Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series

Index Numbers: Meaning, Uses and Types

Updated 10 October 2026 · Fact-checked

An index number is a statistical measure that shows the relative change in a variable, such as price or quantity, over time or place compared with a base period. It is usually expressed as a percentage with the base equal to 100. Find it by dividing the current value by the base value and multiplying by 100.

Understand Index Numbers: Meaning, Uses and Types

An index number tells you how much a group of related items has changed compared with a fixed point. That fixed point is the base period, and its index is set at 100. The period you compare is the current period.

Suppose the index of prices is 125 this year with the base year at 100. This means prices are 25% higher than in the base year. If it is 80, prices are 20% lower. You read the index by comparing it with 100.

Index numbers are needed because different items cannot simply be added. Rice is in kg, milk in litres and cloth in metres. An index converts all of them into one relative figure. For this reason, an index is often called an economic barometer, because it shows the general direction of the economy.

The main types are:

Price index: measures change in prices, such as the Consumer Price Index or the Wholesale Price Index.
Quantity index: measures change in physical output or volume, such as an index of industrial production.
Value index: measures change in total value, which is price × quantity, such as sales or turnover.

Uses: index numbers help to measure changes in the cost of living, fix dearness allowance and wages, compare prices or output across years, support government policy, and deflate money values to real values.

Limitations: they are only approximate. Results depend on the base year, the items chosen, the weights and the formula used. Samples may not represent everyone. Comparison across very distant periods is unreliable, because consumption habits and product quality change. An index can also be misused to show a result the user wants.

Characteristics: index numbers are specialised averages, they are expressed in percentages, they measure changes that cannot be measured directly, and they are comparative in nature.

Key formulas to remember

Simple price index: Index = (Current price ÷ Base price) × 100; Use for a single item. Base period index is always 100.
Price relative: P = (p₁ ÷ p₀) × 100; p₀ is the base year price and p₁ is the current year price.
Value index: V = (Σp₁q₁ ÷ Σp₀q₀) × 100; Value = price × quantity. It combines price and quantity changes.
Percentage change from index: Change % = Index − 100; Valid when the base index is 100. A positive result is a rise, a negative result is a fall.
Quantity index (simple form): Q = (q₁ ÷ q₀) × 100; Use for a single item's quantity.

How to solve Index Numbers: Meaning, Uses and Types questions

Most theory and numerical questions on this topic can be handled with the same approach.

1Read the question and decide what is being measured: price, quantity or value.
2Identify the base period and the current period. Do not swap them.
3For a theory question, recall the definition, types, uses or limitations and match the option to the exact wording.
4For a numerical question, write the correct formula with the right symbols.
5Substitute the values carefully, placing current figures on top and base figures below.
6Multiply by 100 to express the result as an index.
7Interpret the answer by comparing it with 100 and check that the base year equals 100.
8Match your result with the options and eliminate those that are clearly too high or too low.

Quickest way: Compare with 100 and eliminate

When to use it: Use this for MCQs where you are given an index or a pair of values and must judge the change.

Subtract 100 from the index to get the percentage change at once.
Estimate the ratio current ÷ base. If it is above 1, the index must exceed 100.
Remove options that show an index below 100 when the value has risen.
For value index, multiply price and quantity first, then divide the totals.
For theory, recall that the base year index is always 100 and that index numbers are percentages without a % sign.

Common mistakes in Index Numbers: Meaning, Uses and Types

Putting the base value in the numerator.
Students rush and write p₀ ÷ p₁.
Fix: Remember that the current year always goes on top. Check that a price rise gives an index above 100.
Forgetting to multiply by 100.
The ratio looks like a finished answer.
Fix: An index is a percentage figure. Always multiply the ratio by 100 before choosing an option.
Confusing value index with price index.
Both use p and q in similar-looking formulas.
Fix: Value index uses p₁q₁ and p₀q₀ only. Price and quantity indices keep one of them as a weight.
Reading an index of 120 as a 120% rise.
Students forget the base is 100.
Fix: Subtract 100. An index of 120 means a 20% rise.
Saying index numbers give exact results.
They look precise because they are numbers.
Fix: State that they are approximate and depend on the base year, items, weights and formula.

Worked examples

Example 1

The price of a kilogram of sugar was ₹40 in 2020 (base year) and ₹50 in 2024. Find the price index for 2024 and the percentage rise in price.

Show the solution

Base price p₀ = ₹40 and current price p₁ = ₹50.
Price index = (50 ÷ 40) × 100.
50 ÷ 40 = 1.25, so the index = 125.
Percentage change = 125 − 100 = 25.

Answer: The price index is 125, so the price has risen by 25%.

Example 2

A shop sold 10 units at ₹20 each in the base year and 12 units at ₹25 each in the current year. Find the value index.

Show the solution

Base value Σp₀q₀ = 20 × 10 = ₹200.
Current value Σp₁q₁ = 25 × 12 = ₹300.
Value index = (300 ÷ 200) × 100.
300 ÷ 200 = 1.5, so the index = 150.

Answer: The value index is 150, which means total sales value has risen by 50%.

Exam tips

Learn the three types by definition. Questions often ask which type a given example represents.
Remember that the base year index is 100 and use it to check every answer.
Revise the limitations as a short list: approximate, base year dependent, sample bias, formula choice, and poor long-term comparison.
Practise one-line numerical questions on simple price and value indices, as they are quick marks.
Since there is no negative marking, attempt every question and eliminate wrong options first.

Practice questions from Index Numbers and Time Series

Index Numbers: Meaning, Uses and Types in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Index Numbers: Meaning, Uses and Types: frequently asked questions

What is an index number in simple words?

It is a figure that shows how much a variable such as price or output has changed compared with a base period. The base period is set at 100. A value above 100 shows a rise and below 100 shows a fall.

What are the main types of index numbers?

The main types are price index, quantity index and value index. A price index tracks prices, a quantity index tracks volume of goods, and a value index tracks total money value, which is price times quantity.

What are the limitations of index numbers?

They are approximate measures. Their results depend on the base year, items selected, weights and formula used. They may not suit every group of people, and comparisons over long periods are unreliable.

Why is the base year index always 100?

The base year is the reference point. Dividing its value by itself gives 1, and multiplying by 100 gives 100. Every other year is measured relative to it.