## What is Quartile Deviation?

** Quartile Deviation** (

*) divides the distribution into multiple quarters. Quartile Deviation is calculated as the average of the difference of the upper quartile (Q*

*absolute measure*_{3}) and the lower quartile (Q

_{1}).

Where,

Q_{3} = Upper Quartile (Size of item)

Q_{1} = Lower Quartile (Size of item)

## What is Interquartile Range?

Interquartile Range refers to the difference between two quartiles.

Interquartile Range = Q

_{3 }– Q_{1}

## 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,

Q_{3} = Upper Quartile (Size of item)

Q_{1} = 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:

Q_{1} lies in the group 10-15.

l_{1} = 10, c.f. = 24, f = 30, i = 5

**Q**_{1}** = 14.33**

Q_{3} lies in the group 20-25.

l_{1} = 20, c.f. = 100, f = 60, i = 5

**Q**_{3}** = 24.16**

** Interquartile Range** = Q

_{3}– Q

_{1}= 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:

Q_{1} lies in the group 20-30.

l_{1} = 20, c.f. = 14, f = 20, i = 10

**Q**_{1}** = 23**

Q_{3} lies in the group 30-40.

l_{1} = 30, c.f. = 34, f = 28, i = 10

**Q**_{3}** = 39.28**

** Interquartile Range** = Q

_{3}– Q

_{1}= 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:

Q_{1} lies in the group 10-20.

l_{1} = 10, c.f. = 4, f = 3, i = 10

**Q**_{1 }**= 15.83**

Q_{3} lies in the group 40-50.

l_{1} = 40, c.f. = 13, f = 8, i = 10

**Q**_{3}** = 45.31**

** Interquartile Range** = Q

_{3}– Q

_{1}= 45.31 – 15.83 = 29.48

** Quartile Deviation** =

** Coefficient of Quartile Deviation** =

#### Example 4:

#### Solution:

Q_{1} lies in the group 8.5-13.5.

l_{1} = 8.5, c.f. = 3, f = 4, i = 5

**Q**_{1}** = 9.75**

Q_{3} lies in the group 18.5-23.5.

l_{1} = 18.5, c.f. = 10, f = 2, i = 5

**Q**_{3}** = 23.5**

** Interquartile Range** = Q

_{3}– Q

_{1}= 23.5 – 9.75 = 13.75

** Quartile Deviation** =

** Coefficient of Quartile Deviation **=