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CONTENTS

IntroductionDefinitionCharacteristicsUses

ProblemsClassificationMethods

Value index numbers

Chain index numbers.


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WHA T I S A N I NDEX NUMBER


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DEF I N I T I ON

Index numbers are quantitative measures of growth of prices, production, inventory andother quantities of economic interest .

y

-Ronold


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C HA R A CTER I ST I CS OF I NDEX NUMBERS

Index numbers are specialised averages.

Index numbers measure the change in the level

of a phenomenon.

Index numbers measure the effect of changesover a period of time.


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USES OF I NDEX NUMBERS

o To framing suitable policies.

o They reveal trends and tendencies.

o Index numbers are very useful in deflating.


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P ROBLEMS REL A TED TO I NDEX NUMBERS

Choice of the base period.

Choice of an average.

Choice of index.

Selection of commodities.

Data collection.


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CL A SS I F I C A T I ON OF I NDEX NUMBERS

Price IndexPrice Index

Quantity IndexQuantity Index

Value Index Value Index

Composite IndexComposite Index


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MET H ODS OF CONSTRUCT I NG I NDEX NUMBERS

IndexNumbers

Simple A ggregative

Simple A verage of

Price Relative

Unweighted

Weighted

Weighted A ggregated

Weighted A verage of

Price Relatives


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S I M P LE A GGREG A T IV E MET H OD

It consists in expressing the aggregate price of allcommodities in the current year as a percentage of theaggregate price in the base year.

P 01 = Index number of the current year.= Total of the current years price of all commodities.= Total of the base years price of all commodities.

1000

101 v!

p p

P

1 p0 p


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EX A M P LE: -

F ROM THE D ATA G IV E N B EL OW CONS TRUC T THEIND EX NUMB E R F OR THE YEA R 2007 ON THE B A SE YEA R 2008 IN R AJA STHA N S TATE .

COMMOD I T I ES UN I TSP R I CE (Rs)

2007P R I CE (Rs)

2008

Sugar Quintal 2200 3200

Milk Quintal 18 20

Oil Litre 68 71

Whe at Quintal 900 1000

Clot h ing Meter 50 60


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S I M P LE AV ER A GE OF REL A T IV ESMET H OD .

The current year price is expressed as a pricerelative of the base year price. These price relativesare then averaged to get the index number. Theaverage used could be arithmetic mean, geometricmean or even median.

N

p p

v

!100

0

1

01

W here N is Numb ers Of ite ms .

W hen ge om etric mean is used -

N

p p

v

!100log

log 01

01


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E XA MP LE -

F rom the data given below construct the indexnumber for the year 2008 taking 2007 as byusing arithmetic mean.

Commoditi e s P ric e (2007) P ric e (2008)

P 6 1 0

Q 2 2

R 4 6

S 1 0 1 2

T 8 1 2


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SOLU TION -

Index number using arithmetic mean-

Commoditi e s P ric e (2007) P ric e (2008) P ric e R e lativ e

P 6 10 166.7

Q 12 2 16.67

R 4 6 150.0

S 10 12 120.0

T 8 12 150.0

1000

1 v p

p

v 100

0

1

p

p=6 03.37

63.12 05

37.6 03100

0

1

01 !!

v

!

N

p p

P

1 p0 p


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W E I G H TED I NDEX NUMBERS

These are th ose index numbers in which rati onal wei ghts areassi gned t o vari ous chains in an exp licit fashi on.

( A) Weighted aggregative index numbers-These index numbers are the simple aggregative typewith the fundamental difference that weights areassigned to the various items included in the index.Dorbish and bowleys method.F ishers ideal method.Marshall- E dgeworth method.Laspeyres method.Paasche method.Kellys method.


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L ASPEYRES M ETHOD -This meth od was devised by Laspeyres in 187 1. In this

meth od the wei ghts are determined by quantities in the base .

10000

0101 v!

q p

q p p

Paasches Method.

This meth od was devised by a German statistician Paasche

in 187

4.

The wei ghts of current year are used as base year in c onstructin g the Paasches Index number .

10010

1101 v!

q p

q p p


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DORBISH & B OWLEYS M ETHOD .

This meth od is a c ombinati on of Laspeyres and Paaschesmeth ods . If we find out the arithmetic avera ge of Laspeyres and Paasches index we get the index su ggested

by D orbish & B owley.

Fishers Ideal Index.F ishers dea l index number is the geometric mean of the

Laspeyres and Paasches index numbers .

1002

10

11

00

01

01v!

q p

q p

q p

q p

p

v!

10

11

00

01

01 q p

q p

q p

q p P 100v


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M ARSHALL -E DGEWORTH M ETHOD .In this index the numerat or consists of an a ggregate of the

current years price mu ltiplied by the wei ghts of both the baseyear as we ll as the current year .

Kellys Method.K elly thinks that a rati o of aggregates with se lected wei ghts

(not necessari ly of base year or current year) gives the base

index number .

1001000

110101

v!

q pq p

q pq p p

1000

101 v!

q p

q p p

q refers t o the quantities of the year which is se lected as the base .

It may be any year, either base year or current year .


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E XA MP LE -Given below are the price quantity data,with price

quoted in Rs. per kg and production in qtls.F ind- (1) Laspeyers Index (2) Paasches Index(3)F isher Ideal Index.

I TEMS P R I CE P RODUCT I ON P R I CE P RODUCT I ON

BEEF 15 500 20 600

MU TT ON 18 590 23 640

CH ICK E N 22 450 24 500

2002 2007


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SOLU TION -

I TEMS P R I CE P RODUCT I ON

P R I CE P RODUCT I ON

BEEF 15 500 20 600 10000 7500 12000 9000

MU TT ON 18 590 23 640 13570 10620 14720 11520

CH ICK E N 22 450 24 500 10800 9900 12000 11000

TOTAL 34370 28020 38720 31520

0 p 0q 1q 1 p 01q p 00q p 11q p 10q p


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S OLU TION -

66.1221002 802 03 437 0100

00

0101 !v!v!

q pq p p

2. P aasches Index :

84.1221003 152 0

3 872 0100

10

1101

!v!v!

q p

q p p

3. F isher Ideal Index

100v 69.1221003 152 0

3 872 02 802 0

3 437 0 !vv!

v!

10

11

00

01

01q p

q p

q p

q p

1 .Las pe yres index :


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W E I G H TED AV ER A GE OF P R I CE REL A T IV E

In weighted A verage of relative, the price relativesfor the current year are calculated on the basis of the base year price. These price relatives aremultiplied by the respective weight of items. Theseproducts are added up and divided by the sum of

weights.Weighted arithmetic mean of price relative-

!

V

P V P 01

1000

1 v! P P

P W here -

P = P rice relative

V= Value weights = 00q p


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V A LUE I NDEX NUMBERS

Value is the product of price and quantity. A simpleratio is equal to the value of the current yeardivided by the value of base year. If the ratio ismultiplied by 100 we get the value index number.

10000

11 v!

q p

q pV


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C HAI N I NDEX NUMBERS

When this method is used the comparisons are notmade with a fixed base, rather the base changesfrom year to year. F or example, for 2007,2006 willbe the base; for 2006, 2005 will be the same and soon.

Chain index for current year-

100year previ ousof indexChainyear currentof relativelink Avera ge v!


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E XA MP LE -

F rom the data given below construct an index

number by chain base method.Price of a commodity from 2006 to 2008.

Y E A R P R I CE

2006 50

2007 60

2008 65


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SO LU TION -

Y E A R P R I CE L I NKREL A T IV E

C HAI N I NDEX (B A SE 200 6 )

2006 50 100 100

2007 60

2008 65

12 01005 0

6 0!v

1081006 065 !v

12 0100

10012 0 !v

6 0.129100

12 0108 !v


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R EFERENCES1. Statistics for management.

Richard i. Levin & David S. Rubin.

2. Statistics for Business and economics.R.P. H ooda.

3. Business Statistics.B.M. A garwal.

4. Business statistics.S.P. Gupta.


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