Spotting Outliers With the 1.5 × IQR Rule
October 21, 2026
A common test for outliers uses the interquartile range (IQR): any value more than 1.5 × IQR below the first quartile or above the third quartile is flagged. For the data 3, 5, 7, 8, 9, 10, 12, 40, Q1 is 6 and Q3 is 11, so the IQR is 5. The fences are 6 − 7.5 = −1.5 and 11 + 7.5 = 18.5, which makes 40 an outlier.
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Sort the data and split it in half. The lower half is 3, 5, 7, 8 with a median of 6, which is Q1. The upper half is 9, 10, 12, 40 with a median of 11, which is Q3. The IQR = 11 − 6 = 5. The upper fence is 11 + 1.5 × 5 = 18.5. The value 40 exceeds it, so it is an outlier.
Quartile methods differ slightly between textbooks and software, so the exact fences may shift a little, but obvious outliers are caught by any of them.
| Statistic | With 40 | Without 40 |
|---|---|---|
| Mean | 11.75 | 7.71 |
| Median | 8.5 | 8 |
| Range | 37 | 9 |
Effect on the Mean and Median
A single extreme value moved the mean from 7.71 to 11.75, an increase of more than 50%, but the median changed only from 8 to 8.5. That is why the median is called a resistant measure, and why reports of income and house prices usually give the median.
The standard deviation is also sensitive to outliers, so the IQR is often paired with the median for skewed data.
What to Do With an Outlier
Do not delete a value just because it is extreme. First check for errors such as typos, unit mix-ups, or a sensor fault. If the value is genuine, it may carry the most interesting information, such as a fraud case or an exceptional customer.
If you do exclude outliers, report that you did so and why, and show results both ways when the decision could affect conclusions.
Frequently Asked Questions
What is the 1.5 × IQR rule?
A rule that flags values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as potential outliers.
Is an outlier always an error?
No. It may be a real extreme value. Investigate before removing it.
Which is more resistant to outliers, the mean or the median?
The median.
How do I calculate the IQR?
Subtract the first quartile (25th percentile) from the third quartile (75th percentile).