Tag: introduction to index number

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Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Consumer price index numbers are obtained by:

  1. Laspeyre's formula

  2. Fisher ideal formula

  3. Marshall Edgeworth formula

  4. Paasche's formula
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CPI figures for most countries are usually calculated by using a Laspeyre's Index or Lowe Index.


The CPI calculated via a Paasche index, helps give an idea of what today basket would have cost at yesterday prices.
Answer. (A)

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Most commonly used index number is:

  1. Volume index number

  2. Value index number

  3. Price index number

  4. Simple index number
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Price Index Number is a normalized average (typically a weighted average) of price relatives for a given class of goods or services in a given region, during a given interval of time. It is the most commonly used index number.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

When the price of a year is. divided by the price of a particular year we get:

  1. Simple relative

  2. Link relative

  3. (a) and (b) both

  4. None of them
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  When the price of year is divided by the price of particular year we get : $Simple\,\,relative.$

$\Rightarrow$  Under this method, the price Index for a given year is calculated as the simple average of the price relatives of the different items included in the index numbers. 
$\Rightarrow$  The simple average used, here, may be of any type viz. arithmetic mean, geometric mean, harmonic mean, median or mode, but arithmetic mean is usually preferred to, for its simplicity in calculation and geometric mean for its ability of measuring the relative changes which is the inherent feature of an index number.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

When the price of a divided by the price of the preceding year, we, get:

  1. Value index

  2. Link relative

  3. Simple relative

  4. None of them
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  When the price of divided by the price of the preceding year, we get : $Link\,\,relative.$

$\Rightarrow$  This method is based on the assumption that the trend is linear and cyclical variations are of uniform pattern. 
$\Rightarrow$  The link relatives are percentages of the current period (quarter or month) as compared with the previous period. With the computations of the link relatives and their average, the effect of cyclical and the random components is minimized. Further, the trend gets eliminated in the process of adjustment of chain relatives
$\Rightarrow$  This method is less complicated than the ratio to moving average and the ratio to trend methods.However, this method is based upon the assumption of a linear trend which may not always hold true.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

If the price of potatoes is reduced by $25\%$, one can buy $6.25$ kg more for Rs. $100$. The reduced price of potatoes is  

  1. Rs. $3$/- per kg
  2. Rs. $3.50$ per kg
  3. Rs. $4$/- per kg
  4. Rs. $4.50$ per kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original price per kg $=x$.

Reduction $=25$%
$\therefore $  New price per kg $=x\left( 1-\dfrac { 25 }{ 100 }  \right) $
                                   $=\dfrac { 3x }{ 4 } $
Now, for $Rs100$, let customer buy $'y'$ kg of potatoes.
$\therefore \quad 100=$ (initial price per kg) $\times $ (weight bought)
$\Rightarrow \quad 100=xy\quad \longrightarrow (i)$
For the reduced cost,
$100=$ (new price per kg) $\times $ (weight bought)
$\Rightarrow \quad 100=\left( \dfrac { 3x }{ 4 }  \right) \left( y+6.25 \right) $
But from eq $(i)$   $100=xy$
$\therefore \quad xy=\dfrac { 3x }{ 4 } \left( y+6.25 \right) $
$\Rightarrow \quad 4y=3y+18.75$
$\Rightarrow \quad y=18.75$
$\therefore \quad x=\dfrac { 100 }{ 18.75 } =\dfrac { 100\times 100 }{ 1875 } $
$\therefore $  Reduced price $=\dfrac { 3x }{ 4 } =\dfrac { 3 }{ 4 } \times \dfrac { 100\times 100 }{ 1875 } $  per kg
                              $=4$  per kg

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Fisher's Ideal Formula satisfies __________ test.

  1. Both B & C

  2. Factor Reversal Test

  3. Time Reversal Test

  4. None of above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Fisher's Ideal Formula refers to the geometric mean of Laspeyres and Paasche formula. It is also known as Ideal formula also. It satisfies Factor Reversal Test as well as Time Reversal Test.