Interquartile range
Interquartile range (IQR) is the distance between the first and third quartiles of ordered data (Q3 − Q1), capturing the spread of the middle 50%. It is resistant to outliers, unlike the full range.
See it move
Eight weekly sales figures ordered from €12,000 to €40,000 split into four quarters. The lower quartile Q1 is €16,500 and the upper quartile Q3 is €32,500, so the interquartile range — the middle 50% of the data — is €16,000. Because it excludes the top and bottom quarters, extreme outliers do not distort it.
The formula
Variables
- Lower quartile: median of the bottom half of the ordered data (25th percentile)
- Upper quartile: median of the top half of the ordered data (75th percentile)
- Interquartile range: spread of the central 50% of the data
Because IQR excludes the lowest and highest quarters, extreme outliers do not distort it.
Check yourself
An analyst summarises 12 months of a firm's monthly operating costs. The full range is €290,000 (from the lowest to the highest month), but the interquartile range is only €24,000. What does this pattern most likely indicate?