Quantitative Aptitude · Index Numbers

Limitations and Problems in Index Numbers

Updated 1 October 2026 · Fact-checked

Index numbers measure relative change in a group of related variables, but they are only approximate. Problems arise in choosing the base year, items, weights, prices, formula and purpose. To answer MCQs, match the error or problem to its cause, and match special indices like WPI and Sensex to what they measure.

Understand Limitations and Problems in Index Numbers

An index number shows how a variable, such as price, changes over time compared with a base period. The base period is set at 100. If the index today is 125, the variable is 25% higher than in the base period.

An index is built from a sample of items, not from every item in the economy. It uses chosen weights, a chosen base year and a chosen formula. Each choice can introduce error. This is why index numbers are called economic barometers that give a rough guide, not exact truth.

The main problems in construction are: defining the purpose, selecting the base year, selecting items, collecting reliable prices, choosing weights, and choosing the averaging method and formula. If the purpose is unclear, the whole index may measure the wrong thing.

Base year should be a normal year. It should be free from wars, floods, famines, or booms and slumps. It should also not be too far back, or comparisons lose meaning because tastes and products change.

Items must be representative and of standard quality. Weights must reflect the importance of each item. Wrong or outdated weights give biased results.

The limitations are: sampling error, choice error, bias from the formula, difficulty of comparing across different periods or places, and the fact that an index for one group (say, factory workers) may not suit another. Changes in quality and new products are hard to capture.

Special-purpose indices include the Wholesale Price Index (WPI), which tracks price changes of goods at the wholesale level, and the Sensex, a stock market index of 30 large, well-established companies listed on the BSE. Sensex is a market-capitalisation based index, adjusted for free-float shares. The Consumer Price Index (CPI) tracks retail prices paid by consumers. WPI covers goods only, not services.

Key formulas to remember

Index number for base year: Index in base year = 100; Every index is expressed relative to its base period.
Simple price relative: Index = (p₁ ÷ p₀) × 100; p₀ is base year price, p₁ is current year price. Use it to read percentage change: Index − 100.
Percentage change from index: % change = Index − 100; Valid when the base is 100. An index of 80 means a 20% fall.
Time reversal test: P₀₁ × P₁₀ = 1; A test of consistency of a formula. It is covered in detail in tests of adequacy.

How to solve Limitations and Problems in Index Numbers questions

Theory questions on this topic are matched to a cause, a stage of construction or an index type. Work in this order.

1Read the question and decide what is asked: a limitation, a construction problem, a property of the base year, or a special index.
2Identify the stage of construction involved: purpose, base year, items, prices, weights or formula.
3Recall the ideal condition for that stage, such as a normal base year, representative items and appropriate weights.
4Check each option against that ideal. Reject options that state the opposite, such as an abnormal base year being acceptable.
5For special indices, recall what is covered: WPI is wholesale goods, CPI is retail consumer prices, Sensex is 30 BSE companies.
6For numerical parts, apply Index = (p₁ ÷ p₀) × 100 and % change = Index − 100.
7Choose the option that is correct in all its parts. Reject options with words like always or never unless they are certain.

Quickest way: Match the keyword, then eliminate

When to use it: Use for theory MCQs where two options look close. This saves time in a 2-hour paper with negative marking.

Spot the keyword: base year, weights, items, sample, quality, barometer, Sensex, WPI.
Recall the one-line rule: base year normal and recent; items representative; weights reflect importance.
Cross out options that contradict the rule.
If two options remain, pick the one that is more specific to the keyword in the question.
If you cannot cut to two options, skip. A wrong answer costs 0.25 marks.

Common mistakes in Limitations and Problems in Index Numbers

Choosing an abnormal year such as a boom or a famine year as the base year.
Students think a year with big events is more important or well documented.
Fix: Remember the base year must be a normal, stable year with no unusual events.
Saying the Sensex covers all listed companies on the stock exchange.
The word index suggests the whole market.
Fix: Sensex is based on 30 large, actively traded companies on the BSE, so it is a sample.
Treating WPI as including services and retail prices.
Students mix WPI with CPI.
Fix: WPI tracks wholesale prices of goods. CPI tracks retail prices paid by consumers.
Believing a properly built index is free from error.
The numbers look exact.
Fix: Index numbers are approximate because of sampling, choice of weights and formula. They are relative measures.
Reading an index of 80 as a fall of 80%.
Forgetting the base is 100.
Fix: Percentage change = Index − 100, so 80 means a 20% fall.

Worked examples

Example 1

Which of the following is the most suitable choice of base year for an index number?
(a) A year of severe drought
(b) A normal year with stable prices
(c) A year of a major war
(d) A year of exceptional stock market boom

Show the solution

The base year is the reference for all comparisons.
It must be free from abnormal events so that the comparison is fair.
Drought, war and boom are abnormal conditions, so (a), (c) and (d) are rejected.
A normal year with stable prices fits the requirement.

Answer: (b) A normal year with stable prices

Example 2

The price index of a commodity in the current year is 135 with the base year 100. The price in the base year was ₹40. What is the current price?
(a) ₹50
(b) ₹54
(c) ₹56
(d) ₹135

Show the solution

Index = (p₁ ÷ p₀) × 100, so 135 = (p₁ ÷ 40) × 100.
p₁ = 135 × 40 ÷ 100.
135 × 40 = 5,400. Dividing by 100 gives 54.

Answer: (b) ₹54

Example 3

Which statement about the Sensex is correct?
(a) It measures wholesale prices of goods
(b) It is based on 30 well-established companies listed on the BSE
(c) It measures retail prices paid by consumers
(d) It covers all the companies listed on the NSE

Show the solution

Sensex is a stock market index, not a price index of goods, so (a) and (c) are rejected.
Sensex belongs to the BSE, not the NSE, so (d) is rejected.
It is based on 30 large and actively traded BSE companies.

Answer: (b) It is based on 30 well-established companies listed on the BSE

Exam tips

Theory questions here are usually direct. Learn the one-line rule for each stage of construction.
Know the difference between WPI, CPI and Sensex in one line each. Examiners like to mix them up in options.
Be careful with absolute words such as always, never and all. They are usually in wrong options.
For numerical parts, convert between index and percentage change before reading the options.
If two options both seem right, ask which one fits the keyword in the stem more precisely.

Practice questions from Index Numbers

Limitations and Problems in Index Numbers: frequently asked questions

What are the main limitations of index numbers?

They are approximate because they rest on a sample of items, chosen weights and a chosen formula. They may not suit every group or period. Changes in quality and new products are hard to capture.

Why must the base year be a normal year?

All later values are compared with it. If the base year is abnormal, the comparison is distorted and the index misleads.

What is the difference between WPI and CPI?

WPI measures price changes of goods at the wholesale level. CPI measures changes in retail prices that consumers pay.

What does the Sensex represent?

It is the index of the Bombay Stock Exchange, based on 30 large and actively traded companies. It acts as a barometer of market movement.