Interquartile Range

The interquartile range, or IQR, is the spread of the middle half of the data: the value at the 75th percentile minus the value at the 25th percentile. By ignoring the lowest and highest quarters, it measures spread without being thrown off by extremes.

If a shop's daily sales have an IQR from 80 to 120 units, you know the typical middle range is 40 units wide, regardless of a few freak holiday spikes. The IQR is the box in a boxplot (盒鬚圖), and it powers a common rule for flagging outliers: points lying more than 1.5 IQRs beyond the quartiles are worth a second look. It pairs naturally with the median, which is the robust measure of centre.