What is Coefficient of Quartile Deviation?

As Quartile Deviation is an absolute measure of dispersion, one cannot use it for comparing the variability of two or more distributions when they are expressed in different units. Therefore, in order to compare the variability of two or more series with different units it is essential to determine the relative measure of Quartile Deviation, which is also known as the Coefficient of Quartile Deviation. It is studied to make the comparison between the degree of variation in different series. The formula for determining Coefficient of Quartile Deviation is as follows:

Where,

Q₃ = Upper Quartile (Size of  item)

Q₁ = Lower Quartile (Size of  item)

Example:

Calculate Coefficient of Quartile Deviation of the following data:

150, 110, 200, 300, 180, 320

Solution:

Q₁ = 

Size of 1.75^th item = Size of 1^st item + 0.75(Size of 2^nd item – Size of 1^st item)

Q₁ = 110 + 0.75(150 – 110)

Q₁ = 110 + 30

Q₁ = 140

Q₃ = 

Size of 5.25^th item = Size of 5^th item + 0.25(Size of 6^th item – Size of 5^th item)

Q₃ = 300 + 0.25(320 – 300)

Q₃ = 300 + 5

Q₃ = 305

Coefficient of Quartile Deviation = 0.37

Note: The Coefficient of Quartile Deviation is calculated for making a comparison between the degree of variation in the given series. 

The extent to which the values of a distribution differ from the average of that distribution is known as Dispersion. The measures of dispersion can be either absolute or relative. The Measures of Absolute Dispersion consist of Range, Quartile Deviation, Mean Deviation, Standard Deviation, and Lorenz Curve.