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प्रश्न
Calculate Fisher’s index number to the following data. Also show that it satisfies Time Reversal Test.
| Commodity | 2016 | 2017 | ||
| Price (Rs.) | Quantity (kg) | Price (Rs.) | Quantity (kg) | |
| Food | 40 | 12 | 65 | 14 |
| Fuel | 72 | 14 | 78 | 20 |
| Clothing | 36 | 10 | 36 | 15 |
| Wheat | 20 | 6 | 42 | 4 |
| Others | 46 | 8 | 52 | 6 |
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उत्तर
| Commodity | 2016 (Base year) |
2017 (Current year) |
p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| Food | 40 | 12 | 65 | 14 | 480 | 560 | 780 | 910 |
| Fuel | 72 | 14 | 78 | 20 | 1008 | 1440 | 1092 | 1560 |
| Clothing | 36 | 10 | 36 | 15 | 360 | 540 | 60 | 540 |
| Wheat | 20 | 6 | 42 | 4 | 120 | 80 | 252 | 168 |
| Others | 46 | 8 | 52 | 6 | 68 | 276 | 416 | 312 |
| Total | `sum"p"_0"q"_0` = 2336 | `sum"p"_0"q"_1` =2896 | `sum"p"_1"q"_0` = 2900 | `sum"p"_1"q"_1` = 3490 | ||||
Fisher’s Price Index Number
`"P"_01^"F" = sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1)) xx 100`
= `sqrt((2900 xx 3490)/(2336 xx 2896)) xx 100`
= `sqrt((10121000)/(6765056)) xx 100`
= `sqrt(1.4961) xx 100`
= `1.2232 xx 100`
= 122.32
Time Reserved Test: P01 × P10 = 1
= `sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1 xx sum"q"_1"p"_0 xx sum"q"_0"p"_0)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1 xx sum"p"_1"q"_1 xx sum"p"_0"p"_1))`
= `sqrt((2900 xx 3490 xx 2896 xx 2336)/(2336 xx 2896 xx 3490 xx 2900)`
= 1
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संबंधित प्रश्न
Complete the Correlation:
__________ : Single variable :: Composite index : Group of variables
Features of index numbers:
- It is useful in framing suitable economic policies.
- It is useful to present financial data in real terms
- Index numbers are statistical devices.
- Index numbers are specialized averages.
Index number was originally developed to measure ______.
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.
Write note on Fisher’s price index number
Define Time Reversal Test
Calculate by a suitable method, the index number of price from the following data:
| Commodity | 2002 | 2012 | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 20 | 16 | 10 |
| B | 12 | 34 | 18 | 42 |
| C | 15 | 30 | 20 | 26 |
Calculate the cost of living index by aggregate expenditure method:
| Commodity | Weight 2010 |
Price (Rs.) | |
| 2010 | 2015 | ||
| P | 80 | 22 | 25 |
| Q | 30 | 30 | 45 |
| R | 25 | 42 | 50 |
| S | 40 | 25 | 35 |
| T | 50 | 36 | 52 |
Choose the correct alternative:
Another name of consumer’s price index number is:
Choose the correct alternative:
Which of the following Index number satisfy the time reversal test?
