Tag: construction of index numbers

Questions Related to construction of index numbers

If all the values are of equal importance, the index numbers are called: 

business mathematics and statistics applied statistics weighted methods to calculate index numbers construction of index numbers index numbers

  1. Weighted

  2. Unweighted

  3. Composite

  4. Value index

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Correct Option: B
Explanation:

$\Rightarrow$  If all the values are of equal importance, the index numbers are called: $Unweighted$.

$\Rightarrow$  There are two methods of constructing unweighted index numbers: $(1)$ Simple Aggregative Method $(2)$ Simple Average of Relative method.
$\Rightarrow$  Simple Aggregative Method - In this method, the total price of commodities in a given (current) year is divided by the total price of commodities in a base year and expressed as percentage.
$\Rightarrow$  Simple Average of Relative method - In this method, we compute price relatives or link relatives of the given commodities and then use one of the averages such as the arithmetic mean, geometric mean, median, etc.

Using $2005$ as base year , the price of a commodity in $2007$ is 125. Calculate the index number for 2007 if 2006 is taken as the base year.

business mathematics and statistics applied statistics weighted methods to calculate index numbers construction of index numbers index numbers

  1. 105.93

  2. 104.23

  3. 103.93

  4. 112.3

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Correct Option: A

Using $2005$ as base year , the price of a commodity in $2006$ are 118. Calculate the index number for 2005 if 2006 is taken as the base year.

business mathematics and statistics applied statistics weighted methods to calculate index numbers construction of index numbers index numbers

  1. 84.75

  2. 82.18

  3. 81.18

  4. 78.07

Show answer
Correct Option: A
Explanation:

$N=1$ (Since only one commodity)

Take price $=Rs.100$  as base price for $2005$
$\implies p _1=100$
$p _0=118$ (given)
$\implies $ index no. $=\cfrac{1}{N}(\sum\cfrac{p _1}{p _0}\times 100)$
$\implies\cfrac{1}{1}(\sum\cfrac{100}{118}\times 100)=84.775\approx 84.75$