Construct Paasche’s index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 We know that, Paasche’s index price method formula P 01 P = ∑ p 1 q 1 ∑ p 0 q 1 × 100 Now, P 01 P = 1880 1344 × 100 = 139 . 7 ∴ P 01 P = 139 . 7 , is Paasche’s index number.

Construct Fisher ideal index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 We know that, Fisher’s ideal index formula is P 01 F = ∑ p 1 q 0 ∑ p 0 q 0 × ∑ p 1 q 1 ∑ p 0 q 1 Now, P 01 F = 1900 1360 × 1880 1344 = 139 . 7 × 139 . 7 = 139 . 7 . ∴ P 01 F = 139 . 7 , is Fisher ideal index number.

Construct the price indices from the following data by applying Fisher ideal number by taking 2010 as the base year Commodity 2010 2011 Price in Rs Quantity Price in Rs Quantity A 15 15 22 12 B 20 5 27 4 C 4 10 7 5

Given that, Commodity 2010 2011 Price in Rs Quantity Price in Rs Quantity A 15 15 22 12 B 20 5 27 4 C 4 10 7 5 Let p 0 , p 1 are the prices of commodities of base year 2010 and q 0 , q 1 are quantities of the commodities of current year 2011 . Tabular form: Commodity 2010 2011 Price in Rs ( p 0 ) Quantity ( q 0 ) Price in Rs ( p 1 ) Quantity q 1 p 1 q 0 p 1 q 1 p 0 q 1 p 0 q 0 A 15 15 22 12 330 264 180 225 B 20 5 27 4 135 108 80 100 C 4 10 7 5 70 35 20 40 We know that, Laspeyre’s price index method P 01 L = ∑ p 1 q 0 ∑ p 0 q 0 × 100 Now, P 01 L = 535 365 × 100 = 146 . 5 We know that, Paasche’s price index method P 01 P = ∑ p 1 q 1 ∑ p 0 q 1 × 100 ⇒ 407 280 × 100 = 145 . 35 We know that, in Fisher price index method P 01 F = P 01 L × P 01 P = 146 . 5 × 145 . 35 = 145 . 96 . ∴ P 01 F = 145 . 96 , is price index .

Construct Marshall-Edgeworth index for the following data taking 2014 as base year Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36

Given that, Items year 2014 year 2015 Price Quantity Price Quantity A 6 50 10 56 B 2 100 2 120 C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 Let p 0 , q 0 are prices and quantities of items of base year 2014 and p 1 , q 1 are prices and quantities of items of current year 2015 . Tabular form: Items year 2014 year 2015 Price p 0 Quantity q 0 Price p 1 Quantity q 1 p 0 q 0 p 1 q 0 p 0 q 1 p 1 q 1 A 6 50 10 56 300 500 336 560 B 2 100 2 120 200 200 240 240 C 4 60 6 60 240 360 240 360 D 10 30 12 24 300 360 240 288 E 8 40 12 36 320 480 288 432 ∑ p 0 q 0 = 1360 ∑ p 1 q 0 = 1900 ∑ p 0 q 1 = 1344 ∑ p 1 q 1 = 1880 We know that, Marshall-Edgeworth index P 01 M = ∑ p 1 q 0 + ∑ p 1 q 1 ∑ p 0 q 0 + ∑ p 0 q 1 × 100 Now, P 01 M = 1900 + 1880 1360 + 1344 × 100 = 3780 2704 = 139 . 8 ∴ P 01 M = 139 . 8 , is Marshall-Edgeworth index number.

Construct the price indices from the following data by applying Lapeyre’s method Commodity 2010 2011 Price in Rs Quantity Price in Rs Quantity A 15 15 22 12 B 20 5 27 4 C 4 10 7 5

Given that, Commodity 2010 2011 Price in Rs Quantity Price in Rs Quantity A 15 15 22 12 B 20 5 27 4 C 4 10 7 5 Let p 0 , p 1 are the prices of commodities of base year 2010 and q 0 , q 1 are quantities of the commodities of current year 2011 . Tabular form: Commodity 2010 2011 Price in Rs ( p 0 ) Quantity ( q 0 ) Price in Rs ( p 1 ) Quantity q 1 p 1 q 0 p 0 q 0 A 15 15 22 12 330 225 B 20 5 27 4 135 100 C 4 10 7 5 70 40 We know that, Laspeyre’s price index method P 01 L = ∑ p 1 q 0 ∑ p 0 q 0 × 100 Now, P 01 L = 535 365 × 100 = 146 . 5 ∴ P 01 L = 146 . 5 is the Laspeyre’s price index.

Construct the price indices from the following data by applying Paasche’s method Commodity 2010 2011 Price in Rs Quantity Price in Rs Quantity A 15 15 22 12 B 20 5 27 4 C 4 10 7 5

Given that, Commodity 2010 2011 Price in Rs Quantity Price in Rs Quantity A 15 15 22 12 B 20 5 27 4 C 4 10 7 5 Let p 0 , p 1 are the prices of commodities of the base year 2010 and q 0 , q 1 are quantities of the commodities of the current year 2011 . Tabular form: Commodity 2010 2011 Price in Rs ( p 0 ) Quantity ( q 0 ) Price in Rs ( p 1 ) Quantity q 1 p 1 q 1 p 0 q 1 A 15 15 22 12 264 180 B 20 5 27 4 108 80 C 4 10 7 5 35 20 We know that, Paasche’s price index method P 01 P = ∑ p 1 q 1 ∑ p 0 q 1 × 100 ⇒ 407 280 × 100 = 145 . 35 ∴ P 01 P = 145 . 35 is Paasche’s index number.

Construct MarshallEdgeworth price index number for the following data taking 2016 as base year Commodity Year2016 Year2017 Price Quantity Price Quantity A 6 42500 3 23100 B 42 13680 53 12450 C 5 36320 7 23065 D 27 23140 10 80400 E 4 15700 8 11600

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The weighted aggregative price index numbers for $2001$ with $2000$ as the base year using Paasche's Index Number is:

Commodity	Price (in $254240$ )		Quantities
	$2000$	$2001$	$2000$	$10$
$A$	$10$	$12$	$20$	$22$
$4$	$15700$	$8$	$11600$	$62800$
$C$	$5$	$6$	$10$	$11$
$D$	$4$	$4$	$7$	$8$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

If Laspeyre’s index number is

110

and Fisher’s ideal index number is

\sum p_{1} q_{1} = 1193540

. Then Paasche’s Index number is

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Fisher’s ideal index does not satisfy ______ test

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The weighted aggregative price index numbers for $2001$ with $2000$ as the base year using Marshal - Edgeworth Index Number is:

Commodity	Price (in $₹$ )		Quantities
	$2000$	$2001$	$2000$	$2001$
$A$	$10$	$12$	$20$	$22$
$B$	$8$	$8$	$16$	$18$
$C$	$5$	$6$	$10$	$11$
$D$	$4$	$4$	$7$	$8$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The weighted aggregative price index hymbers for $2001$ with $2000$ as the base year using Fisher's Index Number is

Commodity	Price (in $₹$ )		Quantities
	$2000$	$2001$	$2000$	$2001$
$A$	$10$	$12$	$20$	$22$
$B$	$8$	$8$	$16$	$18$
$C$	$5$	$6$	$10$	$11$
$D$	$4$	$4$	$7$	$8$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

The value of the base time period serves as a standard point of comparison:

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Fisher's ideal formula does not satisfy test______.

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct the index of 2014 from the following data for the year 2012 taking 2011 as base year as base using geometric mean

Item	Price Rs in $2014$	Price Rs in $2015$
A	$6$	$10$
B	$2$	$2$
C	$4$	$6$
D	$10$	$12$
E	$8$	$12$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct Paasche’s index for the following data taking 2014 as base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$6$	$50$	$10$	$56$
B	$2$	$100$	$2$	$120$
C	$4$	$60$	$6$	$60$
D	$10$	$30$	$12$	$24$
E	$8$	$40$	$12$	$36$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct the index from the following data for the year

2015

taking

2014

as base year using arithmetic mean

Item	Price Rs in $2014$	Price Rs in $2015$
A	$6$	$10$
B	$2$	$2$
C	$4$	$6$
D	$10$	$12$
E	$8$	$12$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Compute price index for the following data by applying weighted average of price relative method using geometric mean.

Item	Price Rs in $2006$	Price Rs in $2007$	quantity
A	$2$	$2.5$	$40$
B	$3$	$3.25$	$20$
C	$1.5$	$1.75$	10

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

From the data given, in problem. Obtain the following Compute Index number using Fisher’s formula and show it satisfies time reversal test and factor reversal test

commodity	Base year		current year
commodity	Prices	Quantity	Price	Quantity
A	$10$	$12$	$12$	$15$
B	$7$	$15$	$5$	$20$
C	$5$	$24$	$9$	$20$
D	$16$	$5$	$14$	$5$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct Fisher ideal index for the following data taking 2014 as base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$6$	$50$	$10$	$56$
B	$2$	$100$	$2$	$120$
C	$4$	$60$	$6$	$60$
D	$10$	$30$	$12$	$24$
E	$8$	$40$	$12$	$36$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Compute price index for the following data by applying weighted average of price relative method using arithmetic mean

Item	Price Rs in $2006$	Price Rs in $2007$	quantity
A	$2$	$2.5$	$40$
B	$3$	$3.25$	$20$
C	$1.5$	$1.75$	10

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Compute Paasche’s index numbers for the 2000 from the following table(Answer up to three decimal values)

Commodity	Price		Quantity
Commodity	$2002$	$2010$	$2002$	$2010$
A	$4$	$6$	$8$	$7$
B	$3$	$5$	$10$	$8$
C	$2$	$4$	$14$	$12$
D	$5$	$7$	$19$	$11$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

If Laspeyre’s price index is

324

and Paasche’s price index is

144

then Fisher’s ideal index is

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct the price indices from the following data by applying Fisher ideal number by taking 2010 as the base year

Commodity	$2010$		$2011$
Commodity	Price in Rs	Quantity	Price in Rs	Quantity
A	$15$	$15$	$22$	$12$
B	$20$	$5$	$27$	$4$
C	$4$	$10$	$7$	$5$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct Marshall-Edgeworth index for the following data taking 2014 as base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$6$	$50$	$10$	$56$
B	$2$	$100$	$2$	$120$
C	$4$	$60$	$6$	$60$
D	$10$	$30$	$12$	$24$
E	$8$	$40$	$12$	$36$

EASY

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct the price indices from the following data by applying Lapeyre’s method

Commodity	$2010$		$2011$
Commodity	Price in Rs	Quantity	Price in Rs	Quantity
A	$15$	$15$	$22$	$12$
B	$20$	$5$	$27$	$4$
C	$4$	$10$	$7$	$5$

MEDIUM

Mathematics>Statistics>Index Numbers>Weighted Index Numbers

Construct the price indices from the following data by applying Paasche’s method

Commodity	$2010$		$2011$
Commodity	Price in Rs	Quantity	Price in Rs	Quantity
A	$15$	$15$	$22$	$12$
B	$20$	$5$	$27$	$4$
C	$4$	$10$	$7$	$5$

Important Questions on Index Numbers

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Commodity	Year $2016$		Year $2017$
Commodity	Price	Quantity	Price	Quantity
A	$6$	$42500$	$3$	$23100$
B	$4.2$	$13680$	$5.3$	$12450$
C	$5$	$36320$	$7$	$23065$
D	$2.7$	$23140$	$10$	$80400$
E	$4$	$15700$	$8$	$11600$

Construct Marshall–Edgeworth price index number for the following data taking 2016 as base year Commodity Year 2016 Year 2017 Price Quantity Price Quantity A 6 42500 3 23100 B 4.2 13680 5.3 12450 C 5 36320 7 23065 D 2.7 23140 10 80400 E 4 15700 8 11600

Important Questions on Index Numbers

Learn and Prepare for any exam you want !