Chapter 7
Index Numbers
Detailed Study Notes
Statistics — Complete Concept Guide with Real-Life Examples
7.1 The Concept of Index Number
What is an Index Number?
An index number is a statistical tool (or device) that helps us compare the level or magnitude of a group
of related variables across two or more situations — usually across different time periods or different
places.
Simply put: it converts raw data into a single number that tells you how much things have changed
compared to a starting point (called the base period). The base period is always assigned a value of 100.
■ Real-Life Example: Price of Rice
Suppose a bag of rice cost ■40 in 2010 (base year) and ■56 in 2023 (current year).
The price index for 2023 = () × 100 = 140.
This tells us: rice is 40% more expensive in 2023 compared to 2010. Simple and clear!
■ Key Insight
The index number does NOT tell the actual price — it tells the PERCENTAGE CHANGE from a base.
Base period index is always = 100. Values above 100 mean increase; below 100 mean decrease.
7.2 Types of Index Numbers
Index numbers are classified in two major ways:
A) By What They Measure
Type What It Measures Real-Life Example
Consumer Price Index (CPI) — tracks
Price Index Change in price of goods
grocery prices
, Change in quantity/output of Wheat production index — how much
Quantity Index
goods wheat is produced
B) By Number of Commodities Involved
Index numbers are also classified by how many items (commodities) they cover:
• Simple Index Number — Built for a single commodity only. For example, just wheat output or just
rice price.
• Composite (Aggregate) Index Number — Built for a group of commodities together. Like a "basket
of goods" approach.
Composite indices are further divided into:
1. Simple Aggregative Indices — All commodities treated equally (no weighting).
2. Weighted Aggregative Indices — Different commodities given different importance (weights)
based on their significance.
■ Real-Life Analogy: Basket of Groceries
Imagine tracking price changes for a monthly grocery basket: milk, rice, wheat, and cooking oil.
A Simple Aggregative Index just adds all prices — so if cooking oil (expensive) doubles, it
dominates the index.
A Weighted Index gives more weight to items you buy more of (like rice) and less to luxury items —
much fairer!
7.3 Notations Used in Index Numbers
Before jumping into formulas, it is important to understand the notation system used throughout index
number theory:
Symbol Meaning Example
p Price of a commodity Price of rice = p
q Quantity of a commodity Kg of rice produced = q
p0 Price in the BASE year (period 0) Price of rice in 1961 = p0
p1 Price in period 1 (current year) Price of rice in 1963 = p1
Price index for period 1 relative to Index comparing 1963 prices to 1961
P01
period 0 base
Index Numbers
Detailed Study Notes
Statistics — Complete Concept Guide with Real-Life Examples
7.1 The Concept of Index Number
What is an Index Number?
An index number is a statistical tool (or device) that helps us compare the level or magnitude of a group
of related variables across two or more situations — usually across different time periods or different
places.
Simply put: it converts raw data into a single number that tells you how much things have changed
compared to a starting point (called the base period). The base period is always assigned a value of 100.
■ Real-Life Example: Price of Rice
Suppose a bag of rice cost ■40 in 2010 (base year) and ■56 in 2023 (current year).
The price index for 2023 = () × 100 = 140.
This tells us: rice is 40% more expensive in 2023 compared to 2010. Simple and clear!
■ Key Insight
The index number does NOT tell the actual price — it tells the PERCENTAGE CHANGE from a base.
Base period index is always = 100. Values above 100 mean increase; below 100 mean decrease.
7.2 Types of Index Numbers
Index numbers are classified in two major ways:
A) By What They Measure
Type What It Measures Real-Life Example
Consumer Price Index (CPI) — tracks
Price Index Change in price of goods
grocery prices
, Change in quantity/output of Wheat production index — how much
Quantity Index
goods wheat is produced
B) By Number of Commodities Involved
Index numbers are also classified by how many items (commodities) they cover:
• Simple Index Number — Built for a single commodity only. For example, just wheat output or just
rice price.
• Composite (Aggregate) Index Number — Built for a group of commodities together. Like a "basket
of goods" approach.
Composite indices are further divided into:
1. Simple Aggregative Indices — All commodities treated equally (no weighting).
2. Weighted Aggregative Indices — Different commodities given different importance (weights)
based on their significance.
■ Real-Life Analogy: Basket of Groceries
Imagine tracking price changes for a monthly grocery basket: milk, rice, wheat, and cooking oil.
A Simple Aggregative Index just adds all prices — so if cooking oil (expensive) doubles, it
dominates the index.
A Weighted Index gives more weight to items you buy more of (like rice) and less to luxury items —
much fairer!
7.3 Notations Used in Index Numbers
Before jumping into formulas, it is important to understand the notation system used throughout index
number theory:
Symbol Meaning Example
p Price of a commodity Price of rice = p
q Quantity of a commodity Kg of rice produced = q
p0 Price in the BASE year (period 0) Price of rice in 1961 = p0
p1 Price in period 1 (current year) Price of rice in 1963 = p1
Price index for period 1 relative to Index comparing 1963 prices to 1961
P01
period 0 base
