Tag: business economics and quantitative methods

Quizzes (24) Questions (932)

Questions Related to business economics and quantitative methods

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

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

  1. mode

  2. arithmetic mean

  3. geometric mean

  4. median
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Median is the most suitable measure for qualitative data (ordinal data) because it is based on the position of values rather than their magnitude, which cannot be averaged numerically.

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

Mean of a set of values is based on _______.

  1. all values
  2. $50$ percent values

  3. first and last value

  4. maximum & minimum value
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The arithmetic mean is calculated by summing all values in a dataset and dividing by the count, making it dependent on every single observation.

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

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

  1. $Q _1$
  2. $Q _2$
  3. $Q _3$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $63$
$\therefore\quad Q _3 = Rs.\space 63$

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

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

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

  1. 4.5

  2. 5.5

  3. 6.2

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.$5.5$