Indexnumbers

INDEXNUMBER
DR.SIJI k
Associate professor
Gopalan college of commerce

MEANING
An Index number is a statistical
device for measuring changes in the
magnitude of a group of related
variables on a particular date in
comparison to their level on some
previous date. It measures relative
changes in two or more related
variable over time.

DEFINITIONS
 According to croxton and cowden
“index numbers are devices for
measuring differences in the
magnitude of a group of related
variables”.
 According to Spiegal “ An index
number is a statistical measure
designed to show changes in a
variable or a group of related
variables with respect to time,
geographic location or other
characteristics”.

CHARACTERISTICS
OF INDEXNUMBERS
 Specialised averages
 Expressed in percentages
 Measure the change in the
level of phenomenon
 Measure changes not
capable of direct
measurement
 Meant for comparison
 Measures the effect of
change over periods of
time or from one place to
another.

USES OF INDEX NUMBERS
 To measure and compare
changes
 To provide guidelines to
policy
 To study trends and
tendencies
 Useful for deflating

Limitations
 Based on samples
 Approximate indicators of
the relative level of
phenomenon
 Not good for all purposes
 Specialised type of
averages
 Liable to be misused
 Different method yield
different results
 Chances of error are so
many

Problems in the construction of
index numbers
 Purpose of index
 Selection of the base
period
 Selection of number of
items
 Obtaining price quotations
 Selection of an average
 Selection of appropriate
weights
 Selection of an
appropriate formula

Methods of construction
of Index numbers
Simple aggregative
method
Simple average of
relatives
Weighted aggregative
method
Weighted average of
relative

Simple aggregative
method
 This method is the simplest
of all the methods of
constructing Index
numbers.
 The aggregate of price of
all the commodities in the
current year is expressed as
a percentage of the
aggregate of prices of the
base year.
 Formula
Po1= ΣP1/Σp0×100
Where
ΣP1=Aggregate of prices in the current year
Σp0=Aggregate of prices in the base year

Simple average of
price relative method
 In this method average of
price relative is calculated.
 Formula :
P01=ΣI/n where
I=P1/p0×100
Where
P1= price of the current year
P0 = Price of the base year

Weighted Aggregative Method
 Appropriate weights are
assigned to various
commodities to reflect their
relative importance.
 Various Methods are
 Laspeyers formula
 Paasches formula
 Fishers Formula
 Marshall Edgeworth formula
 Bowley-Dorbish formula
 Kellys formula

 LASPEYERS INDEXNUMBER
In this index number the base year quantities are used as
weights, so it also called the base year weighted index.
Po1=∑P1qo/∑Poqo×100
 PAASCHES INDEXNUMBER
The quantities of various commodities actually
produced or consumed in the current year are taken as
weight and their value at current price is compared with
their value at the base price
Po1=∑P1q1/∑Poq1×100

 FISHERS INDEXNUMBER
The geometric mean of Laspeyre’s and Paasche’s index
numbers is known as Fisher’s ideal index number. It is
called ideal because it satisfies the time reversal and factor
reversal test.It is based on both base year and current year
quantities.

 MARSHALL EDGEWORTH INDEX
The average of the base year and current year
quantities are used as weights.
Po1=∑P1q0+∑P1q1/∑Poqo+∑Poq1×100
 BOWLEY –DORBISH INDEX
Arithmetic mean of Laspeyers and paasches index
numbers

 KELLEYS INDEX
weights are the quantities which may refer to some
period, not necessarily the base year or current year.
Thus the average quantity of two or more years may
be used as weights.
Kelly’s formula the average of the quantities of two
years is used as weights.

WEIGHTED AVERAGE
RELATIVE METHOD
Different weights are used for
the items according to their
relative importance.
P01=ΣIV/ΣV;I=P1/P0×100
V=P0q0
Where ΣV=Sum of the
weight of other commodities.
ΣI=Sum of price relatives

VALUE INDEX NUMBERS
 Value is the product of
price and quantity. The
ratio is equal to the value
of current year divided by
value of base year
multiplied by 100.
 V=ΣP1q1/ ΣP0q0×100

Indexnumbers

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