Relative measures of dispersion

Definition of Relative measures of dispersion:

A relative measure of dispersion is a statistical value that may be utilized to compare variations in two or more samples.The measures of dispersion are normally expressed as decimals or percentages and generally they do not have any type of other units

Illustration

The average distance covered by vehicles in a motor rally may be given as 2000 kilometer along with a standard deviation of 5 kilometer.

In another competition set of vehicles covered 3000 kilometer along with a standard deviation of 10 kilometer

NB: The two standard deviations described above are referred to as absolute measures of dispersion. These are real deviations of the measurements from their respective mean

Conversely, these are not extremely useful while comparing dispersions among samples.

Hence the following measures of dispersion are generally employed in order to assess the degree of dispersion.

i. Coefficient of mean deviation

= (mean deviation)/mean

ii. Coefficient of quartile deviation

 = ½(Q₃ - Q₁)/Q₂

Whereas:  Q₁ = first quartile

                  Q₃ = third quartile

iii.Coefficient of standard deviation

= standard deviation /mean

iv. Coefficient of variation

= ( standard deviation /mean) * 100

Illustration sees information above

First group of cars: mean = 2000 kilometre

           Standard deviation = 5 kilometre

∴ C.O.V            = (5 /2000) x 100

                        = 0.25%

Second group of cars: mean = 3000 kilometre

            Standard deviation = 10 kilometre

∴ C.O.V            = (10/3000)    x 100

= 0.33%

Conclusion

Because the coefficient of variation is greater in the 2^nd group, than in the first group we may conclude that the distances covered in the 1^st group are much closer to the 2nd group.