Tag: measures of dispersion and skewness

Quizzes (4) Questions (166)

Questions Related to measures of dispersion and skewness

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 measure of dispersion is most affected by extreme values?

  1. Standard deviation

  2. Mean deviation

  3. Range

  4. Quartile deviation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Range is the most simple and commonly understandable measures of dispersion.Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

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

Semi inter-quartile deviation is given by the formula _______.

  1. $Q _3 - Q _1$
  2. $\frac{Q _3 - Q _1}{8}$
  3. $\frac{(Q _3 - Q _1)}{2}$
  4. $\frac{(Q _3 - Q _1)}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Semi inter-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 .


Semi inter-quartile deviation = (Q3-Q1) /2

                             = (29-17)/2

                             = 12/2

                             = 6

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 measure of dispersion ensures lowest degree of reliability?

  1. Range

  2. Mean deviation

  3. Quartile deviation

  4. Standard deviation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most affected measures of dispersion by the extreme values of the series therefore it has the lowest degree of reliability. 

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 co-efficient of range from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

  1. $0.6$
  2. $0.5$
  3. $0.55$

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

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion.

Range = H - L 
In the given series, H= 34 and L+ 10 
Range = 34-10 = 24.
Coefficient of range is found by dividing the range with the sum of highest and lowest value of the series. 
Coefficient of range (CR) = R/ (H+L) 
                                          =24 / (34+10) 
                                          = 24/ 44 = 0.55 

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 co-efficient of quartile deviation from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

  1. $0.26$
  2. $0.16$
  3. $0.06$
  4. $0.36$
Reveal answer Fill a bubble to check yourself
A 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 .

The coefficient of quartile deviation is found by dividing the difference between the first quartile and the third quartile by the sum between the first quartile and the third quartile.

In the given series, 10, 15,17,18,20,22,25,28,29,32,34. 

Q1= 17 and Q3=29 

Coefficient of quartile deviation =(Q3-Q1)/ (Q3+Q1)

                                            = (29-17)/ (29+17)

                                            = 12/46 = 0.26 



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 variance of $1, 2, 4, 5$ and x is $2$, then x is _____.

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

Variance = sum((x_i - mean)^2) / n = 2. For data 1, 2, 4, 5, x, the mean is (12 + x) / 5. Solving for x where variance is 2 leads to x = 3.

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 measure of dispersion is least affected by extreme values?

  1. Range

  2. Mean deviation

  3. Standard deviation

  4. Quartile deviation
Reveal answer Fill a bubble to check yourself
D 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 . Therefore, quartile deviation is not affected by the extreme values of the series. 

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

Sum of squares of the deviations is minimum when deviations are taken from ________.

  1. mean

  2. median

  3. mode

  4. zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Mean deviation is the arithmetic average of the deviations of the observed values from an  average of the observed values. 
Mean deviation from the mean calculates the arithmetic average of the deviations of the observed values from mean of the observed values. Sum of the squares of the deviations is minimum when deviations are taken from mean as mean is the arithmetic average of the series and disperse the whole series into individual minimum value therefore the sum of their squares is minimum. 
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 from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

  1. $8$
  2. $6$
  3. $10$
  4. $5$
Reveal answer Fill a bubble to check yourself
B 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 .

In the given series, 10, 15,17,18,20,22,25,28,29,32,34 

Q1= 17 and Q3=29

Therefore, Quartile deviation = (Q3-Q1) /2

                                                 = (29-17)/2

                                                  = 12/2

                                                  = 6

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

Given the following set of data, what is the range 12 23 34 54 21 8 9 67:

  1. 55

  2. 59

  3. 8

  4. 56
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

Range = H - L 

In the given series, H= 67 and L= 12 

Range = 67 -12 = 55 .