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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 - Business Mathematics and Statistics

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प्रश्न

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
तक्ता
बेरीज

उत्तर

Commodity 2002
(Base year)
2012
(Current year)

p0q0

p0q1

p1q0

p1q1
p0 q0 p1 q1
A 10 20 16 10 200 100 320 160
B 12 34 18 42 408 504 612 756
C 15 30 20 26 450 390 600 520
Total `sum"p"_0"q"_0` = 1058 `sum"p"_0"q"_1` = 1054 `sum"p"_1"q"_0` = 1532 `sum"p"_1"q"_0` = 1436

Laspeyres price index number

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

= `1532/1058 xx 100`

= 144.8

Peasche's price index number

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

= `1436/1054 xx 100`

= 136.24

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पाठ 9: Applied Statistics - Exercise 9.2 [पृष्ठ २१९]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
पाठ 9 Applied Statistics
Exercise 9.2 | Q 14 | पृष्ठ २१९

संबंधित प्रश्‍न

Explain the features of index numbers.


Define Time Reversal Test


State the uses of cost of Living Index Number


Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?

Commodity Price in Rupees per unit Number of units
Basic year Current year Base year Current year
A 6 10 50 56
B 2 2 100 120
C 4 6 60 60
D 10 12 50 24
E 8 12 40 36

Choose the correct alternative:

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:


Choose the correct alternative:

Cost of living at two different cities can be compared with the help of


Choose the correct alternative:

Most commonly used index number is:


Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Base Year Current Year
Price Quantity Price  Quantity
A 170 562 72 632
B 192 535 70 756
C 195 639 95 926
D 1987 128 92 255
E 1985 542 92 632
F 150 217 180 314
7 12.6 12.7 12.5 12.8
8 12.4 12.3 12.6 12.5
9 12.6 12.5 12.3 12.6
10 12.1 12.7 12.5 12.8

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

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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