Introduction to Index Number Test

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Introduction to Index Number Test - 10

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Question 1

1 / -0

Calculate the index number for the year 2006 with 1996 as the base year by the weighted average of price relatives method from the following data.

Commodity	A	B	C	D	E
Weight	40	25	5	20	10
Price(Rs) per unit 1996	32	80	1	10.24	4
Price(Rs) per unit 2006	40	120	1	15.36	3

130

133.34

138.34

139.45 Solution

$$Commodity$$	$$Weight$$ $$w$$	$$Price\,in\,1996$$ $$(Rs.)\,\,P_0$$	$$Price\,in\,2006$$ $$(Rs.)\,\,P_1$$	$$Price\,relative$$ $$I=\dfrac{P_1}{P_0}\times 100$$	$$I.w$$
$$A$$	$$40$$	$$32$$	$$40$$	$$125$$	$$5000$$
$$B$$	$$25$$	$$80$$	$$120$$	$$150$$	$$3750$$
$$C$$	$$5$$	$$1$$	$$1$$	$$100$$	$$500$$
$$D$$	$$20$$	$$10.24$$	$$15.36$$	$$150$$	$$3000$$
$$E$$	$$10$$	$$4$$	$$3$$	$$75$$	$$750$$
$$Total$$	$$100$$				$$13000$$

$$\Rightarrow$$ $$P_{01}=\dfrac{\sum Iw}{\sum w}=\dfrac{13000}{100}=130$$

Question 2
1 / -0

When the price of a divided by the price of the preceding year, we, get:

A
Value index

B
Link relative

C
Simple relative

D
None of them

Solution

$$\Rightarrow$$ When the price of divided by the price of the preceding year, we get : $$Link\,\,relative.$$
$$\Rightarrow$$ This method is based on the assumption that the trend is linear and cyclical variations are of uniform pattern.
$$\Rightarrow$$ The link relatives are percentages of the current period (quarter or month) as compared with the previous period. With the computations of the link relatives and their average, the effect of cyclical and the random components is minimized. Further, the trend gets eliminated in the process of adjustment of chain relatives
$$\Rightarrow$$ This method is less complicated than the ratio to moving average and the ratio to trend methods.However, this method is based upon the assumption of a linear trend which may not always hold true.
Question 3
1 / -0

When the price of a year is. divided by the price of a particular year we get:

A
Simple relative

B
Link relative

C
(a) and (b) both

D
None of them

Solution

$$\Rightarrow$$ When the price of year is divided by the price of particular year we get : $$Simple\,\,relative.$$
$$\Rightarrow$$ Under this method, the price Index for a given year is calculated as the simple average of the price relatives of the different items included in the index numbers.
$$\Rightarrow$$ The simple average used, here, may be of any type viz. arithmetic mean, geometric mean, harmonic mean, median or mode, but arithmetic mean is usually preferred to, for its simplicity in calculation and geometric mean for its ability of measuring the relative changes which is the inherent feature of an index number.
Question 4
1 / -0

The current price of a soap is Rs 10. The base price is 4. Find price relative.

A
0.4

B
0.25

C
0.30

D
None of the above

Solution

Price relative $$=$$ Base Price $$/$$ Current Price
$$=\dfrac{4}{10} = 0.25$$
Question 5
1 / -0

If all the values are not of equal importance the index number is called:

A
Simple

B
Unweighted

C
Weighted

D
None

Solution

$$\Rightarrow$$ If all the values are not of equal importance the index number is called : $$Weighted$$
$$\Rightarrow$$ The ratio of the sum of weighted prices of current and base time periods multiplied by 100 is called weighted aggregate price index.
$$\Rightarrow$$ This index is calculated after allocating weight to each commodity on the basis of their relative importance.
$$\Rightarrow$$ Weight of these commodities are then multiplied by the prices of base and current time periods. these prices are called weighted price.
Question 6
1 / -0

A weighted aggregate price index where the weight for each item is its base period quantity is known as the

A
Paasche Index

B
Consumer Price Index

C
Producer Price Index

D
Laspeyres Index

Solution

A weighted aggregate price index where the weight for each item is its base period quantity is known as the Laspeyres Index.
Question 7
1 / -0

The current price of a soap is Rs 11. The base price is 3, find price relative.

A
$$2.7$$

B
$$2.5$$

C
$$3.6$$

D
None of the above

Solution

$$\Rightarrow$$ Current price of soap is $$Rs.11.$$
$$\Rightarrow$$ Base price of soap is $$Rs.3$$
$$\Rightarrow$$ $$Price\, relative$$ = $$\dfrac{Current\,price}{Base\,price}=\dfrac{11}{3}=3.6$$
Question 8
1 / -0

Which of the following statement is incorrect?

A
index number is a relative measurement

B
in fact all index numbers are weighted

C
theoretically the best average in construction of index numbers is Geometric mean

D
it is not possible to shift the base if it is the case of fixed base index

Solution

$$\textbf{Step 1: Check whether the given statements are correct or not.}$$

$$\text{Most index numbers are subjected to revision from time to time due to different reasons.}$$
$$\text{In most cases it becomes compulsory to change the base year because numerous changes}$$
$$\text{took place with the passage of time. For example change may happen due to disappearance}$$
$$\text{of old items, inclusion of new ones, change in weights of commodities or changes in conditions,}$$
$$\text{habits and standard of life etc.}$$

$$\textbf{Hence, Option D is answer}$$

Question 9

1 / -0

Construct a composite index number as a weighted mean from the following data:

Index Number	122	145	101	98	137	116
Weight	7	2	4	1	6	5

120

122

130

132 Solution

$$Index\,number$$ $$I$$	$$Weight$$ $$w$$	$$I.w$$
$$122$$	$$7$$	$$854$$
$$145$$	$$2$$	$$290$$
$$101$$	$$4$$	$$404$$
$$98$$	$$1$$	$$98$$
$$137$$	$$6$$	$$822$$
$$116$$	$$5$$	$$580$$
$$Total$$	$$\sum w=25$$	$$\sum Iw=3048$$

$$\Rightarrow$$ Composite index number = $$\dfrac{\sum Iw}{\sum w}=\dfrac{3048}{25}=121.92\approx 122$$.

Question 10
1 / -0

If all the values are not of equal importance the index number is called:

A
Simple

B
Unweighted

C
Weighted

D
None

Solution

If all the values are not of equal importance, the index number is called Weighted.

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Introduction to Index Number Test - 10

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Introduction to Index Number Test - 10

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Question 1

130

133.34

138.34

139.45

Solution

Question 2

Value index

Link relative

Simple relative

None of them

Solution

Question 3

Simple relative

Link relative

(a) and (b) both

None of them

Solution

Question 4

0.4

0.25

0.30

None of the above

Solution

Question 5

Simple

Unweighted

Weighted

None

Solution

Question 6

Paasche Index

Consumer Price Index

Producer Price Index

Laspeyres Index

Solution

Question 7

$$2.7$$

$$2.5$$

$$3.6$$

None of the above

Solution

Question 8

index number is a relative measurement

in fact all index numbers are weighted

theoretically the best average in construction of index numbers is Geometric mean

it is not possible to shift the base if it is the case of fixed base index

Solution

Question 9

120

122

130

132

Solution

Question 10

Simple

Unweighted

Weighted

None

Solution

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