What does the interquartile range (IQR) represent?

The interquartile range (IQR) represents the difference between the third quartile (Q3) and the first quartile (Q1) of a data set. Specifically, Q1 is the 25th percentile, and Q3 is the 75th percentile, meaning that the IQR captures the middle 50% of the data. By calculating the IQR, one can assess the spread of the central portion of the dataset, which is useful for identifying potential outliers and understanding the variability without being affected by extreme values.

This measure is particularly beneficial in descriptive statistics because it gives a clearer picture of data dispersion than just using the range, which includes all data points. The IQR is a robust measure since it focuses on the central values, making it less sensitive to outliers than the total range or the difference between the highest and lowest values.