Tag: applied statistics

Questions Related to applied statistics

If all the values are not of equal importance the index number is called:

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

  1. Simple

  2. Unweighted

  3. Weighted

  4. None

Show answer
Correct Option: C
Explanation:

If all the values are not of equal importance, the index number is called Weighted.

A weighted aggregate price index where the weight for each item is its base period quantity is known as the

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

  1. Paasche Index

  2. Consumer Price Index

  3. Producer Price Index

  4. Laspeyres Index

Show answer
Correct Option: D
Explanation:

A weighted aggregate price index where the weight for each item is its base period quantity is known as the Laspeyres Index.

Index for base period is always taken as: 

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

  1. One

  2. Zero

  3. Hundred

  4. None of these

Show answer
Correct Option: C
Explanation:

Index for base period is always taken as Hundred.

For the given data calculate cost of living index number. is?

Group Food Clothing Fuel and lighting House Rent Miscellenious
I $70$ $90$ $100$ $60$ $80$
W $5$ $3$ $2$ $4$ $6$
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. $78$

  2. $77$

  3. $92$

  4. $58$

Show answer
Correct Option: B
Explanation:

Cost of living index number $= \dfrac{\sum I _{i}W _{i}}{\sum W _{i}}$

$\sum I _{i}W _{i} = 1540$

$\sum W _{i} = 20$


$\Rightarrow$ Cost of living index number $= \dfrac{1540}{20} = 77$

An index number is called a simple index when it is computed from: 

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

  1. Multiple variable

  2. Bi-variable

  3. Single variable

  4. None of these

Show answer
Correct Option: C
Explanation:

An index number is called a simple index when it is computed from Single variable.

A quantity index that is designed to measure changes in physical volume or production levels of industrial goods over time is known as the

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

  1. physical volume index

  2. time index

  3. Index of Industrial Production and Capacity Utilization

  4. none of the above

Show answer
Correct Option: C
Explanation:

A quantity index that is designed to measure changes in physical volume or production levels of industrial goods over time is known as the Index of Industrial Production and Capacity Utilization.

The CLI for the year 1996 and 1999 are $140$ and $200$ respectively.A person earns Rs $11200$ p.m in the year 1996.What should be his earnings in the year 1999 so as to maintain his former standard of living.

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

  1. Rs$14000$

  2. Rs$15600$

  3. Rs$16000$

  4. Rs$12500$

Show answer
Correct Option: C
Explanation:

CLI for the year $1996 = 140$

CLI for the year $1999 = 200$

Earning p.m. in $1996 = 11200$
Earning p.m. in $1999 = x$

$\Rightarrow$ $140:200 :: 11200:x$
$\Rightarrow$ $x = \dfrac{200}{140}\times 11200$

$\therefore x =$ Rs $16000$ 

Find $y$,if cost of living index number is $200$

Group Food Clothing Fuel and lighting House rent Miscellaneous
I $180$ $120$ $160$ $300$ $200$
W $4$ $5$ $3$ $y$ $2$
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. $12$

  2. $6$

  3. $11$

  4. $7$

Show answer
Correct Option: B
Explanation:

Cost of living index number $= \dfrac{\sum I _{i}W _{i}}{\sum W _{i}}$

$\sum I _{i}W _{i} = 2200 + 300y$

$\sum W _{i} = 14 + y$


$\Rightarrow$ Cost of living index number $= \dfrac{2200 + 300y}{14 + y} = 200$

$\Rightarrow 2200 + 300y = 2800 + 200y$

$\therefore y = 6$

Calculate a price index for the following by using price relative method:

Commodity A B C D E
Price in 1991 (in Rs) 20 40 60 80 100
Price in 1992( in Rs) 70 45 70 90 105
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. 152.24

  2. 153.33

  3. 159.33

  4. 161.24

Show answer
Correct Option: C
Explanation:
 $Commodity$ $Price\, in\,1991$$(in\,Rs.)$ $P _0$   $Price\,in\,1992$$(in\,Rs.)$  $P _1$ $Price\, Relative$[$\dfrac{P _1}{P _0}\times 100$ ]
 $A$  $20$  $70$  $350$ 
 $B$  $40$  $45$   $112.5$
 $C$  $60$  $70$  $116.66$
 $D$  $80$  $90$  $112.5$
 $E$  $100$  $105$  $105$
 $Total$      $796.66$

$\Rightarrow$  Price index by using price relative method = $\dfrac{\sum\dfrac{ P _1}{ P _0}\times 100}{N}=\dfrac{796.66}{5}=159.33$

Construct an index for 1998 taking 1997 as base by average of Relatives:

Commodity A B C D E
Price in 1997 5 4 8 11 2
Price in 1998 7 6 9 12 2
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. 122.32

  2. 126.04

  3. 132.32

  4. 134.45

Show answer
Correct Option: A
Explanation:
 $Commodity$ $Price\,in\,1997$$(in Rs.)\, [P _0]$  $Price\,in\,1998$$(in\,Rs.)\,[P _1]$  $Price\,relative$$\dfrac{P _1}{P _0}\times 100$ 
 $A$ $5$  $7$  $140$ 
$B$  $4$  $6$  $150$ 
$C$  $8$  $9$  $112.5$ 
$D$  $11$  $12$  $109.09$ 
$E$  $2$  $2$  $100$ 
$Total$      $611.59$ 

$\Rightarrow$  $P _{01}=\dfrac{\sum \dfrac{P _1}{P _0}\times 100}{N}=\dfrac{611.59}{5}=122.32$

$\therefore$   Price index for $1998$, takin $1997$ base year is $122.32$