Tag: business economics and quantitative methods

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Questions Related to business economics and quantitative methods

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

Mode is that value in a frequency distribution which possesses __________.

  1. minimum frequency

  2. maximum frequency

  3. frequency one

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By definition, the mode of a frequency distribution is the value that occurs most frequently, meaning it has the maximum frequency.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

In a discrete series having $(2n+1)$ observations, median is ______.

  1. nth observation
  2. $(n+1)$th observation
  3. $[(n+2)/2]th$ observation
  4. $[(2n+1)/2]th$ observation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a series with N observations, if N is odd, the median is the ((N+1)/2)th observation. Substituting N = 2n+1 gives ((2n+1+1)/2)th = (2n+2)/2 = (n+1)th observation.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

The average runs of a cricketer in four innings is $32$. How many runs he should score in the fifth inning so that his averages score becomes $50$ runs?

  1. $132$
  2. $122$
  3. $128$
  4. $126$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total runs in 4 innings = 4 * 32 = 128. Total runs needed for 5 innings = 5 * 50 = 250. Runs needed in 5th inning = 250 - 128 = 122.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

In a moderately skewed distribution the arithmetic mean is $10$ units and the mode is $7$ units, the median is ______.

  1. $9$
  2. $5$
  3. $8$
  4. $6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a moderately skewed distribution, the empirical relationship is: Mean - Mode = 3(Mean - Median). Given Mean = 10 and Mode = 7, we have 10 - 7 = 3(10 - Median), so 3 = 3(10 - Median), which means 1 = 10 - Median, so Median = 9.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

The mean annual salary of all employees in a company is Rs$25,000$. The mean salaries of male and female employees are Rs$27,000$ and $Rs17,000$ respectively, the percentage of males and females employees by the company is _______.

  1. $80,20$
  2. $20,80$
  3. $30,70$
  4. $70,30$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, the mean annual salary of all employees in a company is $Rs\ 25,000$ & mean salaries of male and female employees are $Rs\ 27,000$ and $Rs\ 17,000$ respectively.


Let us consider mean salaries of male as $Rs. 27000$ and female as $17,000$

$\dfrac{27,000x+17,000y}{x+y}=25,000$
$27,000x+17,000y=25,000x+25,000y$
$2000x=8000y$

$x=4y$

Percentage of males $(4y/5y)\times 100=80\%$

Percentage of females $=20\%$

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

In distribution $25\%$ of the observations are less than $46$ and $25\%$ of the observations are more than $54$. The quartile deviation of the distribution is _______.

  1. $3$
  2. $7$
  3. $4$
  4. $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 . 

Q1= 46 and Q3=54

Quartile deviation = (Q3-Q1) /2

                             = (54-46)/2

                             = 8/2

                             = 4

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

Probability is expressed as _______.

  1. percentage

  2. ratio

  3. proportion

  4. all (a), (b), (c)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1.
Multiple choice business economics and quantitative methods linear correlation spearman's coefficient of correlation spearman's rank correlation method correlation coefficients

Correlation rank coefficient for the tied rank is 

  1. $1-\dfrac{6\sum D^2}{n(n^2-1)}$
  2. $\dfrac{1}{n}\sum(x-\overline x)(y-\overline y)$
  3. $\dfrac{\dfrac{1}{n}\sum(x-\overline x)(y-\overline y)}{\sigma _x\sigma _y}$
  4. $1-\dfrac{6[\sum D^2+\dfrac{1}{12}(m _1^3-m _1)+frac{1}{12}(m-2^3-m _2)+....]}{n(n^2-1)}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When ranks are tied, Spearman's rank correlation formula requires a correction term: 1 - [6ΣD² + Σ(m³-m)/12]/[n(n²-1)], where m is the number of tied observations in each group. This adjusts for the fact that tied ranks affect the correlation calculation. Option D shows this correction (though there's a typo in 'frac').

Multiple choice business economics and quantitative methods linear correlation spearman's coefficient of correlation spearman's rank correlation method correlation coefficients

Rank correlation depends on________________.

  1. a specific distribution

  2. the ranks of observations

  3. the ranks of unknown value

  4. the ranks of known value
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rank correlation is the measure of association or strength between the ranked variables. For example: the rank of this  numerical data 65, 25, 75, 69 would be 3, 4, 1, 2 respectively.

Multiple choice business economics and quantitative methods linear correlation spearman's coefficient of correlation spearman's rank correlation method correlation coefficients

The value of Spearman's rank coefficient lies between 

  1. $2$ and $3$
  2. $1$ and $2$
  3. $0$ and $1$
  4. $-1$ and $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Spearman's rank cofficient : $R=1-\dfrac { 6\sum { { d } _{ i }^{ 2 } }  }{ n({ n }^{ 2 }-1) } $

Its values lies between $-1$ and $1$
So option $D$ is correct.