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 =