Definition
Interquartile range
The interquartile range is Q3 minus Q1, measuring the spread of the middle half of data.
What it means
Order the data and locate the two quartiles that mark off the middle half. Subtract the lower one from the upper one. Because the lowest and highest quarters lie outside those markers, the IQR is less affected by extreme values than the full range.
Remember it
Middle-half width: Q3 − Q1.
Example
On a box plot, the lower edge of the box is Q1 = 6 and the upper edge is Q3 = 14. The interquartile range is 14 − 6 = 8, so the middle half spans 8 units.
Watch for
When quartiles are calculated from raw data, use the quartile convention stated by the task; different conventions can differ for small data sets.
Common mix-up
The full range is maximum minus minimum. The IQR uses Q3 minus Q1 and ignores the outer quarters.
Exact meaning
The interquartile range, or IQR, is the upper quartile Q3 minus the lower quartile Q1. The interval from Q1 to Q3 contains the middle 50% of the ordered data under the chosen quartile convention, so the IQR measures that central spread.