EconomicsCBSE Class 11 · Index Numbers

Index Numbers: Meaning, Simple Aggregative and Weighted Methods

Updated 17 October 2026 · Fact-checked

An index number is a statistical measure of the relative change in a variable or group of variables over time or place compared with a base. The simple aggregative price index is (Sum p1 / Sum p0) x 100; the average of price relatives is Sum(p1/p0 x 100) / n; the weighted index is Sum(I x W) / Sum W. The base period is 100.

Add the prices in each period, divide current by base, multiply by 100: the base is 100, so 116.8 means prices rose about 16.8%.

Illustration drawn for QuestionBuddy.

Understand Constructing Index Numbers

Meaning. An index number measures the relative change in a variable (or group) over time, place or other characteristic, compared with a base whose index is fixed at 100. It is an average of relative changes, a specialised average; expressed as a percentage but written without % sign.

Features. Expressed in percentages; measures change not shown directly; average of changes; compares different periods; it is relative, not absolute. The base period should be normal and not too distant; the current period is the one compared.

Types. Price index (change in prices), quantity index (output, e.g. IIP), value index (expenditure). Price indices include the consumer and wholesale price indices.

Simple aggregative method. Add the prices of the selected items in each period.
Price index = (Σp₁ ÷ Σp₀) × 100, where p₀ = base prices and p₁ = current prices. Weakness: items with large unit prices dominate; units of measure matter; all items are treated equally.

Average of price relatives. Price relative of an item = (p₁ ÷ p₀) × 100. Index = Σ(p₁/p₀ × 100) ÷ n.

Weighted index (CPI-type). Items have weights W (importance, e.g. share in household expenditure). With I = price relative: Index = Σ(I × W) ÷ ΣW. This gives more weight to items consumers spend more on.

Worked example. Items: wheat, rice, sugar, oil. Base prices p₀: 20, 30, 40, 100; current prices p₁: 25, 33, 44, 120.

Simple aggregative: Σp₀ = 190, Σp₁ = 222; index = 222 ÷ 190 × 100 = 116.84.
Price relatives: 125, 110, 110, 120; simple average = 465 ÷ 4 = 116.25.
Weighted with weights 4, 3, 2, 1: ΣIW = 500 + 330 + 220 + 120 = 1170; ΣW = 10; index = 117.

Different methods give slightly different values; the weighted index better reflects importance.

Steps for constructing a price index. Decide purpose and scope; choose the base year; select items; collect prices; choose the method and weights; compute and interpret.

Interpretation. An index of 117 means prices are 17 per cent higher than in the base.

Table: item, p₀, p₁, relative, weight, relative × weight.

Constructing Index Numbers: key facts

Simple aggregative: Index = (Sum p1 / Sum p0) x 100; Base = 100
Price relative: (p1 / p0) x 100; Per item
Average of relatives: Sum(price relatives) / n; Equal weights
Weighted index: Sum(I x W) / Sum W; W = weights

How to answer Constructing Index Numbers questions

Questions give prices (and weights) for base and current periods.

1Choose the method named in the question.
2Compute the sums or relatives carefully.
3For weighted index multiply relatives by weights and divide by total weight.
4Interpret: index minus 100 gives the percentage change.
5Mention limitations (choice of base and weights).

Constructing Index Numbers 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.

Kitchen basket

Suppose a family buys wheat, rice, sugar and oil, and their prices have risen.

Find the percentage rise in the basket using the simple aggregative index and explain.

Try it first, then show the solutionSolution

Add base prices: 20 + 30 + 40 + 100 = 190.
Add current prices: 25 + 33 + 44 + 120 = 222.
Index = 222 / 190 x 100 = 116.84, i.e. prices have risen about 16.8 per cent.

Answer: Index 116.84; rise 16.8 per cent.

Memory hook: Total today over total then.

Tricks to remember Constructing Index Numbers

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

Base is 100
Base period index is 100.
Use it when: Base
I times W over W
Weighted index = sum IW / sum W.
Use it when: Weighted
Index minus 100
Index minus 100 is the percent change.
Use it when: Interpretation

Constructing Index Numbers: solved examples

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

Example 1: Meaning · 2 marks · Very short answerBoard level

Define an index number and state two features.

Try it first, then show the solutionSolution

A statistical measure of relative change in a variable or group over time or place compared with a base (1 mark).
Expressed as a percentage with base 100; it is a specialised average (1 mark).

Answer: Relative change against a base.

Example 2: Simple aggregative · 4 marks · Short answerBoard level

Prices (Rs): wheat 20 to 25, rice 30 to 33, sugar 40 to 44, oil 100 to 120. Find the simple aggregative price index and the percentage rise.

Try it first, then show the solutionSolution

Sum p0 = 20 + 30 + 40 + 100 = 190 (1 mark).
Sum p1 = 25 + 33 + 44 + 120 = 222 (1 mark).
Index = 222/190 x 100 = 116.84 (1 mark).
Rise = 16.84 per cent (1 mark).

Answer: 116.84; 16.84 per cent.

Example 3: Average of relatives · 4 marks · Short answerHarder board level

For the same data find the price relatives and their simple average. Why does it differ from the aggregative result?

Try it first, then show the solutionSolution

Relatives: 125, 110, 110, 120 (1 mark).
Average = 465/4 = 116.25 (1 mark).
Aggregative index gives more weight to dearer items like oil (1 mark).
Relatives treat each item equally, so values differ (1 mark).

Answer: 116.25; different weighting.

Example 4: Weighted index · 4 marks · Short answerHarder board level

With weights 4, 3, 2, 1 for wheat, rice, sugar, oil, find the weighted price index for the same data.

Try it first, then show the solutionSolution

Relatives I: 125, 110, 110, 120 (1 mark).
IW: 500, 330, 220, 120; sum 1170 (1 mark).
Sum W = 10 (1 mark).
Index = 1170/10 = 117 (1 mark).

Answer: 117.

Example 5: Choosing weights · 5 marks · Long answerHOTS / competency

Suppose a family spends more on food than on transport. Explain why a weighted index suits this family better than the simple aggregative method, and find the effect on the index if the food weight is doubled (food relative 125, transport relative 105, original weights 3 and 1).

Try it first, then show the solutionSolution

Weights reflect the importance of items in the budget (1 mark).
Original index = (125 x 3 + 105 x 1) / 4 = 480/4 = 120 (1 mark).
Doubling food weight: (125 x 6 + 105 x 1) / 7 = 855/7 = 122.14 (1 mark).
The index moves toward the food relative as its weight rises (1 mark).
Simple methods ignore importance, so they misrepresent the budget (1 mark).

Answer: 120 to 122.14; weights matter.

Where students lose marks in Constructing Index Numbers

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

Mistake: Base index 1
Base mis-set.
Wrong working
Index in base year is 1.
Right working
Index in base year is 100.
Do this: 100.
Usually costs: 1 mark.
Mistake: Index equals percent rise
Subtract 100 forgotten.
Wrong working
Index 117 means 117 per cent rise.
Right working
It means a 17 per cent rise.
Do this: Index minus 100.
Usually costs: 1 mark.
Mistake: Weights not divided
Sum W forgotten.
Wrong working
Index = Sum IW.
Right working
Index = Sum IW / Sum W.
Do this: Divide.
Usually costs: 1 mark.

Exam tips

Show every sum.
Write the formula before substitution.
Interpret with percentage change.
Mention that weights matter.

Practice questions on Constructing Index Numbers

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

Q1 · 1 mark · MCQBoard level
If a price index reads 108 in the current year (base = 100), prices have
(a) fallen by 8 per cent (b) risen by 108 per cent (c) risen by 8 per cent (d) not changed
Hint
Index minus 100.
Answer
(c).
Q2 · 1 mark · Assertion-reasonHarder board level
Assertion (A): The simple aggregative method treats all items as equally important.
Reason (R): It ignores weights based on spending.
(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 but R is false.
(d) A is false but R is true.
Hint
No weights.
Answer
(a).
Q3 · 2 marks · Very short answerBoard level
If an index for the current year is 132 with the base year at 100, find the percentage rise in prices and the price of an item that cost Rs 250 in the base year (assuming it follows the index).
Hint
Index minus 100.
Answer
Rise = 32 per cent; price = 250 x 132/100 = Rs 330.
Q4 · 4 marks · Case-basedHarder board level
Read and answer.
Suppose the prices of 3 items are 10, 20, 30 in the base year and 12, 25, 33 now.
(a) Find the simple aggregative index. (2)
(b) Find the average of price relatives. (2)
Hint
Compute both.
Answer
(a) Sum p0 = 60, Sum p1 = 70, index = 70/60 x 100 = 116.67. (b) Relatives 120, 125, 110; average = 355/3 = 118.33.
Q5 · 3 marks · Short answerHOTS / competency
Suppose an index shows 150 for the current year with 2010 as the base. A worker's money wage rose from Rs 12,000 (when the index was 100) to Rs 16,000 in this period. Judge whether real purchasing power rose.
Hint
Deflate.
Answer
Real wage in base prices = 16,000 / 150 x 100 = Rs 10,667, which is less than Rs 12,000. Although the money wage rose, prices rose faster, so purchasing power fell.

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.Base index?Show answer
100.
2.Simple aggregative formula?Show answer
Sum p1 / Sum p0 x 100.
3.Weighted index formula?Show answer
Sum IW / Sum W.
4.Price relative?Show answer
p1 / p0 x 100.
5.Is it an average?Show answer
Yes, of relatives.
6.Why weights?Show answer
To reflect importance.

Constructing Index Numbers: frequently asked questions

What is an index number?

A measure of relative change against a base.

What is the base period?

The reference period with index 100.

Why weighted?

Items differ in importance.

What is a price relative?

Current price as a percentage of base price.

What does index 117 mean?

Prices are 17 per cent higher than the base.