Base year · 1 mark · MCQBoard level

The index number of the base year is always taken as:
(a) 0 (b) 1 (c) 100 (d) 1,000

Try it first, then show the solutionSolution
  1. By convention base = 100.

Answer: (c) 100

Example 2: Uses · 3 marks · Short answerBoard level

State three uses of index numbers. (3 marks)

Try it first, then show the solutionSolution
  1. Measure change in price level.
  2. Adjust wages and allowances.
  3. Deflate money values to real values.

Answer: They measure inflation, are used to adjust wages and pensions and convert nominal incomes into real incomes.

Example 3: Two simple methods · 6 marks · Long answerHarder board level

Prices (Rs per kg) in the base year and the current year: Rice 40 and 50; Wheat 30 and 33; Milk (per litre) 50 and 60; Sugar 40 and 44. Find the price index by (a) the simple aggregative method and (b) the average of price relatives method. (6 marks)

Try it first, then show the solutionSolution
  1. Sum P0 = 40 + 30 + 50 + 40 = 160; Sum P1 = 50 + 33 + 60 + 44 = 187.
  2. (a) Index = 187 / 160 x 100 = 116.875, about 116.9.
  3. Price relatives: 125, 110, 120, 110; sum = 465.
  4. (b) Index = 465 / 4 = 116.25.

Answer: Aggregative index about 116.9; average of relatives 116.25. Both show a price rise of roughly 16% to 17%.

Example 4: Shifting the base · 4 marks · Short answerHarder board level

Index numbers with base 2018 = 100 are: 2018: 100; 2019: 110; 2020: 125; 2021: 150; 2022: 165. Shift the base to 2020 and state the price rise from 2020 to 2022. (4 marks)

Try it first, then show the solutionSolution
  1. New index = Old index / 125 x 100.
  2. 2018: 80; 2019: 88; 2020: 100; 2021: 120; 2022: 132.
  3. Price rise from 2020 to 2022 = 32%.

Answer: With 2020 = 100: 80, 88, 100, 120, 132; prices rose 32% between 2020 and 2022.

Example 5: Real wage and DA · 5 marks · Long answerHOTS / competency

A worker's monthly wage was Rs 30,000 when the price index was 100 (base year). Two years later the index is 125. Find the wage needed to keep the real wage unchanged, the real value of an unchanged wage of Rs 30,000, and the dearness allowance as a percentage of the basic wage required. (5 marks)

Try it first, then show the solutionSolution
  1. Required money wage = 30,000 x 125 / 100 = Rs 37,500.
  2. Real value of Rs 30,000 = 30,000 / 125 x 100 = Rs 24,000.
  3. Dearness allowance = 7,500, which is 25% of the basic wage of Rs 30,000.
  4. So a 20% fall in real purchasing power (6,000 on 30,000) is made good by a 25% rise in money wage.

Answer: Wage needed Rs 37,500; real value of Rs 30,000 is Rs 24,000; DA of Rs 7,500, i.e., 25% of basic.

Where students lose marks in Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages

The slips examiners see most often, and what to write instead.

  • Mistake: Forgetting to multiply by 100

    Missing the base.

    Wrong working

    187 / 160 = 1.169

    Right working

    1.169 x 100 = 116.9

    Do this: Index numbers are percentages.

    Usually costs: 1-2 marks.

  • Mistake: Averaging the price relatives with the wrong n

    Counting error.

    Wrong working

    465 / 3

    Right working

    465 / 4

    Do this: n is the number of items.

    Usually costs: 1 mark.

  • Mistake: Using the wrong base year when shifting

    Dividing by the original base.

    Wrong working

    Divide by 100

    Right working

    Divide by the index of the new base year

    Do this: Divide by the new base index.

    Usually costs: 2 marks.

Exam tips

  • Write P0 and P1 headings in the table.
  • Show the check that the base year equals 100.
  • Interpret the final index in words.

Practice questions on Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    If the price index rises from 100 to 150, the purchasing power of money:
    (a) rises by 50% (b) falls to two-thirds (c) stays the same (d) doubles

    Hint

    100 / 150.

    Answer

    (b) falls to two-thirds

  2. Q2 · 3 marks · Short answerBoard level

    Distinguish between the simple aggregative method and the average of price relatives method. (3 marks)

    Hint

    Order of operations; units.

    Answer

    The aggregative method totals the prices and then takes the ratio, so it depends on the units; the relatives method takes the ratio for each item first and then averages, so it is unit-free.

  3. Q3 · 5 marks · Long answerHarder board level

    Prices of four items in 2020 and 2024 (Rs): Pulses 100, 130; Oil 120, 150; Flour 30, 36; Tea 200, 260. Find the index by both simple methods. (5 marks)

    Hint

    Sum P0 = 450, Sum P1 = 576.

    Answer

    Aggregative: 576 / 450 x 100 = 128. Relatives: 130, 125, 120, 130; sum 505; average = 126.25.

  4. Q4 · 5 marks · Long answerHarder board level

    The index numbers (base 2015 = 100) for 2015 to 2019 are 100, 108, 117, 126, 135. Shift the base to 2017. A salary of Rs 50,000 in 2015 becomes Rs 62,000 in 2019: find the real salary of 2019 at 2015 prices and the percentage change in real salary. (5 marks)

    Hint

    62,000 / 135 x 100.

    Answer

    Base 2017 = 100: 85.5, 92.3, 100, 107.7, 115.4 (to one decimal). Real salary 2019 = 62,000 / 135 x 100 = Rs 45,926; change = (45,926 - 50,000) / 50,000 = -8.15%.

  5. Q5 · 3 marks · Short answerHOTS / competency

    A union argues that a wage rise of 10% is enough because the index rose from 100 to 108 in the year. Evaluate with the real wage and the effect of an index with an unrepresentative basket. (3 marks)

    Hint

    Compare 10% with 8%.

    Answer

    Real wage rises by about 1.85% (1.10 / 1.08 = 1.0185), so the claim is acceptable on the numbers. But if workers' own basket (food, rent) rose faster than the index, their real gain may be smaller, so the index should match the workers' consumption.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.Base year index?Show answer

    100.

  2. 2.Real wage formula?Show answer

    Money wage / Price index x 100.

  3. 3.Price relative?Show answer

    P1 / P0 x 100.

  4. 4.Base shifting?Show answer

    Divide by the index of the new base year, times 100.

  5. 5.A quantity index?Show answer

    IIP.

Simple Index Numbers: Aggregative and Price Relatives Methods, Base Shifting, Real Wages: frequently asked questions

Why are index numbers called economic barometers?

They show changes in the economy.

What is WPI?

Wholesale price index.

What is CPI?

Consumer price index.

Can the index be below 100?

Yes, if prices fall.