CBSE Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 9 - MCQExams.com

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. 

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

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. 

Variance is the mean of the squares of the deviations from the mean. Therefore, if a constant value that is 15 is subtracted from each observations of the set, then the variance will not be altered as the effect of such a act will be managed at the time of calculating the deviations of the series. 

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. So the deviations are affected by division and multiplication. Therefore, if each observation of the set id divided by 10 then the whole standard deviation also becomes 1/10 th of the prior standard deviation. 

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. 

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. 

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 = 60 

In the given series, H= 80 and L= x 

Range => 80-x = 60

            => x = 80-60 = 20 

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 .

Quartile deviation = (Q₃-Q₁) /2

                             = 74/2

                             = 37

In the given series, 13,13,13,13 

Mean = 52/4 = 13 

Since all the deviations will be zero. Therefore the sum of the deviations will also be zero. 

Standard deviation = { sum of the deviations / number of terms}^1/2

                               = {0/4} ^½

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 = 55

In the given series, H= x and L= 15

Range => x-15 = 55

            => x = 55+15 = 70 

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

Quartile deviation also known as 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 .

Quartile deviation or semi inter-quartile deviation = (Q₃-Q₁) /2

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Standard deviation = { (sum of the squares of the observations/ number of observations ) – (sum of observations/ number of observations ) } ^½

                                = { (2800/10) –(110/10) } ^½

                                = { 280- 11}^1/2

                                = (169) ^½

                                = 13 

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.

Coefficient of variation = ( standard deviation / mean )

=> 80 /100 = S.D / 40 

=> S.D = 32 

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 . Since quartile deviation is not affected by the extreme values of the series. Therefore, it can be calculated in case of open end intervals also. 

Variance is the mean of the squares of the deviations from the mean. Variance is not affected by the addition, subtraction, multiplication and division of the given values. Therefore, if each value of the series is multiplied by 15, the coefficient of variation will be unaltered.