The interquartile range (IQR) is a measure of statistical dispersion that describes the spread of the middle 50% of a data set. It is calculated as the difference between the third quartile (Q3, the 75th percentile) and the first quartile (Q1, the 25th percentile), so:

IQR=Q3−Q1\text{IQR}=Q3-Q1IQR=Q3−Q1

This means the IQR captures the range within which the central half of the data lies, excluding the lowest 25% and the highest 25% of values. It is a robust measure of variability because it is not affected by extreme values or outliers as much as the total range is

. The IQR is often used to:

• Understand the spread of the central portion of the data
• Identify outliers (values that fall below Q1 - 1.5×IQR or above Q3 + 1.5×IQR)
• Visualize data distribution in box plots, where the box represents the IQR

In summary, the interquartile range tells you how spread out the middle half of your data is, providing a clearer picture of variability than just the total range