# T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 13 – Index Numbers

T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 13 â€“ Index Numbers is regarded as an important concept to be studied thoroughly by the students. Here, we have providedÂ T.R. Jain and V.K. Ohri Solutions for Class 11.

 Board CBSE Class Class 11 Subject Statistics for Economics Chapter Chapter 13 Chapter Name Index Numbers Category T.R. Jain and V.K. Ohri

## T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 13 â€“ Index Numbers

#### Question 1:

Using Simple Aggregate Method and Price Relatives Method, find out index values for the year 2018 from the following data:

 Items A B C D E 2004 Price (â‚¹) 15 33 38 25 50 2018 Price (â‚¹) 30 35 57 35 63

Simple Aggregate Method

 Items 2004 Price (P0) 2018 Price (P1) A B C D E 15 33 38 25 50 30 35 57 35 63 ΣP0 = 161 ΣP1 = 220

Price Relative Method

 Items 2004 Price(P0) 2018 Price (P1) Price relative = $P1P0×100$ A 15 30 $3015×100=200$ B 33 35 $3533×100=106.06$ C 38 57 $5738×100=150$ D 25 35 $3525×100=140$ E 50 63 $6350×100=126$ N = 5 $ΣP1P0×100=722.06$

#### Question 2:

Find out index value by the Price Relative Method for the year 2018 from the following data:

 Items A B C D E F G 2004 Price (â‚¹) 100 10 5 4 1 2 3 2018 Price (â‚¹) 100 9 4 2 1 2.50 2.25

 Items 2004 Price (P0) 2018 Price (P1) Price relative $=P1P0×100$ A 100 100 $100100×100=100$ B 10 9 $910×100=90$ C 5 4 $45×100=80$ D 4 2 $24×100=50$ E 1 1 $11×100=100$ F 2 2.50 $2.502×100=125$ G 3 2.25 $2.253×100=75$ N = 7 $ΣP1P0×100=620$

Hence, Price Index = 88.57

#### Question 3:

Construct an index number by Price Relatives Method using 2004 as base year:

 Goods A B C D 2004 Price (â‚¹) 8 10 15 20 2017 Price (â‚¹) 10 12 18 22 2018 Price (â‚¹) 12 14 20 25

 Goods 2004 Price (P0) 2017 Price (P1) 2018 Price (P2) Price relatives of 2017 in relation to 2004 $P1P0×100$ Price relatives of 2018 in relation to 2004 $P2P0×100$ A 8 10 12 $108×100=125$ $128×100=150$ B 10 12 14 $1210×100=120$ $1410×100=140$ C 15 18 20 $1815×100=120$ $2015×100=133.33$ D 20 22 25 $2220×100=110$ $2520×100=125$ N = 4 $ΣP1P0×100=475$ $ΣP2P0×100=548.33$

#### Question 4:

Construct and index of prices using 2004 as the base year and Price Relatives Method:

 Goods Weight 2004 2017 2018 A B C 5 3 2 10 5 4 12 6 5 14 8 7

Construction of Price Index for the year 2017

 Goods Weight (W) 2004 Price (P0) 2017 Price (P1) $R=P1P0×100$ RW A 5 10 12 $1210×100=120$ 600 B 3 5 6 $65×100=120$ 360 C 2 4 5 $54×100=125$ 250 ΣW = 10 ΣRW = 1210

Construction of Price Index for the year 2018

 Goods Weight (W) 2004 Price (P0) 2018 Price (P2) $R=P2P0×100$ RW A 5 10 14 $1410×100=140$ 700 B 3 5 8 $85×100=160$ 480 C 2 4 7 $74×100=175$ 350 ΣW = 10 ΣRW = 1530

#### Question 1:

Taking 2004 as base year, construct the index numbers of the years 2014 and 2018.

 Year 2004 2014 2015 2016 2017 2018 Prices (â‚¹) 10 14 16 20 22 24

 Year Price 2004 10 2014 $14$ 2015 16 2016 20 2017 22 2018 $24$

Since, base year is given as 2004
P0 = 10
Index number for year 2014

Here, P1 = 14

Index number for year 2018
Here, P1 = 24
Substituting the values in the formula

$P01=2410×100=240$

#### Question 2:

Construct index number by Price Relative Method taking 2004 as base year:

 Year A B C D 2004 2016 2017 2018 25 20 25 28 18 22 20 24 16 24 25 30 21 22 25 26

Here, we construct the index number for each of the years from 2016-2018.
Base Year 2004, Current year 2016

 2004 ( P0) 2016 (P1) Price Relative = $P1P0×100$ A 25 20 $2025×100=80$ B 18 22 $2218×100=122.22$ C 16 24 $2416×100=150$ D 21 22 $2221×100=104.76$ ∑=456.96

According to the Price Relative Method, price index is calculated using the following formula.

$P01=456.984=114.245$

Base Year 2004, Current year 2017

 2004 (P0) 2017 (P1) Price Relative = $P1P0×100$ A 25 25 $2525×100=100$ B 18 20 C 16 25 $2516×100=156.25$ D 21 25 $2521×100=119.04$ ∑= 486.4

$P01=486.44=121.60$

Base Year 2004, Current Year 2018

 2004 (P0) 2018 (P1) Price Relative = $P1P0×100$ A 25 28 $2825×100=280$ B 18 24 $2418×100=133.33$ C 16 30 $3016×100=187.5$ D 21 26 $2621×100=123.80$ ∑ 556.63

$P01=556.634=139.157$

#### Question 3:

Compute a Price Index for the following by (i) Simple Aggregative Method, and (ii) Average of Price Relative Method:

 Commodities A B C D E F Price in 2004 (â‚¹) 20 30 10 25 40 50 Price in 2018 (â‚¹) 25 30 15 35 45 55

(i) Simple Aggregate Method

 2004 (P0) 2018 (P1) A B C D E F 20 30 10 25 40 50 25 30 15 35 45 55 ∑P0 =â€‹175 ∑P1= 205

(ii) Price Relative Method

 2004 â€‹(P0) 2018 â€‹(P1) Price Relative = $P0P1×100$ A 20 25 $2520×100=125$ B 30 30 $3030×100=100$ C 10 15 $1510×100=150$ D 25 35 $3525×100=140$ E 40 45 $4540×100=112.5$ F 50 55 $5550×100=110$ ∑= 737.5

#### Question 4:

Construct price index number of the following data by using:
(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.

 Items Base Year Current Year Quantity Price Quantity Price A B C D 3 7 4 6 5 4 7 6 2 5 3 5 8 6 10 7

 q0 p0 p0q0 p1 q1 p1q1 p1q0 p0q1 A B C D 3 7 4 6 5 4 7 6 15 28 28 36 8 6 10 7 2 5 3 5 16 30 30 35 24 42 40 42 10 20 21 30

(i) Laspeyre's Price index:

(ii) Paasche's Price index:

(iii) Fisher's Price index:

#### Question 5:

Construct an index number for the year 2018, taking 2004 as base year by any method you deem ideal:

 Year Good I Good II Good III Price Quantity Price Quantity Price Quantity 2004 2018 5 4 10 12 8 7 6 7 6 5 3 4

 P0 q0 P1 q1 P0q0 P1q1 P0q1 P1q0 I II III 5 8 6 10 6 3 4 7 5 12 7 4 50 48 18 48 49 20 60 56 24 40 42 15

Fisher's Method

#### Question 6:

Given the following data and taking 2004 as the base year, construct index of prices using:

(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.

 Year Commodities A B C D Price Quantity Price Quantity Price Quantity Price Quantity 2004 2018 24 30 8 10 9 10 3 4 16 20 5 8 10 9 3 4

 P0 q0 P0q0 P1 q1 P1q1 P1q0 P0q1 A B C D 24 9 16 10 8 3 5 3 192 27 80 30 30 10 20 9 10 4 8 4 300 40 160 36 240 30 100 27 240 36 128 40 ∑P0q0=329 ∑P1q1=536 ∑P1q0=397 ∑P0q1â€‹=444

Laspeyre's Price index

Paasche'sPrice index

Fisher's Price index

#### Question 7:

Construct a weighted index number of the following data using price relative method:

 Item A B C D E Base Year (Quantity) 24 14 8 4 8 Base Year (Price) 2 4 6 10 5 Current Year (Price) 3 5 9 12 5

 P0 q0 P1 P0q0 â€‹(W) $R=P1P0×100$ RW A 2 24 3 48 $32×100=150$ 7200 B 4 14 5 56 $54×100=125$ 7000 C 6 8 9 48 $96×100=150$ 7200 D 10 4 12 40 $1210×100=120$ 4800 E 5 8 5 40 $55×100=100$ 4000

Weighted index number

01=130.17

#### Question 8:

Find out the index number of the following data with Laspeyre's Method:

 Commodity 2017 2018 Price Quantity Price Quantity A B 70 62 7 3 80 74 6 2

 P0 q0 P0q0 P1 q1 P1q0 A B 70 62 7 3 490 186 80 74 6 2 560 222 ∑ P0q0 =676 ∑P1q0=782

Laspeyre'sPrice index

#### Question 9:

Construct Index number of the following data with Laspeyre's and Paasche's Methods:

 Commodity Base Year Current Year Quantity Price Quantity Price A B C 10 8 5 0.80 0.85 1.30 11 9 5.5 0.70 0.90 0.80

 P0 q0 P0q0 P1 q1 P1q1 P0q1 P1q0 A B C 0.8 0.85 1.35 10 8 5 8 6.8 6.5 0.7 0.9 0.8 11 9 5.5 7.7 8.1 4.4 8.8 7.65 7.15 7 7.2 4

Laspeyre'sPrice Index

Passche's Price index

$P01=ΣP1q1ΣP0q1or,P01=20.223.60×100=85.59$

#### Question 10:

Construct index numbers of the following data by Fisher's Method:

 Commodity Base Year Current Year Price Value Price Value A B C D E 3 5 6 4 8 18 35 42 32 24 7 10 11 6 9 10 100 55 60 36

 P0 Value (Base Year) $q0=ValueP0$ P0q0 P1 Value (Current Year) P1q1 P1q0 P0q1 A B C D E 3 5 6 4 8 18 35 42 32 24 6 7 7 8 3 18 35 42 32 24 7 10 11 6 9 14 100 55 60 36 2 10 5 10 4 14 100 55 60 36 42 70 77 48 27 6 50 30 40 32 151

Fisher's Price Index

#### Question 11:

Construct Cost of Living Index on the basis of the following data:

 Items Price Weight Wheat Rice Maida Pulses Oil 241 150 200 170 125 10 4 2 2 2

 Items Price (P) Weights (W) PW Wheat Rice Maida Pulses Oil 241 150 200 170 125 10 4 2 2 2 2410 600 400 340 250 ∑W=20 ∑PW = 4000

Cost of living Index

$=∑PW∑W=4000620=200$

#### Question 12:

Construct Consumer Price Index Number with the help of the following data:

 Consumer Items Price Weight Food Fuel Cloth House Rent Miscellaneous 125 120 66.67 120 150 40 10 25 15 10

 Items Price (P) Weights (W) PW Food Fuel Cloth House rent Miscellaneous 125 120 66.67 120 150 40 10 25 15 10 5000 1200 16 66.75 1800 1500

Consumer price index

#### Question 13:

From the following data find Consumer Price Index or Cost of Living Index:

 Items Quantity Consumed in Current Year Price in Base year Price in Current Year Rice Pulses Oil Clothing Housing Miscellaneous 30 qt 36 kg 24 l 72 metres per month per month 12 0.4 1.5 0.75 20 20 25 0.6 2.2 10 30 15

 Items q1 P0 P1 P1q1 P0q1 Rice Pulses Oil Clothing Housing Miscellaneous 30 36 24 72 1 1 12 0.4 1.5 0.75 20 20 25 0.6 2.2 10 30 15 750 21.6 52.8 720 30 15 360 14.4 36 54 20 20

â€‹Note that here we are given the current year quantities for different items. So, the Consumer Price Index is calculated using the following formula.

#### Question 14:

Construct Cost of Living Index Number for the year 2018 from the following statistics:

 Commodity 2004 Price 2004 Quantity 2018 Price A B C D E 25 36 12 6 28 16.0 7.0 3.5 2.5 4.0 35 48 16 10 28

 P0 q0 P1 P1q0 P0q0 A B C D E 25 36 12 6 28 16 7 3.5 2.5 4 35 48 16 10 28 560 336 56 25 112 400 252 42 15 112

Cost of Living Index

#### Question 15:

Find the Consumer Price Index from the following data. Using
(i) Aggregative Expenditure Method, and
(ii) Family Budget Method.
Is there any difference between the two results?

 Commodity Quantity Consumed in the year 2004 Unit Price in 2004 (â‚¹) Price in 2018 (â‚¹) Rice Wheat Bajra Arhar Desi Ghee Sugar 6 8 1 2 20 1 Quintal Quintal Quintal Quintal kg Quintal 100 80 70 120 12 160 120 90 70 115 15 170

 q0 P0 P1 W = P0q0 P1q0 $R=P1P0×100$ WR Rice 6 100 120 600 720 $120100×100=120$ 72,000 Wheat 8 80 90 640 720 $9080×100=112.5$ 72,000 Bajra 1 70 70 70 70 $7070×100=100$ 70,000 Arhar 2 120 115 240 230 $115120×100=95.83$ 22,999.2 Ghee 20 12 15 240 300 $1512×100=125$ 30,000 Sugar 1 160 170 160 170 $170160×100=106.25$ 17,000 283999.2

(i) Aggregate expenditure methodâ€‹

(ii) Family Budged Method

$CPI=∑WR∑W=283999.21950=145.64$

Yes, there is a difference between the values calculated by the two methods.
Difference = 145.64 – 113.33 = 32.31

#### Question 16:

Construct index number of industrial production in the year 2018 from the following data on the basis of 2005's production:

 Industry Units 2005 2018 Weight Electrical and Electronics Metallurgical Mechanical Mining Textiles Miscellaneous Mill. Nos. Th. Tonnes Th. Tonnes Th. Tonnes Mill. Mtrs. Th. Tonnes 12 22 72 100 60 123 70 37 105 123 130 270 36 12 10 22 8 12

 Industry q0 q1 Weight (W) $R=q1q0×100$ WR Electronics 12 70 36 $7012×100=583.33$ 20999.88 Metallurgical 22 37 12 $3722×100=168.18$ 2018.16 Mechanical 72 105 10 $10572×100=145.83$ 1458.3 Mining 100 123 22 $123100×100=123$ 2706 Textiles 60 130 8 $13060×100=216.67$ 1733.36 Misce. 123 270 12 $270123×100=219.51$ 2634.12 ∑W = 100 ∑WR = 31549.82

Index number of Industrial Production

#### Question 17:

Construct index number of industrial production from the following data:

 Item Units Production or Output Weight Base year Current Year Mechanical Sugar and Tea Textile Mining Transportation Electricity and Electronics Mill. Nos. Th. Tonnes Mill. Mtrs. Th. Tonnes Mill. Nos. Mill. Nos. 237 62 572 165 335 87 400 150 820 200 727 323 5 10 35 15 20 15

 Item Base year (q0) Current year (q1) Relatives values $R=q1q0×100$ Weight (W) WR Mechanical 237 400 168.78 5 843.85 Sugar and Tea 62 150 241.19 10 2419.35 Textile 572 820 143.35 35 5017.48 Mining 165 200 121.21 15 1818.15 Transportation 335 727 217.01 20 4340.2 Electricity and electronics 87 323 371.26 15 5568.9 ∑W = 100 ∑RW = 20008.3

Index number of Industrial Production

#### Question 18:

Construct index number of industrial production from the following data:

 Industry Number of Items Weight Base Year Current Year Mining and Quarrying Manufacturing Electricity and Electronics 35 413 10 107 1225 27 10 85 5

 Industry Base year (q0) Current year (q1) Relatives values R $=q1q0×100$ Weight (W) WR Mining and quarrying Manufacturing Electricity and electronics 35 413 10 107 1225 27 305.71 296.61 270 10 85 5 3057.1 25211.85 1350 ∑W = 100 ∑RW = 29618.95
$=∑RW∑W=29618.95100=296.19$