Measures of Dispersion Test - 34

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.

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

                               = { (1444) –(18.4) } ^½

                                = (1425.6) ^½

                                = 37.75 

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

Coefficient of variation = ( standard deviation / mean )x 100 

                                     = ( 37.75/ 18.4)x100

                                     = 20.51 

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 is not affected by the increase of decrease of observations in the series. 

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

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. If each value of the series is multiplied by 2, then the overall standard deviation will also be doubled as standard deviation is affected by the multiplication and division of the values. 

 

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

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 value. Therefore, if each value of the series is multiplied by 15, the coefficient of variation will be unaltered.

Each outcome of a random experiment is known as a primary event as these are the independent events which are not dependent on each other. The probability of all these primary event is always same.