Tag: applied statistics

Questions Related to applied statistics

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.

Indices calculated by the chain base method are free from:

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

  1. Seasonal variations

  2. Errors

  3. Percentages

  4. Ratios

Show answer
Correct Option: A
Explanation:

Indices calculated by chain base method are free from seasonal variations.

The chain base indices are not suitable for:

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

  1. Long range comparisons

  2. Short range comparisons

  3. Percentages

  4. Ratios

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  The chain base indices are not suitable for : $Long\,range\,comparisons.$

$\Rightarrow$  In chain base method method, there is no fixed base period.
$\Rightarrow$  The chief advantage of this method is that the price relatives of a year can be compared with the price levels of the immediately preceding year. Businesses mostly interested in comparing this time period rather than comparing rates related to the distant past will utilize this method.

$\Rightarrow$  Another advantage of the chain base method is that it is possible to include new items in an index number or to delete old times which are no longer important. But the chain base method has the drawback that comparisons cannot be made over a long period.

In chain base method, the base period is:

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

  1. Fixed

  2. Not fixed

  3. Constant

  4. Zero

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  In chain base method, the base period is : $Not\,fixed.$

$\Rightarrow$  In this method, there is no fixed base period; the year immediately preceding the one for which the price index has to be calculated is assumed as the base year. 
$\Rightarrow$  Thus, for the year 1994 the base year would be 1993, for 1993 it would be 1992, for 1992 it would be 1991, and so on. In this way there is no fixed base and it keeps on changing.
$\Rightarrow$  advantage of the chain base method is that it is possible to include new items in an index number or to delete old times which are no longer important. 

Two hundred items were sold at a snack stand for a total of $Rs$. $130.00$. The only items sold were cansof pop for $Rs$. $0.50$ and bags of popcorn for $Rs$. $0.75$. How many of each item were sold?

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

  1. $120$ cans of pop, $80$ bags of popcorn

  2. $80$ cans of pop, $120$ bags of popcorn

  3. $160$ cans of pop, $40$ bags of popcorn

  4. $40$ cans of pop, $160$ bags of popcorn

Show answer
Correct Option: B
Explanation:

  Let us assume no of cans of pop sold =x
no of bags of pop sold=200-x
So, as per question,
$0.50*x+0.75(200-x)=130$
$0.50x+150-0.75x=130$
$0.25x=20$
$x=80$
So, no of bags of pop sold=200-x=200-80=120
Answer (B) 80 cans of pop, 120 bags of popcorn

For consumer price index, price quotations are collected from:

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

  1. Fair price shops

  2. Government depots

  3. Retailers

  4. Whole-sale dealers

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  For consumer price index, price quatations are collected from: $Retailers.$

$\Rightarrow$   A retailer is a company that buys products from a manufacturer or wholesaler and sells them to end users or customers. In a sense, a retailer is an intermediary or middleman that customers use to get products from the manufacturers.
$\Rightarrow$  Retailers are experts in marketing, sales, merchandise inventory, and knowing their customers. They purchase the goods from the manufacturers at cost and market them to consumers at retail prices. 
$\Rightarrow$  The retail price can be anywhere from 10 percent to 50 percent higher than the manufacturer cost. 

When the prices of rice are to be compared, we compute: 

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

  1. Volume index

  2. Value index

  3. Price index

  4. Aggregative index

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  When the prices of rice are to be compared, we compute: $Price\,Index.$

$\Rightarrow$  Price index, measure of relative price changes, consisting of a series of numbers arranged so that a comparison between the values for any two periods or places will show the average change in prices between periods or the average difference in prices between places. 
$\Rightarrow$  In most countries price indexes are used to measure inflation, each focusing on the prices of a collection of goods and services important to a particular segment of the economy.

Price relatives computed by chain base method are called: 

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

  1. Price relatives

  2. Chain indices

  3. Link relatives

  4. None of them

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  Price relatives computed by chain base method are called $Link\,\,relatives.$

$\Rightarrow$  Under this method, the base year’s price does not remain fixed but moves step from year to year. In other words, the immediately preceding year’s price becomes the base year’s price for each of the succeeding years.
$\Rightarrow$  Under this method, the base year’s price does not remain fixed but moves step from year to year. In other words, the immediately preceding year’s price becomes the base year’s price for each of the succeeding years.

$\Rightarrow$  $Chain\, index$ = $\dfrac{Average\, link\, relative\, of\, current\, year \times Chain\, index\, of\, previous\, year}{100}$