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).
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)
Example 1:
From the following table, calculate the interquartile range, quartile deviation, and coefficient of quartile deviation.
Solution:
Q1 = 155 centimeters
Q3 = 163 centimeters
Interquartile Range = Q3 – Q1 = 163 – 155 = 8
Quartile Deviation =
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:
Q1 = 4
Q3 = 12
Interquartile Range = Q3 – Q1 = 12 – 4 = 8
Quartile Deviation =
Coefficient of Quartile Deviation =
Example 3:
Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following data.
Solution:
Q1 = 47 Kilograms
Q3 = 53 Kilograms
Interquartile Range = Q3 – Q1 = 53 – 47 = 6
Quartile Deviation =
Coefficient of Quartile Deviation =
Example 4:
Calculate the interquartile range, quartile deviation, and coefficient of quartile deviation from the following data.
Solution:
Q1 = 40 Years
Q3 = 60 Years
Interquartile Range = Q3 – Q1 = 60 – 40 = 20
Quartile Deviation =
Coefficient of Quartile Deviation =
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