Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

Construct a composite index number from the following index numbers and weights:

Index Numbers 127 142 186 172 115
Weight 5 4 3 6 8
business mathematics and statistics index numbers weighted methods to calculate index numbers construction of index numbers applied statistics

  1. $134$

  2. $145$

  3. $143$

  4. $149$

Show answer
Correct Option: C
Explanation:

Composite index no. $=\cfrac { \sum _{ i=1 }^{ 5 }{ { \left( \text{index no. }\right)  } _{ i } } \times { \left( \text{Index no.Weight} \right)  } _{ i } }{ \sum _{ i=1 }^{ 5 }{ { \left(\text{ weight }\right)  } _{ i } }  } $
$=\cfrac { 127\times 5+142\times 4+186\times 3+172\times 6+115\times 8 }{ 5+4+3+6+8 } $
$=\cfrac { 635+568+558+1038+920 }{ 26 } $
$=\cfrac { 3713 }{ 26 } =142.8$
$\simeq 143$

The following commodities have the given price indices relative to a base of $100$. The weights are also given:

Commodity Relative Index Weight
Butter 181 4
Bread 116 12
Tea 110 3
Bacon 152 7

Calculate the new index for this set of commodities

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

  1. $132$

  2. $133$

  3. $134$

  4. $135$

Show answer
Correct Option: D
Explanation:

New index $=\cfrac { \sum _{ i=1 }^{ 4 }{ { \left( \text{Relative index }\right)  } _{ i } } \times { \left( \text{Index no. Weight }\right)  } _{ i } }{ \sum _{ i=1 }^{ 4 }{ { \left( \text{weight }\right)  } _{ i } }  } $
$=\cfrac { 181\times 4+116\times 12+110\times 3+152\times 7 }{ 4+12+3+7 } $
$=\cfrac { 724+1392+330+1064 }{ 26 } $
$=\cfrac { 3510 }{ 26 } =\cfrac { 1755 }{ 13 } $
$=135$

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

Show answer
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

Show answer
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. $=\cfrac{1}{N}(\sum\cfrac{p _1}{p _0}\times 100)$
$\implies\cfrac{1}{1}(\sum\cfrac{100}{118}\times 100)=84.775\approx 84.75$

Which of the following is not one of the four types of variation that is estimated in time-series analysis?

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Predictable

  2. Trend

  3. Cyclical

  4. Irregular

Show answer
Correct Option: A
Explanation:

Four types of variations estimated in time-series analysis are :-

1. Trend
2. Seasonal
3. Cyclical
4. Irregular

Hence, A) Predictable is the correct option

The unsystematic sequence which follows irregular pattern of variations is called:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Noise

  2. Signal

  3. Linear

  4. Non-Linear

Show answer
Correct Option: A
Explanation:

By definition,
Noise is a component of time series which is the unsystematic sequence which follows irregular pattern of variations

A time series consists of:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Short-term variations

  2. Long-term variations

  3. Irregular variations

  4. All of the above

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  A time series consist of $Short-term\,variations,\,Long-term\,variations\, and\, Irregular\,variation.$

$\Rightarrow$  $Short \,term\, variation -$ Seasonal trends are short term movements occurring in data due to seasonal factors. For example,  it is commonly observed that the consumption of ice-cream during summer is generally high and hence an ice-cream dealer's sales would be higher in some months of the year while relatively lower during winter months.
$\Rightarrow$  $Long\,term\, variation -$ The secular trend is the main component of a time series which results from long term effects of socio-economic and political factors. Prices and export and import data, for example, reflect obviously increasing tendencies over time.
$\Rightarrow$  $Irregular\,variation-$These are sudden changes occurring in a time series which are unlikely to be repeated. They are components of a time series. Floods, fires, earthquakes, revolutions, epidemics, strikes etc., are the root causes of such irregularities

Depression in business is:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Cyclical

  3. Seasonal

  4. Irregular

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Depression in business is : $Cyclical $.

$\Rightarrow$  Depression phase - The depression or trough is the bottom of a cycle where economic activity remains at a highly low level. Income, employment, output, price level, etc. go down. 
$\Rightarrow$  A depression is generally characterized by high unemployment of labor and capital and a low level of consumer demand in relation to the economy’s capacity to produce. 
$\Rightarrow$  This deficiency in demand forces firms to cut back production and lay-off workers.

An orderly set of data arranged in accordance with their time of occurrence is called:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Arithmetic series

  2. Harmonic series

  3. Geometric series

  4. Time series

Show answer
Correct Option: D
Explanation:

From the definition of Time series,

Time series is an orderly set of data arranged in accordance with their time of occurrence.