The interquartile range (IQR) quantifies the spread of the central 50% of a dataset. It is computed by subtracting the first quartile (Q1, the 25th percentile) from the third quartile (Q3, the 75th percentile). For instance, consider a dataset of exam scores. The IQR would indicate the range within which the middle half of the scores fall, providing a measure of score variability that is less sensitive to outliers than the standard deviation.
Employing the IQR offers several advantages. It provides a robust measure of statistical dispersion, meaning it is less affected by extreme values compared to methods based on the mean and standard deviation. This makes it particularly useful when analyzing data that may contain errors or outliers. Furthermore, the IQR is a foundational concept in descriptive statistics, playing a vital role in constructing boxplots, which are valuable tools for visualizing and comparing distributions.