Tag: introduction to index numbers

Questions Related to introduction to index numbers

Purchasing power of money can be accessed through:

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

  1. Simple index

  2. Fishers index

  3. Consumer price index

  4. Volume index

Show answer
Correct Option: C
Explanation:

Purchasing Power is just a short phrase for how much your money buys you.

Purchasing power of money can be accessed through Consumer Price Index

In constructing index number geometric mean relatives are: 

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

  1. Non-reversible

  2. Reciprocal

  3. Reversible

  4. None of them

Show answer
Correct Option: C
Explanation:

In constructing index number geometric means relatives are Reversible.

Consumer price index numbers are obtained by:

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

  1. Laspeyre's formula

  2. Fisher ideal formula

  3. Marshall Edgeworth formula

  4. Paasche's formula

Show answer
Correct Option: A
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)

Most commonly used index number is:

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

  1. Volume index number

  2. Value index number

  3. Price index number

  4. Simple index number

Show answer
Correct Option: C
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.

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

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

  1. Simple relative

  2. Link relative

  3. (a) and (b) both

  4. None of them

Show answer
Correct Option: A
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.

The current price of a soap is Rs 10.  The base price is 4. Find price relative.

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

  1. 0.4

  2. 0.25

  3. 0.30

  4. None of the above

Show answer
Correct Option: B
Explanation:

Price relative $=$ Base Price $/$ Current Price

                       $=\dfrac{4}{10} = 0.25$

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

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

  1. Value index

  2. Link relative

  3. Simple relative

  4. None of them

Show answer
Correct Option: B
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.

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

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

  1. Value index

  2. Consumer price index

  3. Volume index

  4. Un-weighted index

Show answer
Correct Option: B
Explanation:

Consumer Price Index can be used to compare the cost of living at two different cities.

More the CPI, higher is the cost of living in that city.

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  

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

  1. Rs. $3$/- per kg

  2. Rs. $3.50$ per kg

  3. Rs. $4$/- per kg

  4. Rs. $4.50$ per kg

Show answer
Correct Option: C
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

Fisher's Ideal Formula satisfies __________ test.

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

  1. Both B & C

  2. Factor Reversal Test

  3. Time Reversal Test

  4. None of above

Show answer
Correct Option: A
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.