Quartile Deviation in Discrete 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).

Quartile~Deviation=\frac{Q_3-Q_1}{2}

Where,

Q₃ = Upper Quartile (Size of 3[\frac{N+1}{4}]^{th}     item)

Q₁ = Lower Quartile (Size of [\frac{N+1}{4}]^{th}     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.

Coefficient~of~Quartile~Deviation=\frac{Q_3-Q_1}{Q_3+Q_1}

Where,

Q₃ = Upper Quartile (Size of 3[\frac{N+1}{4}]^{th}        item)

Q₁ = Lower Quartile (Size of [\frac{N+1}{4}]^{th}        item)

Examples of Quartile Deviation in Discrete Series

Example 1:

From the following table, calculate the interquartile range, quartile deviation, and coefficient of quartile deviation.

Solution:

Q_1=Size~of~\frac{N+1}{4}^{th}~item=Size~of~\frac{39+1}{4}^{th}~item=Size~of~10^{th}~item

Q₁ = 155 centimeters

Q_3=Size~of~3[\frac{N+1}{4}]^{th}~item=Size~of~3[\frac{39+1}{4}]^{th}~item=Size~of~30^{th}~item

Q₃ = 163 centimeters

Interquartile Range = Q₃ - Q₁ = 163 - 155 = 8

Quartile Deviation = \frac{Q_3-Q_1}{2}=\frac{163-155}{2}=4

Coefficient of Quartile Deviation = \frac{Q_3-Q_1}{Q_3+Q_1}=\frac{163-155}{163+155}=0.025

Example 2:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following data.

Solution:

Q_1=Size~of~\frac{N+1}{4}^{th}~item=Size~of~\frac{19+1}{4}^{th}~item=Size~of~5^{th}~item

Q₁ = 4

Q_3=Size~of~3[\frac{N+1}{4}]^{th}~item=Size~of~3[\frac{19+1}{4}]^{th}~item=Size~of~15^{th}~item

Q₃ = 12

Interquartile Range = Q₃ - Q₁ = 12 - 4 = 8

Quartile Deviation = \frac{Q_3-Q_1}{2}=\frac{12-4}{2}=4

Coefficient of Quartile Deviation = \frac{Q_3-Q_1}{Q_3+Q_1}=\frac{12-8}{12+8}=0.2

Example 3:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following data.

Solution:

Q_1=Size~of~\frac{N+1}{4}^{th}~item=Size~of~\frac{28+1}{4}^{th}~item=Size~of~7.25^{th}~item

Q₁ = 47 Kilograms

Q_3=Size~of~3[\frac{N+1}{4}]^{th}~item=Size~of~3[\frac{28+1}{4}]^{th}~item=Size~of~21.75^{th}~item

Q₃ = 53 Kilograms

Interquartile Range = Q₃ - Q₁ = 53 - 47 = 6

Quartile Deviation = \frac{Q_3-Q_1}{2}=\frac{53-47}{2}=3

Coefficient of Quartile Deviation = \frac{Q_3-Q_1}{Q_3+Q_1}=\frac{53-47}{53+47}=0.06

Example 4:

Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following data.

Solution:

Q_1=Size~of~\frac{N+1}{4}^{th}~item=Size~of~\frac{199+1}{4}^{th}~item=Size~of~50^{th}~item

Q₁ = 40 Years

Q_3=Size~of~3[\frac{N+1}{4}]^{th}~item=Size~of~3[\frac{199+1}{4}]^{th}~item=Size~of~150^{th}~item

Q₃ = 60 Years

Interquartile Range = Q₃ - Q₁ = 60 - 40 = 20

Quartile Deviation = \frac{Q_3-Q_1}{2}=\frac{60-40}{2}=10

Coefficient of Quartile Deviation = \frac{Q_3-Q_1}{Q_3+Q_1}=\frac{60-40}{60+40}=0.2