Tag: histograms and frequency distribution diagrams

Questions Related to histograms and frequency distribution diagrams

If we plot the more than type and less than type frequency distributions of the same set of date, their graph intersect at a point which is known as ______.

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

  1. median

  2. mode

  3. mean

  4. none of the above

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Correct Option: A

Which of the following relations among the location parameters does not hold?

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

  1. $Q _2 = Median$

  2. $P _50 = Median$

  3. $D _5 = Median$

  4. $D _4 = Median$

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Correct Option: D

In a group, $2$ students spend Rs$8$ daily, $3$ students spend Rs$10$ daily and $5$ students spend Rs$6$ daily. The average spending of all $10$ students 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. $7.6$

  2. $5.8$

  3. $8.5$

  4. $6.7$

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Correct Option: A

The $P _82$ for the following distribution is

X 2 3 4 5 6 7 8 9 10 11
Y 3 6 9 18 20 14 10 10 7 2


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

  1. $6$

  2. $5$

  3. $8$

  4. $9$

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Correct Option: D

Which of the following measures of dispersion can attain a negative value?

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

  1. Range

  2. Mean deviation

  3. Standard deviation

  4. None of the above

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Correct Option: D
Explanation:

Measure of dispersion is a statistical method to find a specific value from a dispersed series where the extent to which various values of the series tend to disperse from each other or from the average is measured. So all the measures of dispersion from range to standard deviation has positive value. 

Which measure of dispersion is most affected by extreme values?

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

  1. Standard deviation

  2. Mean deviation

  3. Range

  4. Quartile deviation

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Correct Option: C
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. 

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

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

  1. $Q _3 - Q _1$

  2. $\frac{Q _3 - Q _1}{8}$

  3. $\frac{(Q _3 - Q _1)}{2}$

  4. $\frac{(Q _3 - Q _1)}{4}$

Show answer
Correct Option: C
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

Which measure of dispersion ensures lowest degree of reliability?

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

  1. Range

  2. Mean deviation

  3. Quartile deviation

  4. Standard deviation

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Correct Option: A
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. 

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

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

  1. $0.6$

  2. $0.5$

  3. $0.55$

  4. None of them

Show answer
Correct Option: C
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 

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

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

  1. $0.26$

  2. $0.16$

  3. $0.06$

  4. $0.36$

Show answer
Correct Option: A
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