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Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test? Commodities Price Quantity Base Year - Business Mathematics and Statistics

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प्रश्न

Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?

Commodities Price Quantity
Base Year Current Year Base Year Current Year
Wheat 6 10 50 56
Ghee 2 2 100 120
Firewood 4 6 60 60
Sugar 10 12 30 24
Cloth 8 12 40 36
सारिणी
योग
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उत्तर

Commodities Base Year Current Year p0q0 p0q1 p1q0 p1q1
Price
(p0)
Quantity
(q0)
Price
(p1)
Quantity
(q1)
Wheat 6 10 50 56 300 336 500 560
Ghee 2 2 100 120 200 240 200 240
Firewood 4 6 60 60 240 240 360 360
Sugar 10 12 30 24 300 240 360 288
Cloth 8 12 40 36 320 288 480 432
Total 1360 1344 1900 1880

Fisher's ideal index number = `sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`

`"P"_01^"F" = sqrt((1900 xx 1880)/(1360 xx 1344)) xx 100`

= `sqrt((3,572,000)/(1,827,840)) xx 100`

= `sqrt(1.9542) xx 100`

Factor reversal test

Test is satisfied when `"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`

`"Q"_01 = sqrt((sum"p"_0"q"_1 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_1"q"_0))`

= `sqrt((1344 xx 1880)/(1360 xx 1900))`

`"P"_01 xx "Q"_01 = sqrt((1900 xx 1880)/(1360 xx 1344) xx (1344 xx 1880)/(1360 xx 1900)`

= `sqrt((1880 xx 1880)/(1360 xx 1360))`

= `1880/1360`

= `(sum"p"_1"q"_1)/(sum"p"_0"q"_0)`

Hence Fisher’s Ideal Index satisfies Factor reversal test.

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Applied Statistics - Miscellaneous problems [पृष्ठ २३२]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 9 Applied Statistics
Miscellaneous problems | Q 5 | पृष्ठ २३२

संबंधित प्रश्न

Statements that are incorrect in relation to index numbers:

  1. An index number is a geographical tool.
  2. Index numbers measure changes in air pressure.
  3. Index numbers measure relative changes in an economic variable.
  4. Index numbers are specialized averages.

Complete the Correlation:

__________ : Single variable :: Composite index : Group of variables


State with reason whether you agree or disagree with the following statement:

Index numbers measure changes in the price level only.


Device that measures changes in an economic variable or a group of variables over a period of time –


Identify & explain the concept from the given illustration.

Agricultural Research Institute constructed an index number to measure changes in the production of raw cotton in Maharashtra during the period 2015-2020.


Mention the classification of Index Number


Explain Paasche’s price index number


Explain factor reversal test


State with reasons whether you agree or disagree with the following statement:

Index number measures changes in the price level only.


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.

  1. Explain the meaning of Index Number.
  2. To whom the Index Number is useful?
  3. Express your opinion about the given passage.

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