Quartile Deviation in Discrete Series | Formula, Calculation and Examples

Last Updated : 13 Oct, 2023

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 = $\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{60-40}{60+40}=0.2$

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Chapter 1: Concept of Economics and Significance of Statistics in Economics

Chapter 2: Collection of Data

Chapter 3: Organisation of Data

Chapter 4: Presentation of Data: Textual and Tabular

Chapter 5: Diagrammatic Presentation of Data

Chapter 6: Measures of Central Tendency: Arithmetic Mean

Chapter 7: Measures of Central Tendency: Median and Mode

Chapter 8: Measures of Dispersion

Chapter 9: Correlation

Chapter 10: Index Number

Important Formulas in Statistics for Economics

Quartile Deviation in Discrete Series | Formula, Calculation and Examples

What is Quartile Deviation?

What is Interquartile Range?

What is Coefficient of Quartile Deviation?

Examples of Quartile Deviation in Discrete Series

Example 1:

Solution:

Example 2:

Solution:

Example 3:

Solution:

Example 4:

Solution:

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