![Page 1: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/1.jpg)
INDEX NUMBERS
Quantitative Aptitude & Business Statistics
![Page 2: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/2.jpg)
Index Numbers An index number is a specialized average
designed to measure the changes in a variable with respect to time ,geographical location or characteristics such as income, profession etc.
Quantitative Aptitude & Business Statistics: Index Numbers 2
![Page 3: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/3.jpg)
Features of Index numbers
specialized averages .
measure the net change in a group of
related variables.
measures the effect of changes over a
period of time.
Quantitative Aptitude & Business Statistics: Index Numbers 3
![Page 4: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/4.jpg)
Uses of Index Numbers
1. A guide to business policy.
2. Indices of industrial production are
useful as they are the indicators of
business environment .
3. At times, index numbers can be
combined into one series that may be
relevant to one’s own business.
Quantitative Aptitude & Business Statistics: Index Numbers 4
![Page 5: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/5.jpg)
4. Very helpful in finding out whether a
business firm’s sales are increasing in
physical volume as opposed to rupee
value.
5. Used to adjust wages or salaries on
account of rising prices or inflation.
6. 6.Index numbers can be used for
providing incentive to efficient
workers.
Quantitative Aptitude & Business Statistics: Index Numbers 5
![Page 6: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/6.jpg)
Problems in Index Number Construction
1. Selection of a Base Year
2. Type of Formula
3. Selection of Weights
4. The Data for Index Numbers
Quantitative Aptitude & Business Statistics: Index Numbers 6
![Page 7: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/7.jpg)
Types of Price Index Numbers
Simple Index Numbers
Composite Index Numbers
Simple Average of Price Relatives
Weighted Relative Price Index Numbers
Quantitative Aptitude & Business Statistics: Index Numbers 7
![Page 8: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/8.jpg)
Price Relatives
Price relatives are helpful in
understanding and interpreting
changing economic and business
conditions over time.
Quantitative Aptitude & Business Statistics: Index Numbers 8
![Page 9: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/9.jpg)
Price Relatives
A price relative shows how the current
price per unit for a given item
compares to a base period price per
unit for the same item.
A price relative expresses the unit
price in each period as a percentage
of the unit price in the base period.
9
![Page 10: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/10.jpg)
)100( price period Base
t period in Price= t period in relative Price
Quantitative Aptitude & Business Statistics: Index Numbers 10
![Page 11: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/11.jpg)
Aggregate Price Indexes
An aggregate price index is developed for the specific purpose of measuring the combined change of a group of items.
An unweighted aggregate price index in period t,
Quantitative Aptitude & Business Statistics: Index Numbers 11
![Page 12: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/12.jpg)
)100(P
PI
0i
it
t
Quantitative Aptitude & Business Statistics: Index Numbers 12
Where, Pit = unit price for item i in period t Pi 0 = unit price for item i in the base period
![Page 13: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/13.jpg)
Laspyre’s Price index number
Where
P1=Price of the current year
P0=Price of the base year
qo=Quantity of the base year
100qp
qpP
00
01
01
13 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 14: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/14.jpg)
Paachee’s Price index number
Where
P1=Price of the current year
P0=Price of the base year
q1=Quantity of the current year
10010
11
01
qp
qpP
14 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 15: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/15.jpg)
Dorbish-Bowley’s Price index number
Where,
L=Laspyre’s Price index number
P=Paachee’s Price index number
10022
10
11
00
01
01
qp
qp
qp
qp
PLP
15 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 16: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/16.jpg)
Marshall-Edgewoths’s Price index
number
Where
P1=Price of the current year
P0=Price of the base year
qo=Quantity of the current year
q1=Quantity of the current year
100
010
110
01
pqq
pqqP
16 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 17: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/17.jpg)
Fisher's Price index number
Where
L = Laspyre’s Price Index number
P = Paachee’s Price Index number
10010
11
00
01
01
01
qp
qp
qp
qpp
PLP
17 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 18: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/18.jpg)
Kelly’s Price index number
Where
P1=Price of the current year
P0=Price of the base year
q=Quantity of the current/base year
1000
1
01
qp
qpP
2
21 qqq
18 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 19: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/19.jpg)
Weighted Price index number
If Arithmetic Mean is used
Where
P1=Price of Current Year
P0=Price of base year
10001
V
PVP
1000
1 p
pP
19 Quantitative Aptitude & Business Statistics: Index Numbers
V=P0q0
![Page 20: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/20.jpg)
Weighted Price index number
If Geometric Mean is used
Where
P1=Price of Current Year
P0=Price of base year
V=P0q0
100log
log01
V
PVAntiP
20 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 21: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/21.jpg)
Quantity Indexes
An index that measures changes in
quantity levels over time is called a
quantity index.
Probably the best known quantity
index is the Index of Industrial
Production.
Quantitative Aptitude & Business Statistics: Index Numbers 21
![Page 22: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/22.jpg)
A weighted aggregate quantity index is
computed in much the same way as a
weighted aggregate price index.
)100(0 ii
iit
twQ
wQI
22 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 23: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/23.jpg)
Tests of adequacy of Index numbers
1.Unit test
2.Time reversal test
3.Factor reversal test
4.Circular test
Quantitative Aptitude & Business Statistics: Index Numbers 23
![Page 24: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/24.jpg)
Unit test
The unit test requires that the formula
for constructing an index should be
independent of the units in which ,or
for which ,prices and quantities are
quoted. All formulae except the simple
(unweighted )aggregate index formula
satisfy this test.
Quantitative Aptitude & Business Statistics: Index Numbers 24
![Page 25: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/25.jpg)
Time Reversal Test
A method satisfies time reversal test if
it gives P01 * P10 = 1 where P01 is the
price index number for the current
year with the base year 100 and P10 is
the index number of the base year,
taking current year as the base, both
the indices without the factor 100.
Quantitative Aptitude & Business Statistics: Index Numbers 25
![Page 26: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/26.jpg)
Methods which satisfy
the time reversal test
The Fisher’s ideal index number.
Simple geometric mean of price
relatives.
Aggregate with fixed weights.
Marshal-Edge worth Price index
number.
Quantitative Aptitude & Business Statistics: Index Numbers 26
![Page 27: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/27.jpg)
Factor Reversal Test
A method satisfies factor reversal test if it gives
where P01 is the price index for the current year (without the factor 100) and Q01 is the quantity index for the current year (without the factor 100).
Quantitative Aptitude & Business Statistics: Index Numbers 27
00
11
0101qp
qpqp
![Page 28: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/28.jpg)
Fishers index number only satisfies the
factor reversal test.
Quantitative Aptitude & Business Statistics: Index Numbers 28
![Page 29: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/29.jpg)
Circular Test
There is another test with respect to
index numbers. This is known as the
circular test. It is an extension of the
time reversal test. Symbolically, the
circular test may be written as
P01 .P12 . P23 … Pn-1n .Pn0 = 1
Circular test satisfies the simple
geometric mean of price relatives and
weighted aggregate of fixed weights.
Quantitative Aptitude & Business Statistics: Index Numbers 29
![Page 30: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/30.jpg)
Chain base index numbers
Chain base index numbers is one in
which the figures for each are first
expressed as percentage of the
preceding year. The percentage are
chained together by successive
multiplication to form a series of chain
index, in chain base year index method
the base year changes from year to
year .
Quantitative Aptitude & Business Statistics: Index Numbers 30
![Page 31: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/31.jpg)
Link relative=
Current Year Price index
Immediate preceding previous
Year Price relative
31 Quantitative Aptitude & Business Statistics: Index Numbers
X100
![Page 32: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/32.jpg)
Advantages of Chain Base Index
Numbers
1. The chain base index numbers facilitate the introduction of new items as also the deletion of absolute items in a smooth manner.
2. In business, often, comparisons are made in the current period with the immediately preceding period rather than any distant period in the past.
Quantitative Aptitude & Business Statistics: Index Numbers 32
![Page 33: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/33.jpg)
Limitations of Chain Base Index
Numbers
1. If the data for any one year are not available, the chain index number for subsequent period cannot be computed.
2. If an error in the computation of any link relative takes place, then such an error gets compounded and the entire series gives a distorted picture.
Quantitative Aptitude & Business Statistics: Index Numbers 33
![Page 34: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/34.jpg)
3)to splice two overlapping indices
together;
4) construct a chain index and
5)facilitate comparison with some date
of special interest.
Quantitative Aptitude & Business Statistics: Index Numbers 34
![Page 35: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/35.jpg)
Splicing and Shifting the Base of Index
Numbers
When two or more overlapping
series of index numbers are combined
into one series, then this process is
known as splicing.
Quantitative Aptitude & Business Statistics: Index Numbers 35
![Page 36: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/36.jpg)
Splicing
Splicing is a technique of linking two
or more index number series with the
same items and a common
overlapping year but with different
base period in order to form a
continuous series. Splicing may be
forward or backward
Quantitative Aptitude & Business Statistics: Index Numbers 36
![Page 37: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/37.jpg)
Splicing Index no. of old
series
Index
no. of
New
series
Forward
Splicing
={100/Overlapping
index number of old
series }*Given index
of No .of old series
No
change
37 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 38: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/38.jpg)
Splicing Index
no. of
old
series
Index no. of New
series
Backward
Splicing
No
change
={Index number of
old
series/100}*Given
index No.of new
series
38 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 39: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/39.jpg)
Shifting the Base Year
At times it is preferable to shift the
base of an existing index on account
of several reasons.
Quantitative Aptitude & Business Statistics: Index Numbers 39
![Page 40: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/40.jpg)
These reasons are:
1) to make the base more recent, which
will increase its utility;
2) to ensure better comparison with
some other index that is available on
some other base;
Quantitative Aptitude & Business Statistics: Index Numbers 40
![Page 41: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/41.jpg)
New index Number using new base=
Old Index number using old base
Index number Corresponding new base
year
41 Quantitative Aptitude & Business Statistics: Index Numbers
X100
![Page 42: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/42.jpg)
Deflating Prices and Incomes
The process of adjusting prices and
incomes by a price index and
expressing them in terms of base-year
rupees is called deflating prices and
income. 1
Purchasing power of Money =
Price index
number
Quantitative Aptitude & Business Statistics: Index Numbers 42
![Page 43: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/43.jpg)
Money wage=
Money wage index =
Real Wage index =
100'Pr
indexice
Moneywage
100'baseyear'ofthe'Moneywage
alwageRe
43 Quantitative Aptitude & Business Statistics: Index Numbers
100'Pr
'
indexice
indexMoneywage
![Page 44: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/44.jpg)
Caution in using Index Numbers
If the index numbers are defective on
account of one or more reasons, their
interpretation will lead to drawing of
wrong inferences from them. Even if
index numbers are constructed on
sound statistical principles, but we
interpret them in the wrong manner,
our conclusions will be wrong.
Quantitative Aptitude & Business Statistics: Index Numbers 44
![Page 45: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/45.jpg)
As far as construction of index
numbers is concerned, it is the domain
of the statistician who has to ensure
that the index numbers are based on
sound statistical principles. As regards
proper use of index numbers, it is the
user who should ensure that he
interprets index numbers properly
Quantitative Aptitude & Business Statistics: Index Numbers 45
![Page 46: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/46.jpg)
Limitations of Index Numbers
Index numbers are based on sample data.
In case sample size is extremely limited
and its selection is faulty in the sense
that the sample units have not been
selected randomly, index numbers will
give wrong figures.
Quantitative Aptitude & Business Statistics: Index Numbers 46
![Page 47: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/47.jpg)
At times, index numbers can be
manipulated by those who are in
authority. This is purposely done to
support their viewpoint.
Quantitative Aptitude & Business Statistics: Index Numbers 47
![Page 48: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/48.jpg)
A number of formulae can be used in
index number construction. These will
give different results. One who is using
the index should know a little more about
different formulae and their effect on the
magnitude of the index.
Quantitative Aptitude & Business Statistics: Index Numbers 48
![Page 49: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/49.jpg)
Limitations of Index Numbers
Index numbers with the same base and
items are useful for a short period. One
has, therefore, to ensure that index does
not use a very remote year as the base.
One who is interpreting an index must be
familiar with general aspects of the
economy and the factors relevant in this
regard.
Quantitative Aptitude & Business Statistics: Index Numbers 49
![Page 50: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/50.jpg)
As we know, our indices are of prices and quantities. The question is: does our index reflect a change in the quality of a product or item?
Apart from quality changes, there are other aspects, that are pertinent while we are interpreting index numbers. We have to ask whether the weights assigned to different items are appropriate.
Quantitative Aptitude & Business Statistics: Index Numbers 50
![Page 51: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/51.jpg)
Some Important Price Indexes
Consumer Price Index (CPI)
Primary measure of the cost of living .
Based on 985 items including food,
housing, clothing, transportation, and
medical items.
Weighted aggregate price index with fixed
weights derived from a usage survey.
Published monthly by the Bureau of
Statistics.
Its base period is 2001-02 with an index of
100.
Quantitative Aptitude & Business Statistics: Index Numbers 51
![Page 52: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/52.jpg)
Methods of Constructing Consumer
Price index
Aggregate Expenditure method
Family budget method
Aggregate expenditure method is a weighted aggregated price index where weights are the base period quantities. (Laspyre’s Index number)
Quantitative Aptitude & Business Statistics: Index Numbers 52
100qp
qpCPI
00
01
![Page 53: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/53.jpg)
Family budget method is a weighted
aggregated of price relatives method
where index is obtained by taking the
average of weighted price relatives and
the value weights are (P0q0) are used
Quantitative Aptitude & Business Statistics: Index Numbers 53
V
PVCPI
100P
P
0
1
00 Q.PV
![Page 54: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/54.jpg)
Some Important Price Indexes
Producer Price Index (PPI)
Measures the monthly changes in prices in
primary markets .
Used as a leading indicator of the future
trend of consumer prices and the cost of
living.
Covers raw, manufactured, and processed
goods at each level of processing.
Quantitative Aptitude & Business Statistics: Index Numbers 54
![Page 55: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/55.jpg)
Includes the output of manufacturing,
agriculture, forestry, fishing, mining, gas and
electricity, and public utilities.
Weighted average of price relatives using the
Laspeyres method.
Quantitative Aptitude & Business Statistics: Index Numbers 55
![Page 56: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/56.jpg)
Problem
From the following data compute the
Fisher’s Price index number.
Commodity Base Year Current Year
Price Quantity Price Quantity
A
B
C
D
1
2
3
4
6
7
8
9
5
4
3
2
8
7
6
5
56 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 57: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/57.jpg)
Fisher’s Index number is calculated by
42.141
1002
1004800
9600
10060
96
80
100
100qp
qp
qp
qpp
PLP
10
11
00
01
01
01
Quantitative Aptitude & Business Statistics: Index Numbers 57
![Page 58: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/58.jpg)
Problem Calculate chain indices and fixed
base indices with 2000 as base from
the following data
Year 2000 2001 2002 2003 2004
Price of item
Per .Kg
20 25 30 45 63
58 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 59: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/59.jpg)
Quantitative Aptitude & Business Statistics: Index Numbers 59
Year Price of Rice
(Rs. per Kg)
FBIN
2000 20 100
2001 25 (25/20)*100=125
2002 30 (30/20)*100=150
2003 45 (45/20)*100=225
2004 63 (63/20)*100=315
![Page 60: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/60.jpg)
Problem
Convert the following Link relatives
in to price relatives taking 2000 as
base
Year 2000 2001 2002 2003 2004
Link Relative
80 125 120 150 140
60 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 61: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/61.jpg)
Quantitative Aptitude & Business Statistics: Index Numbers
6
1
Year Link relatives
(LR’s)
Price Relatives
(PR’s)
2000 80 100
2001 125 (125/100)*100=125
2002 120 (120/100)*125=150
2003 150 (150/100)*150=225
2004 140 (140/100)*225=315
![Page 62: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/62.jpg)
Problem
From the following data compute the
Consumers Price index number.
(Aggregate Expenditure method
Commodity Base Year Current Year
Price Quantity Price Quantity
A
B
C
D
1
2
3
4
6
7
8
9
5
4
3
2
8
7
6
5
62 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 63: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/63.jpg)
Price Relative= PV
6
14
24
36
500
200
100
50
3000
2800
2400
1800
80 10000
00qpV
Quantitative Aptitude & Business Statistics: Index Numbers 63
100P
P
0
1
![Page 64: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/64.jpg)
125
80
1000
V
PVCPI
Quantitative Aptitude & Business Statistics: Index Numbers 64
![Page 65: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/65.jpg)
Problem
From the following data compute the
Consumers Price index number.
(Family budget method
Commodity Base Year Current Year
Price Quantity Price Quantity
A
B
C
D
1
2
3
4
6
7
8
9
5
4
3
2
8
7
6
5
65 Quantitative Aptitude & Business Statistics: Index Numbers
![Page 66: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/66.jpg)
125
10080
100
100qp
qpCPI
00
01
Quantitative Aptitude & Business Statistics: Index Numbers 66
![Page 67: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/67.jpg)
1. The best average in the construction
of index number is
(a) median
(b) geometric mean
(c) mode
(d) arithmetic mean
Quantitative Aptitude & Business Statistics: Index Numbers 67
![Page 68: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/68.jpg)
1. The best average in the construction
of index number is
(a) median
(b) geometric mean
(c) mode
(d) arithmetic mean
Quantitative Aptitude & Business Statistics: Index Numbers 68
![Page 69: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/69.jpg)
2.The paaschee’s index number is based
on
(a) base year quantities
(b) current year quantities
(c) average of current and base years
(d) none of these
6
9
![Page 70: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/70.jpg)
2.The paaschee’s index number is based
on
(a) base year quantities
(b) current year quantities
(c) average of current and base years
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 70
![Page 71: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/71.jpg)
3.Fisher’s ideal index is the
(a) arithmetic mean of Laspyre’s and
Paasche’s index
(b)median of Laspyre’s and Paasche’s
index
(c) geometric mean of Laspyre’s and
Paasche’s index
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 71
![Page 72: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/72.jpg)
3.Fisher’s ideal index is the
(a) arithmetic mean of Laspyre’s and
Paasche’s index
(b) median of Laspyre’s and Paasche’s
index
(c) geometric mean of Laspyre’s and
Paasche’s index
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 72
![Page 73: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/73.jpg)
4.The circular test is satisfied by
(a) simple aggregate index
(b) Paasche’s index
(c) Laspyre’s index
(d) Fisher’s index
Quantitative Aptitude & Business Statistics: Index Numbers 73
![Page 74: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/74.jpg)
4.The circular test is satisfied by
(a) simple aggregate index
(b) Paasche’s index
(c) Laspyre’s index
(d) Fisher’s index
Quantitative Aptitude & Business Statistics: Index Numbers 74
![Page 75: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/75.jpg)
5.The index used to measure changes in
total money value called
(a) price index
(b) quantity index
(c) value index
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 75
![Page 76: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/76.jpg)
5.The index used to measure changes in
total money value called
(a) price index
(b) quantity index
(c) value index
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 76
![Page 77: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/77.jpg)
6.Fisher’s ideal index number satisfied by
(a) circular test
(b) time reversal
(c) factor reversal test
(d) both (b) and (c)
Quantitative Aptitude & Business Statistics: Index Numbers 77
![Page 78: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/78.jpg)
6.Fisher’s ideal index number satisfied by
(a) circular test
(b) time reversal
(c) factor reversal test
(d) both (b) and (c)
Quantitative Aptitude & Business Statistics: Index Numbers 78
![Page 79: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/79.jpg)
7.The weights used in quantity index are
(a) percentage of total quantity
(b) average quantity
(c) prices
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 79
![Page 80: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/80.jpg)
7.The weights used in quantity index are
(a) percentage of total quantity
(b) average quantity
(c) prices
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 80
![Page 81: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/81.jpg)
8.Symbolically Pon x P no = 1 stands for
(a) circular test
(b) factor reversal test
(c) time reversal test
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 81
![Page 82: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/82.jpg)
8.Symbolically P on x P no = 1 stands for
(a) circular test
(b) factor reversal test
(c) time reversal test
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 82
![Page 83: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/83.jpg)
9.Fixed base index numbers and chain
indexes are
(a) same
(b) different
(c) equal to 100
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 83
![Page 84: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/84.jpg)
9.Fixed base index numbers and chain
indexes are
(a) same
(b) different
(c) equal to 100
(d) none of these
Quantitative Aptitude & Business Statistics: Index Numbers 84
![Page 85: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/85.jpg)
10.Weighted average of price relatives
index using base year value as weighted
is called
(a) Laspyre’s index
(b) Paasche’s index
(c) Bowley’s index
(d) Fisher’s index
Quantitative Aptitude & Business Statistics: Index Numbers 85
![Page 86: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/86.jpg)
10.Weighted average of price relatives
index using base year value as weighted
is called
(a) Laspyre’s index
(b) Paasche’s index
(c) Bowley’s index
(d) Fisher’s index
Quantitative Aptitude & Business Statistics: Index Numbers 86
![Page 87: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/87.jpg)
11. A time series is deflated by
using the following formulae
(a) Deflated value =
Quantitative Aptitude & Business Statistics: Index Numbers 87
yearcurrentofindexprice
valuecurrent
(b) Deflated value = yearbaseofindexprice
valuecurrent
(c) Deflated value =
yearpreviousofindexprice
valuecurrent
(d) none of these
![Page 88: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/88.jpg)
11. A time series is deflated by
using the following formulae
(a) Deflated value =
Quantitative Aptitude & Business Statistics: Index Numbers 88
yearcurrentofindexprice
valuecurrent
(b) Deflated value = yearbaseofindexprice
valuecurrent
(c) Deflated value = yearpreviousofindexprice
valuecurrent
(d) none of these
![Page 89: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/89.jpg)
12. Shifted price index is calculated as
Quantitative Aptitude & Business Statistics: Index Numbers 89
(a) 100*
obtaintoisitwhichonyearofindexprice
indexpriceoriginal
(b) 100xindexpriceoriginal
shiftedbetoisitwhichonyearofindexprice
(c)
100xobtainedbetoisitwhichonyearofindexprice
yearcurrentofindexchainindexpriceoriginal
(d) none of these
![Page 90: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/90.jpg)
12.Shifted price index is calculated as
Quantitative Aptitude & Business Statistics: Index Numbers 90
(a) 100obtaintoisitwhichonyearofindexprice
indexpriceoriginal
(b) 100x
indexpriceoriginal
shiftedbetoisitwhichonyearofindexprice
(c) 100x
obtainedbetoisitwhichonyearofindexprice
yearcurrentofindexchainindexpriceoriginal
(d) none of these
![Page 91: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/91.jpg)
13.Atechnique to link two or
more index number Series
is known as
A) Splicing
B) Base shifting
C) Deflating
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 91
![Page 92: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/92.jpg)
13.Atechnique to link two or more index
number Series is known as
A) Splicing
B) Base shifting
C) Deflating
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 92
![Page 93: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/93.jpg)
14.The Cost of Living index always
A) Weighted index
B) Price index
C) Quantity index
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 93
![Page 94: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/94.jpg)
14.The Cost of Living index always
A) Weighted index
B) Price index
C) Quantity index
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 94
![Page 95: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/95.jpg)
15.Marshall -Edge worth Formula does
satisfy ----test
a) Time reversal test
b) Factor reversal test
c) Circular test
d) none
Quantitative Aptitude & Business Statistics: Index Numbers 95
![Page 96: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/96.jpg)
15.Marshall -Edge worth Formula does
satisfy ----test
a) Time reversal test
b) Factor reversal test
c) Circular test
d) none
Quantitative Aptitude & Business Statistics: Index Numbers 96
![Page 97: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/97.jpg)
16. If the old series is connected, with the
new series of index numbers it is know
as
A) Backward splicing
B) Base shifting
C) Forward splicing
D) None of the above
Quantitative Aptitude & Business Statistics: Index Numbers 97
![Page 98: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/98.jpg)
16. If the old series is connected, with the
new series of index numbers it is know
as
A) Backward splicing
B) Base shifting
C) Forward splicing
D) None of the above
Quantitative Aptitude & Business Statistics: Index Numbers 98
![Page 99: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/99.jpg)
17.If with a rise of 10% in prices the
salaries are increased by 20%, the real
salary increases by
A) 10%
B) More than 10%
C) 20%
D) Less than 10%
Quantitative Aptitude & Business Statistics: Index Numbers 99
![Page 100: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/100.jpg)
17.If with a rise of 10% in prices the
salaries are increased by 20%, the real
salary increases by
A) 10%
B) More than 10%
C) 20%
D) Less than 10%
Quantitative Aptitude & Business Statistics: Index Numbers 100
![Page 101: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/101.jpg)
18. The ______ is satisfied when
P ab P bc Pca = 1
A) Time reversal test
B) Factor reversal test
C) Circular test
D) Unit test
Quantitative Aptitude & Business Statistics: Index Numbers 101
![Page 102: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/102.jpg)
18. The ______ is satisfied when
P ab P bc Pca = 1
A) Time reversal test
B) Factor reversal test
C) Circular test
D) Unit test
Quantitative Aptitude & Business Statistics: Index Numbers 102
![Page 103: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/103.jpg)
19. The total sum of the values of a given
year divided by the sum of the values of
the base year is
A) Price index.
B) Quantity index
C) Value index.
D) None of these.
Quantitative Aptitude & Business Statistics: Index Numbers 103
![Page 104: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/104.jpg)
19. The total sum of the values of a given
year divided by the sum of the values of
the base year is
A) Price index.
B) Quantity index
C) Value index.
D) None of these.
Quantitative Aptitude & Business Statistics: Index Numbers 104
![Page 105: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/105.jpg)
20. Fisher's Ideal formula does not
satisfy_________ test.
A) Circular test
B) Unit test
C) Time Reversal test
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 105
![Page 106: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/106.jpg)
20. Fisher's Ideal formula does not
satisfy_________ test.
A) Circular test
B) Unit test
C) Time Reversal test
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 106
![Page 107: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/107.jpg)
21. If with rise of 10% in prices the
wages are increased by 20%. Find the
percentage of real wage increase
A) 109.29%
B) 9.09%
C) 9.29%
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 107
![Page 108: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/108.jpg)
21. If with rise of 10% in prices the
wages are increased by 20%. Find the
percentage of real wage increase
A) 109.29%
B) 9.09%
C) 9.29%
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 108
![Page 109: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/109.jpg)
22. The price level of a country in a
certain year has increased 20% over the
base period. The Index number is
_____________
A) 20
B) 120
C) 220
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 109
![Page 110: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/110.jpg)
22. The price level of a country in a
certain year has increased 20% over the
base period. The Index number is
_____________
A) 20
B) 120
C) 220
D) None of these
Quantitative Aptitude & Business Statistics: Index Numbers 110
![Page 111: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/111.jpg)
23. The consumer price index is an
example of a
A) Laspeyre’s index
B) Paasche’s index
C) Simple aggregate price index
D) Base year price
Quantitative Aptitude & Business Statistics: Index Numbers 111
![Page 112: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/112.jpg)
23. The consumer price index is an
example of a
A) Laspeyre’s index
B) Paasche’s index
C) Simple aggregate price index
D) Base year price
Quantitative Aptitude & Business Statistics: Index Numbers 112
![Page 113: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/113.jpg)
24. The base year is
A) Is the reference year from which
changes in the index are measured
B) Is always last year
C) Is the first year the index is created
D) Is the current year the index is created
Quantitative Aptitude & Business Statistics: Index Numbers 113
![Page 114: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/114.jpg)
24. The base year is
A) Is the reference year from which
changes in the index are measured
B) Is always last year
C) Is the first year the index is created
D) Is the current year the index is created
Quantitative Aptitude & Business Statistics: Index Numbers 114
![Page 115: Quantitative Aptitude & Business Statistics INDEX NUMBERS · Factor Reversal Test A method satisfies factor reversal test if it gives where P01 is the price index for the current](https://reader030.vdocument.in/reader030/viewer/2022011816/5e769271fd70c319972d2c08/html5/thumbnails/115.jpg)
THE END
Index Numbers