Tag: business economics and quantitative methods

Questions Related to business economics and quantitative methods

if $25%$ of the items are less then $10% and 25%$are more than $40$ then the coefficient of quartile deviation is 

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $30$

  2. $50$

  3. $1.2$

  4. $0.6$

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Correct Option: A

The suitable measure of central tendency for qualitative data is ______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. mode

  2. arithmetic mean

  3. geometric mean

  4. median

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Correct Option: D

The first quartile is also known as ______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. median

  2. lower quartile

  3. mode

  4. third decile

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Correct Option: B

The third quartile is also called ________.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. lower quartile

  2. median

  3. mode

  4. upper quartile

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Correct Option: D

The number of partition values in case of quartiles is ______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $4$

  2. $3$

  3. $2$

  4. $1$

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Correct Option: B

From which average sum of deviations is zero?

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. Median

  2. Mean

  3. Mode

  4. None of them

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Correct Option: B

Mean of a set of values is based on _______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. all values

  2. $50$ percent values

  3. first and last value

  4. maximum & minimum value

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Correct Option: A

For the following data:

Weekly Income (in Rs.): 58 59 60 61 62 63 64 65 66
No. of Workers: 2 3 6 15 10 5 4 3 1


The value of $\displaystyle\frac{Q _1+Q _3}{2}$ is equal to

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $Q _1$

  2. $Q _2$

  3. $Q _3$

  4. None of these

Show answer
Correct Option: D
Explanation:

The cumulative frequency of the table is a given below:

Weekly income ( in Rs.) No. of workers Cumulative frequency
58 2 2
59 3 5
60 6 11
61 15 26
62 10 36
63 5 41
64 4 45
65 3 48
66 1 49
N = 49


Lower Quartile: 
We have $\displaystyle\frac{N}{4} = \displaystyle\frac{49}{4} = 12.25$
The cumulative frequency just greater than $\displaystyle\frac{N}{4}$ is $26$ and the corresponding value of the variable is $61$
$\therefore\quad Q _1 = Rs.\space 61$

Middle Quartile (median): 
We have $\displaystyle\frac{N}{2} = \displaystyle\frac{49}{2} = 24.5$
The cumulative frequency just greater than $\displaystyle\frac{N}{2}$ is $26$ and the corresponding value of the variable is $61$
$\therefore\quad Q _2 = Rs.\space 61$

Upper Quartile:
We have $\displaystyle\frac{3N}{4} = \displaystyle\frac{3\times49}{4} = 36.75$
The cumulative frequency just greater than $\displaystyle\frac{3N}{4}$ is $41$ and the corresponding value of the variable is $63$
$\therefore\quad Q _3 = Rs.\space 63$

$\therefore\quad \displaystyle\frac{Q _1+Q _3}{2} = \displaystyle\frac{61+63}{2} = 62$

If 25% of the items are less than 10 and 25%  are more than 40, then the coefficient of quartile deviation is

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. 30

  2. 50

  3. 1.2

  4. 0.6

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Correct Option: A

The quartile deviation of the income of a certain person given in rupees for 12 months in a year:139, 150, 151,151,157,158,160,161,162,162,173,175

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. 4.5

  2. 5.5

  3. 6.2

  4. none of these

Show answer
Correct Option: B
Explanation:
S.NO. Income(Rs)
1 139
2 150
3 151
4 151
5 157
6 158
7 160
8 161
9 162
10 162
11 173
12 175

$N=12$
${ Q } _{ 1 }=$ Size of $\displaystyle\frac { N+1 }{ 4 } th=3.25th$ item
$=$ size of $3rd$ item $+0.25$(size of $4th$ item)$-$(size of $3rd$ item)
$=151+0.25(151-151)=$Rs.$151$
${ Q } _{ 3 }=$ Size of $\displaystyle\frac { 3(N+1) }{ 4 } th=9.75th$ item
$=$ size of $9th$ item $+0.75$(size of $10th$ item)$-$(size of $9th$ item)
$=162+0.75(162-162)=$Rs.$162$
$\therefore$ Quartile Deviation $\displaystyle=\frac { 1 }{ 2 } \left( { Q } _{ 3 }-{ Q } _{ 1 } \right) =\frac { 11 }{ 2 } =$Rs.$5.5$