Interquartile range

The interquartile range measures the spread of the middle half of a dataset, running from the 25th percentile, the first quartile, to the 75th percentile, the third quartile. It is calculated as IQR = Q3 - Q1, and because it excludes the lowest and highest quarters of the data entirely, it is far less affected by extreme values than the full range or the standard deviation.

The interquartile range is closely tied to the median and percentile: together, the minimum, Q1, median, Q3, and maximum form the five-number summary typically drawn as a box plot, where the box spans the IQR and the line inside it marks the median. This combination gives a fuller picture of a distribution's center and spread than a single average-based statistic.

The IQR matters most for skewed or outlier-prone data, such as income, latency, or deal size, where the mean and standard deviation can be distorted by a small number of extreme values. It is also the basis of a common outlier detection rule: values below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR are flagged for review. The main pitfall is applying that 1.5x rule mechanically to a distribution that is naturally skewed, where it will flag many legitimate values as outliers.