Tag: measures of dispersion and skewness

Questions Related to measures of dispersion and skewness

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?

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

  1. $132$

  2. $122$

  3. $128$

  4. $126$

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Correct Option: B

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

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

  1. $9$

  2. $5$

  3. $8$

  4. $6$

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Correct Option: A

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 _______.

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

  1. $80,20$

  2. $20,80$

  3. $30,70$

  4. $70,30$

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Correct Option: A
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 $=20\%$

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 _______.

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

  1. $3$

  2. $7$

  3. $4$

  4. $6$

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Correct Option: C
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

Probability is expressed as _______.

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

  1. percentage

  2. ratio

  3. proportion

  4. all (a), (b), (c)

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Correct Option: D
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.

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

  2. 80

  3. 70

  4. None of these

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Correct Option: C
Explanation:

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

Which of the following are limitations of range?

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

  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

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Correct Option: D

Which of the following is true with respect to range?

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

  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

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Correct Option: D

Which of the following is another term for quartile division?

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

  1. Inter quartile range

  2. Semi Inter Quartile Range

  3. Inter Quartile Deviation

  4. None of these

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Correct Option: B

Range =

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

  1. Largest value - Smallest value

  2. Largest value divided by 2

  3. Both A and B

  4. None of the above

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Correct Option: A
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.