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Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s Index numbers for the 2010 from the following data. Commodity Price Quantity 2000 2010 2000 2010 A 12 14 18 16 B 15 16 20 15 C 14 15 24 20 D 12 12 - Business Mathematics and Statistics

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Question

Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s Index numbers for the 2010 from the following data.

Commodity Price Quantity
2000 2010 2000 2010
A 12 14 18 16
B 15 16 20 15
C 14 15 24 20
D 12 12 29 23
Chart
Sum
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Solution

Commodity 2000
(Base year)
2010
(Current year)
p0q0 p0q1 p1q0 p1q1
p0 q0 p1 q1
A 12 14 18 16 216 192 252 224
B 15 16 20 15 300 225 320 240
C 14 15 24 20 336 280 360 300
D 12 12 29 23 348 276 348 276
Total `sum"p"_0"q"_0` = 1200 `sum"p"_0"q"_1` = 973 `sum"p"_1"q"_0` = 1280 `sum"p"_1"q"_1` = 1040

(i) Laspeyre's Price Index

`"P"_01^"L" = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`

= `1280/1200 xx 100`

= 106.6

(ii) Paasche's Price Index

`"P"_01^"P" = (sum"P"_1"q"_1)/(sum"p"_0"q"_1) xx 100`

= `1040/973 xx 100`

= 106.8

(iii) Fisher’s price index number

`"P"_01^"F" = sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`

= `sqrt(1280/1200 xx 1040/973) xx 100`

= `sqrt((13,31,200)/(11,67,600)) xx 100`

= `sqrt(1.14) xx 100`

= 106.7

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Chapter 9: Applied Statistics - Exercise 9.2 [Page 219]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 9 Applied Statistics
Exercise 9.2 | Q 16 | Page 219

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Read the given passage and answer the questions:

Index Number is a technique of measuring changes in a variable or group of related variables with reference to time, geographical location and other characteristics.

Index Number is very useful for economists, farmers, traders, government, educationalists and trade union leaders for planning and implementing the plans according to their sector.

The scope of index number is not limited to only one subject but it extends to many subjects such as Economics, Educational science, Psychology, History, Sociology, Geography etc.

While framing index number its objective must be determined. To attain the objective the information is collected in various ways and this information is used for comparing two different time periods. For this purpose, the base year’s index is assumed as 100 and accordingly the value of the current year is calculated.

Laspeyre, Paasche and Fisher have suggested different methods for constructing index numbers.

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Choose the correct pair.

Group A Group B
1) Price Index  a) `(sump_1q_1)/(sump_0q_0)xx100`
2) Value Index b) `(sumq_1)/(sumq_0)xx100`
3) Quantity Index  c) `(sump_1q_1)/(sump_0q_1)xx100`
4) Paasche's Index d) `(sump_1)/(sump_0)xx100`

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