Quartile Deviation in Continuous Series | Formula, Calculation and Examples

What is Quartile Deviation?

Quartile Deviation (absolute measure) divides the distribution into multiple quarters. Quartile Deviation is calculated as the average of the difference of the upper quartile (Q₃) and the lower quartile (Q₁).

Where,

Q₃ = Upper Quartile (Size of  item)

Q₁ = Lower Quartile (Size of  item)

What is Interquartile Range?

Interquartile Range refers to the difference between two quartiles.

Interquartile Range = Q₃ – Q₁

What is Coefficient of Quartile Deviation?

For comparative studies of the variability of two or more series with different units, the Coefficient of Quartile Deviation (relative measure) is used.

Where,

Q₃ = Upper Quartile (Size of  item)

Q₁ = Lower Quartile (Size of  item)

Examples of Quartile Deviation in Continuous Series

Example 1:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following figures:

Solution:

Q₁ lies in the group 10-15.

l₁ = 10, c.f. = 24, f = 30, i = 5

Q₁ = 14.33

Q₃ lies in the group 20-25.

l₁ = 20, c.f. = 100, f = 60, i = 5

Q₃ = 24.16

Interquartile Range = Q₃ – Q₁ = 24.16 – 14.33 = 9.83

Quartile Deviation = 

Coefficient of Quartile Deviation = 

Example 2:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following figures:

Solution:

Q₁ lies in the group 20-30.

l₁ = 20, c.f. = 14, f = 20, i = 10

Q₁ = 23

Q₃ lies in the group 30-40.

l₁ = 30, c.f. = 34, f = 28, i = 10

Q₃ = 39.28

Interquartile Range = Q₃ – Q₁ = 39.28 – 23 = 16.28

Quartile Deviation = 

Coefficient of Quartile Deviation = 

Example 3:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following figures:

Solution:

Q₁ lies in the group 10-20.

l₁ = 10, c.f. = 4, f = 3, i = 10

Q₁ = 15.83

Q₃ lies in the group 40-50.

l₁ = 40, c.f. = 13, f = 8, i = 10

Q₃ = 45.31

Interquartile Range = Q₃ – Q₁ = 45.31 – 15.83 = 29.48

Quartile Deviation = 

Coefficient of Quartile Deviation = 

Example 4:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following figures:

Solution:

Q₁ lies in the group 8.5-13.5.

l₁ = 8.5, c.f. = 3, f = 4, i = 5

Q₁ = 9.75

Q₃ lies in the group 18.5-23.5.

l₁ = 18.5, c.f. = 10, f = 2, i = 5

Q₃ = 23.5

Interquartile Range = Q₃ – Q₁ = 23.5 – 9.75 = 13.75

Quartile Deviation = 

Coefficient of Quartile Deviation =