Interquartile Range
What is the Interquartile Range?
The interquartile range (IQR) is an absolute measure of variability that represents the difference between the third quartile (Q3) and the first quartile (Q1), calculated as $$ \delta_Q = Q_3 - Q_1 $$
The IQR is less affected by outliers and extreme values compared to the range because it only takes into account the middle portion of the distribution.
It’s also fairly simple to compute.
On the downside, the IQR is a less comprehensive measure of variability since it only considers 50% of the data within the distribution.
What are quartiles? Quartiles are positional markers that divide a sorted dataset into four equal parts. The first quartile (Q1) is the value below which 25% of the data falls, while the third quartile (Q3) is the value below which 75% of the data lies.
A Practical Example
Consider a dataset where the first quartile (Q1) is 18 and the third quartile (Q3) is 27.
$$ Q_1 = 18 $$
$$ Q_3 = 27 $$
In this case, the interquartile range is 9.
$$ \delta_Q = Q_3 - Q_1 = 27 - 18 = 9 $$
And that’s how it’s calculated.
