Calculate Index Numbers of Production Using Different Base Periods | Query Point Official

Calculate Index Numbers of Production Using Different Base Periods

Problem Statement

The following table shows production of cotton cloth (in million yards) in Pakistan from 1954 to 1963:

Year	Production (million yards)
1954	282
1955	389
1956	438
1957	470
1958	511
1959	555
1960	564
1961	630
1962	662
1963	681

Index Numbers Explained

An index number is a statistical measure expressing relative changes in a variable over time compared to a base period. It’s widely used in economics and statistics to show how values like prices or production change.

The basic formula for an index number with a base period is:

Index Number = (Value in comparison period ÷ Value in base period) × 100

Part 1: 1954 as Base Year

Year	Production	Index (Base 1954 = 100)
1954	282	100
1955	389	(389/282)×100 = 137.94
1956	438	(438/282)×100 = 155.32
1957	470	(470/282)×100 = 166.67
1958	511	(511/282)×100 = 181.21
1959	555	(555/282)×100 = 196.81
1960	564	(564/282)×100 = 200.00
1961	630	(630/282)×100 = 223.40
1962	662	(662/282)×100 = 234.75
1963	681	(681/282)×100 = 241.49

Part 2: Average of 1958–1960 as Base Period

Calculate the average production in the base period:

Average of 1958–1960 = (511 + 555 + 564) / 3 = 543.33

Year	Production	Index (Base Average = 100)
1954	282	(282/543.33)×100 = 51.90
1955	389	(389/543.33)×100 = 71.59
1956	438	(438/543.33)×100 = 80.61
1957	470	(470/543.33)×100 = 86.50
1958	511	(511/543.33)×100 = 94.04
1959	555	(555/543.33)×100 = 102.15
1960	564	(564/543.33)×100 = 103.80
1961	630	(630/543.33)×100 = 115.95
1962	662	(662/543.33)×100 = 121.84
1963	681	(681/543.33)×100 = 125.34

Explanation

We calculate index numbers to compare how much production has changed relative to a base period. This helps analyze long-term trends. Using a single year (e.g., 1954) or an average base period (e.g., 1958–1960) can change the relative index values because the base reference differs.

FAQ

Q1: What is an index number?

An index number is a statistical measure showing relative change between periods or situations, often expressed as a percentage with a base year set at 100.

Q2: Why use an average base period?

Using an average of multiple years as a base period can reduce short-term fluctuations and give a more stable reference for comparison.

Q3: Where are index numbers used?

Index numbers are widely used in economics and statistics to track changes in prices, production, quantities, and other variables over time.

Related Topics

See Statistics Notes & MCQs for more index number and statistical problems.