Tag: measures of dispersion and skewness

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Questions Related to measures of dispersion and skewness

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

The median of a symmetrical distribution, whose lower and upper quartiles are 60 and 80 respectively, is

  1. 60

  2. 80

  3. 70

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given,  lower quartile $=60$ and upper quartile $=80$ 
$\therefore$ median $=\frac{\mbox{
lower quartile
}+\mbox{
upper quartile
}}{2}=\dfrac{60+80}{2}=70$

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

Which of the following are limitations of range?

  1. It is not based on all the values.

  2. As long as the minimum and maximum values remain unaltered, any change in other values does not affect range.

  3. It can not be calculated for open-ended frequency distribution.

  4. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The range is defined as the difference between the maximum and minimum values. It is limited because it ignores the distribution of intermediate values, is highly sensitive to outliers, and cannot be computed for open-ended distributions.

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

Which of the following is true with respect to range?

  1. Higher value of Range implies higher dispersion and vice-versa

  2. Range is unduly affected by extreme values.

  3. It is not based on all the values.

  4. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Range is the difference between the maximum and minimum values. Because it only considers these two extremes, it is highly sensitive to outliers and does not account for the distribution of all data points.

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

Which of the following is another term for quartile division?

  1. Inter quartile range

  2. Semi Inter Quartile Range

  3. Inter Quartile Deviation

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quartile deviation is defined as half of the interquartile range, which is why it is also known as the semi-interquartile range.

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

Range =

  1. Largest value - Smallest value

  2. Largest value divided by 2

  3. Both A and B

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Range refers to the value of variation between the largest and the smallest values in a particular data set. It can be calculated as the difference between the upper limit and lower limit of a particular set of data.