Calculate Walsh’s Price Index Number for the following data. Commodity Base year Current year Price p0 Quantity q0 Price p1 Quantity q1 I 8 30 12 25 II 10 42 20 16

Commodity Base Year Current Year q0q1 `sqrt("q"_0"q"_1)` `"p"_1/sqrt("q"_0"q"_1)` `"p"_0/sqrt("q"_0"q"_1)` p0 q0 p1 q1 I 8 30 12 25 750 27.39 328.68 219.12 II 10 42 20 16 672 25.92 518.40 259.20 Total – – – – – – 847.08 478.32 From the table,`sum"p"_1sqrt("q"_0"q"_1) = 847.08, sum"p"_0sqrt("q"_0"q"_1) = 478.32` Walsh’s Price Index Number: P01(W) = `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100` = `(847.08)/(478.32) xx 100` = 177.09

Solve the following problem : Calculate Walsh’s Price Index Number for the following data. - Mathematics and Statistics

प्रश्न

Calculate Walsh’s Price Index Number for the following data.

Commodity	Base year		Current year
	Price p₀	Quantity q₀	Price p₁	Quantity q₁
I	8	30	12	25
II	10	42	20	16

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उत्तर

Commodity	Base Year		Current Year		q₀q₁	`sqrt("q"_0"q"_1)`	`"p"_1/sqrt("q"_0"q"_1)`	`"p"_0/sqrt("q"_0"q"_1)`
	p₀	q₀	p₁	q₁
I	8	30	12	25	750	27.39	328.68	219.12
II	10	42	20	16	672	25.92	518.40	259.20
Total	–	–	–	–	–	–	847.08	478.32

From the table,
`sum"p"_1sqrt("q"_0"q"_1) = 847.08, sum"p"_0sqrt("q"_0"q"_1) = 478.32`

Walsh’s Price Index Number:

P₀₁(W) = `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

= `(847.08)/(478.32) xx 100`

= 177.09

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Construction of Index Numbers - Weighted Aggregate Method

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 4.08 Q 4.07 Q 4.09

पाठ 5: Index Numbers - Miscellaneous Exercise 5 [पृष्ठ ९३]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board

पाठ 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.08 | पृष्ठ ९३

संबंधित प्रश्‍न

Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and MarshallEdgeworth’s Price index numbers.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	8	20	11	15
B	7	10	12	10
C	3	30	5	25
D	2	50	4	35

Calculate Walsh’s Price Index Number.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
I	10	12	20	9
II	20	4	25	8
III	30	13	40	27
IV	60	29	75	36

Given that ∑p₀q₀ = 220, ∑p₀q₁ = 380, ∑p₁q₁ = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.

Find x in the following table if Laspeyre’s and Paasche’s Price Index Numbers are equal.

Commodity	Base Year		Current year
Commodity	Price	Quantity	Price	Quantity
A	2	10	2	5
B	2	5	x	2

If Dorbish-Bowley's and Fisher's Price Index Numbers are 5 and 4, respectively, then find Laspeyre's and Paasche's Price Index Numbers.

Laspeyre’s Price Index Number is given by ______.

Fill in the blank :

Paasche’s Price Index Number is given by _______.

Fill in the blank :

Dorbish-Bowley’s Price Index Number is given by _______.

State whether the following is True or False :

`(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is Dorbish-Bowley’s Price Index Number.

`(sum"p"_0sqrt("q"_0"q"_1))/(sum"p"_1sqrt("q"_0"q"_1)) xx 100` is Walsh’s Price Index Number.

Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data

Commodity	Base Year		Current Year
	Price p₀	Quantity q₀	Price p₁	Quantity q₁
A	3	x	2	5
B	4	6	3	5

Solve the following problem :

Find x if Paasche’s Price Index Number is 140 for the following data.

Commodity	Base Year		Current Year
	Price p₀	Quantity q₀	Price p₁	Quantity q₁
A	20	8	40	7
B	50	10	60	10
C	40	15	60	x
D	12	15	15	15

Solve the following problem :

If `sum"p_"0"q"_0 = 120, sum "p"_0"q"_1 = 160, sum "p"_1"q"_1 = 140, and sum "p"_1"q"+0` = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.

Solve the following problem :

Given that `sum "p"_0"q"_0 = 130, sum "p"_1"q"_1 = 140, sum "p"_0"q"_1 = 160, and sum "p"_1"q"_0 = 200`, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.

Choose the correct alternative:

Price Index Number by using Weighted Aggregate Method is given by

Marshall-Edgeworth's Price Index Number is given by ______

State whether the following statement is True or False:

Walsh’s Price Index Number is given by `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

State whether the following statement is True or False:

`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100` is Paasche’s Price Index Number

Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	10	9	50	8
B	20	5	60	4
C	30	7	70	3
D	40	8	80	2

Calculate Walsh’s price Index Number for the following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
I	10	12	40	3
II	20	2	25	8
III	30	3	50	27
IV	60	9	90	36

If Laspeyre’s and Paasche’s Price Index Numbers are 50 and 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers

Given the following table, find Walsh’s Price Index Number by completing the activity.

Commodity	p₀	q₀	p₁	q₁	q₀q₁	`sqrt("q"_0"q"_1)`	p₀`sqrt("q"_0"q"_1)`	p₁`sqrt("q"_0"q"_1)`
I	20	9	30	4	36	`square`	`square`	180
II	10	5	50	5	`square`	5	50	`square`
III	40	8	10	2	16	`square`	160	`square`
IV	30	4	20	1	`square`	2	`square`	40
Total	–	–	–	–			390	`square`

Walsh’s price Index Number is

P₀₁(W) = `square/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

= `510/square xx 100`

= `square`

If ∑ p₀q₀ = 120, ∑ p₀q₁ = 160, ∑ p₁q₁= 140, ∑ p₁q_o= 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.

In the following table, Laspeyre's and Paasche's Price Index Numbers are equal. Complete the following activity to find x :

Commodity	Base Year		Current year
Commodity	Price	Quantity	Price	Quantity
A	2	10	2	5
B	2	5	x	2

Solution: P₀₁(L) = P₀₁(P)

`(sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = square/(sum "p"_0"q"_1) xx 100`

`(20 + 5x)/square xx 100 = square/14 xx 100`

∴ x = `square`

Complete the following activity to calculate, Laspeyre's and Paasche's Price Index Number for the following data :

Commodity	Base Year		Current Year
Commodity	Price p₀	Quantity q₀	Price p₁	Quantity q₁
I	8	30	12	25
II	10	42	20	16

Solution:

Commodity	Base Year		Current Year		p₁q₀	p₀q₀	p₁q₁	p₀q₁
	p₀	q₀	p₁	q₁	p₁q₀	p₀q₀	p₁q₁	p₀q₁
I	8	30	12	25	360	240	300	200
II	10	42	20	16	840	420	320	160
Total					`bb(sump_1q_0=1200)`	`bb(sump_0q_0=660)`	`bb(sump_1q_1=620)`	`bb(sump_0q_1=360)`

Laspeyre's Price Index Number:

P₀₁(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100 = square/660xx100`

∴ P₀₁(L) = `square`

Paasche 's Price Index Number:

P₀₁(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100=(620)/(square) xx 100`

∴ P₀₁(P) = `square`

Solve the following problem : Calculate Walsh’s Price Index Number for the following data. - Mathematics and Statistics

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