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Do My Statistics Assignment Illustrations and Solutions

Question : 1

From the following data obtained for a particular class of people, compute their cost of living

index number for 2003 using both the (1) aggregate expenditure method.

Items Quantity in 2002 Price in 2003 Price in 2004

A B C D E

5 quintals 4 quintals 2 quintals 1 quintal 3 quintals

4 5 6 3 15

6 7 8 2 20

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Solution :

(a) Computation of the cost of living index number by the aggregative

expenditure method

Items Quantity in the base-year 2003 (qo)

Price in the base year 2003 (po)

Price in the current year 2004 (P1)

A B

C D E

5 4

2 1 3

4 5

6 3 15

6 7

8 2 20

30 18

16 2 60

20 20

12 3 45

Total - - - 136 100

The cost of living index number is given by

01 = 10 00

100 = 136

100 100 = 136

(b) Computation of the cost of living index number by the weighted price

relative method

Items Price relative P1/p0

100 (1)

Weights i.e. p0 q0

(V)

(IV)

A B C D E

5 4 2 1 3

4 5 6 3 15

6 7 8 2 20

150 140 133 66 133

20 20 12 3 45

3000 2800 1600 200 6000

Total - - - - 100

13600

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Question : 2

From the following indices calculate the weighted cost of living index numbers for the

years 2002,2003 and 2004.

Indices

Items Weights (W)

2002 2003 2004

1 IW 1 1W 1 1W

Food Clothing Housing

Fuel Sundries

50 30 20 15 5

110 100 95 105 102

5500 3000 1900 1575 510

115 110 120 108 112

5750 3300 2400 1620 560

120 105 104 106 110

600 3150 2080 1590 550

Total 120 - 12485 - 13630 - 13370

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Solution :

From the data given below , the cost of living index number for 2003.

Items Price in 2003 Price in 2004 Percent of total expenditure

Food Fuel

Housing Clothing

Miscellaneous

160 30 80 40

50

140 25 70 35

40

45 15 20 12

8

Here, the percentage of expenses are to be taken as the weights of the respective items of

expenditure.

Computation of the cost of living index number for 2004

Items Weights W

Price in 2003

Price in 2004

Price relative

P1/P0100 1

IW

Food

Fuel Housing Clothing

Misc.

45

15 20 12 8

160

30 80 40 50

140

25 70 35 40

87.5

83.5 87.5 87.5 80

3937.5

1252.5 1750.0 1050.0 640.0

Total 100 - - - 8630.0

The cost of living index number is given by

01 =

=

8630

100 = 86.30

The above index number shows that the cost of living of the selected group of people has

gone down by 13.70% of the price level of 2003.

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Question : 3

From the following data, calculate the cost of living index number using the geometric

means.

Items : Indices : Weights

Food 400 5

Fuel 200 3

Clothing 250 4

Housing 150 1

Misc. 300 2

Solution :

Computation of the cost of living index number using the geometric mean

Items Indices 1

Log 1 Weights W

W log 1

Food Fuel

Clothes Housing

Misc.

400 200 250 150 300

2.6021 2.3010 2.3979 2.1761 2.4771

5 3 4 1 2

13.0105. 6.9030 9.5916 2.1761 4.9542

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Using the geometric mean, the cost of living index number is given by

01 = Antilog of .1

= AL.36.6354

15 =AL. 2.4424

= 276.95

Thus, the required Index no. for the period in issue is 277 approx.

Question : 4

From the following data, compute the consumer price Index for the year 2004 w.r.t the

price level of 2003.

Items Weights W

Percentage increase in

Prices

Index 1

IW

Food Food Rent

Clothing Fuel Misc.

7.5 2

2.5 3 1

50 60 40 30 20

150 160 140 130 120

1125 320 350 390 120

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Solution :

The consumers Price index is given by

01 =

=

2305

16 = 144 approx

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Do My Statistics Assignment