Introduction to Index Number Test

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Introduction to Index Number Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Using $$2005$$ as base year , the price of a commodity in $$2006$$ are 118. Calculate the index number for 2005 if 2006 is taken as the base year.

A
84.75

B
82.18

C
81.18

D
78.07

Solution

$$N=1$$ (Since only one commodity)
Take price $$=Rs.100$$ as base price for $$2005$$
$$\implies p_1=100$$
$$p_0=118$$ (given)
$$\implies $$ index no. $$=\cfrac{1}{N}(\sum\cfrac{p_1}{p_0}\times 100)$$
$$\implies\cfrac{1}{1}(\sum\cfrac{100}{118}\times 100)=84.775\approx 84.75$$

Question 2

1 / -0

Calculate price index for the following data by applying weighted average of price relative method.

Item	Price in 1991 (Rs)	Price in 1992 (Rs)	Quantity in 1991
wheat	2.00	2.50	40 kg
sugar	3.00	3.25	20 kg
Milk	1.50	1.75	10 litre

116.64

117.74

165.43

113.34 Solution

$$Item$$	$$Price\,in\,1991 (Rs)$$ $$P_0$$	$$Price\,in\,1992\,(Rs)$$ $$P_1$$	$$weight $$	$$P_0w$$	$$P_1w$$
$$Wheat$$	$$2.00$$	$$2.50$$	$$40\,Kg$$	$$80$$	$$100$$
$$Sugar$$	$$3.00$$	$$3.25$$	$$20\,Kg$$	$$60$$	$$65$$
$4Milk$$	$$1.50$$	$$1.75$$	$$10\,liter$$	$$15$$	$$17.5$$
$$Total$$				$$\sum P_0w=155$$	$$\sum P_1w=182.5$$

$$\Rightarrow$$ $$P_{01}=\dfrac{\sum P_1 w}{\sum P_0 w}\times 100=\dfrac{182.5}{155}\times 100=117.74$$

Question 3
1 / -0

The formula for a simple aggregative price index is:

A
$$P_{01} = \dfrac{\Sigma p_1}{\Sigma p_0} \times 100$$

B
$$P_{01} = \dfrac{1}{N} { \sum ( \dfrac{p_{1}}{p_{0}}} \times 100)$$

C
Either A or B

D
None of the above

Solution

The formula for Simple Aggregative Price Index is given by:
$$P_{01} = \dfrac{\Sigma p_1}{\Sigma p_0} \times 100$$

Where:
$$\Sigma{p_0}$$ = sum of total prices in base year.
$$\sum{p_1}$$ = sum of total prices in current year.
$$P_{01}$$ = index number of the current year

Question 4

1 / -0

Directions For Questions

Items	Base Year	Base Year	Current Year	Current Year
	$$P_{0} (Rs.)$$	$$Q_{0}$$	$$P_{1}(Rs.)$$	$$Q_1$$
$$A$$	$$4$$	$$20$$	$$10$$	$$15$$
$$B$$	$$8$$	$$4$$	$$16$$	$$5$$
$$C$$	$$2$$	$$10$$	$$4$$	$$12$$
$$D$$	$$10$$	$$5$$	$$20$$	$$6$$

...view full instructions

Calculate Fisher Price Index Number.

$$220.00$$

$$216.30$$

$$219.12$$

$$221.98$$

Solution

ITEM	Base Year $$P_0$$	Base Year $$Q_0$$	Current Year $$P_1$$	Current Year $$Q_1$$	$$P_0Q_0$$	$$P_1Q_0$$	$$P_0Q_1$$	$$P_1Q_1$$
$$A$$	$$4$$	$$20$$	$$10$$	$$15$$	$$80$$	$$200$$	$$60$$	$$150$$
$$B$$	$$8$$	$$4$$	$$16$$	$$5$$	$$32$$	$$64$$	$$40$$	$$80$$
$$C$$	$$2$$	$$10$$	$$4$$	$$12$$	$$20$$	$$40$$	$$24$$	$$48$$
$$D$$	$$10$$	$$5$$	$$20$$	$$6$$	$$50$$	$$100$$	$$60$$	$$120$$
					$$182$$	$$404$$	$$184$$	$$398$$

Laspeyres Price Index Number
$$P^{L}_{01} = \dfrac {\sum P_{1}Q_{0}}{\sum P_{0}Q_{0}}\times 100 = \dfrac {404}{182}\times 100 = 221.98$$
Paasche Price Index Number
$$P^{P}_{01} = \dfrac {\sum P_{1}Q_{1}}{\sum P_{0}Q_{1}}\times 100 = \dfrac {398}{184}\times 100 = 216.30$$
Fisher Price Index Number
$$P^{F}_{01} = \sqrt {\sum P^{L}_{01}\times P^{P}_{01}} = \sqrt {(221.98 \times 216.3)} = 219.12$$.

Question 5
1 / -0

_______ is used in calculating the purchasing power of money and real wage.

A
CPI

B
WPI

C
IIP

D
None
Question 6
1 / -0

Index nos. show _______ changes rather than absolute amounts of change.

A
Relative

B
Percentage

C
Both (a) and (b)

D
None of above
Question 7
1 / -0

Laspeyre's index and Dorbish/Bowley index of a city for the year 2008 are $$104.8$$ and $$111.9$$, find the index number under Paache's method___.

A
$$116.60$$

B
$$114.35$$

C
$$119$$

D
$$117.90$$
Question 8
1 / -0

An index number of 250 indicates that __________.

A
the value is two hundred fifty times that of the base period

B
the value is two hundred fifty more than that of the base period

C
the value is two and half times that of the base period

D
none of the above

Question 9

1 / -0

Directions For Questions

Items	Base Year	Base Year	Current Year	Current Year
	$$P_{0} (Rs.)$$	$$Q_{0}$$	$$P_{1}(Rs.)$$	$$Q_1$$
$$A$$	$$4$$	$$20$$	$$10$$	$$15$$
$$B$$	$$8$$	$$4$$	$$16$$	$$5$$
$$C$$	$$2$$	$$10$$	$$4$$	$$12$$
$$D$$	$$10$$	$$5$$	$$20$$	$$6$$

...view full instructions

Calculate Laspeyres Price Index Number.

$$220.00$$

$$216.30$$

$$219.12$$

$$221.98$$

Solution

Item	Base Year $$P_0$$	Base Year $$Q_0$$	Current Year $$P_1$$	Current Year $$Q_1$$	$$P_0Q_0$$	$$P_1Q_0$$
$$A$$	$$4$$	$$20$$	$$10$$	$$15$$	$$80$$	$$200$$
$$B$$	$$8$$	$$4$$	$$16$$	$$5$$	$$32$$	$$64$$
$$C$$	$$2$$	$$10$$	$$4$$	$$12$$	$$20$$	$$40$$
$$D$$	$$10$$	$$5$$	$$20$$	$$6$$	$$50$$	$$100$$
					$$182$$	$$404$$

Laspeyres Price Index Number
$$P^{L}_{01} = \dfrac {\sum P_{1}Q_{0}}{\sum P_{0}Q_{0}}\times 100 = \dfrac {404}{182}\times 100 = 221.98$$

Question 10
1 / -0

_______ index numbers measure and permit comparison of the prices of certain goods.

A
Quantity

B
Quality

C
Price

D
Product

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Introduction to Index Number Test - 18

Result

Introduction to Index Number Test - 18

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SHARING IS CARING

Question 1

84.75

82.18

81.18

78.07

Solution

Question 2

116.64

117.74

165.43

113.34

Solution

Question 3

$$P_{01} = \dfrac{\Sigma p_1}{\Sigma p_0} \times 100$$

$$P_{01} = \dfrac{1}{N} { \sum ( \dfrac{p_{1}}{p_{0}}} \times 100)$$

Either A or B

None of the above

Solution

Question 4

$$220.00$$

$$216.30$$

$$219.12$$

$$221.98$$

Solution

Question 5

CPI

WPI

IIP

None

Question 6

Relative

Percentage

Both (a) and (b)

None of above

Question 7

$$116.60$$

$$114.35$$

$$119$$

$$117.90$$

Question 8

the value is two hundred fifty times that of the base period

the value is two hundred fifty more than that of the base period

the value is two and half times that of the base period

none of the above

Question 9

$$220.00$$

$$216.30$$

$$219.12$$

$$221.98$$

Solution

Question 10

Quantity

Quality

Price

Product

User

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