What is Interquartile Range?
Range only takes the two extreme values (largest and smallest) into consideration; therefore, it is a crude measure of dispersion. This effect of extreme values on range can be avoided by using the measure of interquartile range. The difference between the values of two quartiles is known as Interquartile Range. The formula for determining Interquartile Range is as follows:
Inter Quartile Range = Q3 – Q1
Example:
Calculate Interquartile Range 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
Interquartile Range = Q3 – Q1 = 305 – 140
Interquartile Range = 165
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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