Course Title: Business Statistics

COURSE INSTRUCTOR:ILTAF MEHDI

1By ILTAF MEHDI, IT Lecturer, MIHE, Kabul

CHAPT

ER_N

O: 04

INDEX

NUM

BERS

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 2

Index Numbers

• Def: ”Index numbers are statistical measures designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc.”

• A collection of index numbers for different years, locations, etc., is sometimes called an index series.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 3

Kinds of Index Numbers

• Simple Index Number: A simple index number is a number that measures a relative change in a single variable with respect to a base.

• Composite Index Number: A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 4

Types of Index Numbers:• Following types of index numbers are usually used:• Price index Numbers:

Price index numbers measure the relative changes in prices of a commodities between two periods. Prices can be either retail or wholesale.

• Quantity Index Numbers:

These index numbers are considered to measure changes in the physical quantity of goods produced, consumed or sold of an item or a group of items.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 5

Construction of Price Index Numbers

• The following steps are considered for the construction of price index numbers:

1. Object2. Selection of Commodities3. Collection of Price Data4. Selection of Base Period

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 6

1.) Object

• The first and the most important step in the construction of index numbers is to decide the object for making the index numbers of prices.

• The prices may be retail or whole-sale.1) The index numbers of retail prices are called

the consumer price index (CPI) numbers and2) if the whole-sale prices are taken into

consideration, the index numbers are called the whole-sale price index numbers.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 7

1.) Object• First of all we decide the purpose of

making the index numbers. Once the purpose is decided, then we decide about the scope and the area or the people who are to be considered.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 8

2.) Selection of Commodities• The second in the construction of index numbers is the

Selection of Commodities.• A list of important commodities is prepared.• Those commodities are taken into account which is

commonly consumed by the consumers.• There is no hard and fast rule about the number of

commodities (20 commodities is a small number and 50 commodities is a reasonable number).

• Sometimes the index numbers of very important commodities like wheat, rice, oil, ghee etc. are calculated.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 9

3.) Collection of Price Data• The most important and difficult step is the

collection of prices.• The prices are to be taken from the field.• For retail price index numbers, retail prices are

needed.• The prices change from place to place and from

time to time.• The prices are taken on daily basis and then

weekly and monthly averages are calculated.• Finally quarterly or yearly averages are

calculated.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 10

4.) Selection of Base Period• The prices of the commodities in the current

period are to be compared with the prices of some period in the past. This period in the past is called the base period or the reference period.

• This period should not be in the remote past.• The period which is economically stable and is

free of disturbances and strikes is taken as the base period.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 11

Methods for finding Index Numbers

• Different methods are used for to find the index numbers. Following four methods are used mostly…

1) Fixed Base Method2) Chain Base Method3) Un-weighted Index Numbers4) Weighted Index Numbers

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 12

1.) Fixed Base Method• In fixed base method, a particular year is generally

chosen randomly and the prices of the subsequent years are expressed as relatives of the prices of the base year.

• Sometimes instead of choosing a single year as the base, a period of a few years is chosen and the average price of this period is taken as the base year’s price.

• The fixed base method is used by the Government in the calculation of national index numbers.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 13

In Fixed Base

Price relative for current year

or

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 14

Fixed Base

• Example: Find index numbers for the following data taking 1980 as base year.

Years 1980 1981 1982 1983 1984 1985 1986 1987

Price 40 50 60 70 80 90 100 110

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 15

`

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 16

2.) Chain Base Method

• In this method, there is no fixed base period. The year immediately preceding the one for which price index have to be calculated is assumed as the base year. Thus, for the year1994 the base year would be 1993, for 1993 it would be 1992 for 1992 it would be 1991 and so on.

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 17

2.) Chain Base Method

By ILTAF MEHDI, IT Lecturer, MIHE, Kabul 18

2.) Chain Base Method

19

Solution: