What is Quartile Deviation?
Quartile Deviation or Semi-Interquartile Range is the half of difference between the Upper Quartile (Q3) and the Lower Quartile (Q1). In simple terms, QD is the half of inter-quartile range. Hence, the formula for determining Quartile Deviation is as follows:
Where,
Q3 = Upper Quartile (Size of item)
Q1 = Lower Quartile (Size of item)
Example:
Calculate Quartile Deviation of the following data:
150, 110, 200, 300, 180, 320
Solution:
Q1 =
Size of 1.75th item = Size of 1st item + 0.75(Size of 2nd item – Size of 1st item)
Q1 = 110 + 0.75(150 – 110)
Q1 = 110 + 30
Q1 = 140
Q3 =
Size of 5.25th item = Size of 5th item + 0.25(Size of 6th item – Size of 5th item)
Q3 = 300 + 0.25(320 – 300)
Q3 = 300 + 5
Q3 = 305
Quartile Deviation = 82.5
Interquartile Range and Quartile Deviation
The extent to which the values of a distribution differ from the average of that distribution is known as Dispersion. The measures of dispersion can be either absolute or relative. The Measures of Absolute Dispersion consist of Range, Quartile Deviation, Mean Deviation, Standard Deviation, and Lorenz Curve.
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