What is the formula for calculating the interquartile range?

The interquartile range (IQR) is a measure of statistical dispersion that indicates the range within which the central 50% of a dataset lies. It is specifically calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

Q3 represents the 75th percentile of the data, which means that 75% of the data points fall below this value. Conversely, Q1 is the 25th percentile, indicating that 25% of the data points fall below this point. Thus, the IQR provides insight into the spread of the middle half of the data, allowing for a more robust measure of variability that is less affected by outliers compared to the total range.

When calculating the IQR using the formula Q3 - Q1, the result reflects how far apart these two quartiles are from each other, effectively giving the width of the central data spread. This calculation is fundamental for understanding distributions, particularly in identifying outliers or assessing data consistency.