How the IQR outlier rule works
The most common rule flags a value as an outlier when it falls below Q1 − 1.5×IQR or above Q3 + 1.5×IQR, where IQR = Q3 − Q1. For 2, 3, 4, 5, 6, 7, 8, 30 the quartiles are Q1 = 3.5 and Q3 = 7.5, so IQR = 4. The upper fence is 7.5 + 1.5×4 = 13.5, and 30 sits above it, so 30 is an outlier. The fences are built from the interquartile range, stretched out by a factor of 1.5.
How to use this calculator
Enter at least four numbers and leave unused fields blank. The result lists any outliers along with the lower and upper fences and the IQR. The quartiles behind these fences come from the quartile calculator.
Why outliers matter
Outliers can be genuine extreme observations or data-entry errors. They strongly pull the mean while leaving the median almost unchanged, so spotting them helps you choose the right summary. Compare the centre with and without them using the mean, median, mode calculator.
Frequently asked questions
- How do I find outliers?
- Compute Q1, Q3 and IQR = Q3 − Q1. Any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is an outlier. For 2–30 above, 30 is flagged.
- What is the 1.5 × IQR rule?
- It is the standard fence rule for outliers: build fences 1.5 interquartile ranges beyond Q1 and Q3, and treat values past them as outliers.
- Should I always remove outliers?
- No. An outlier may be a real, important value. Investigate it before deciding to keep, correct or drop it.
- How many values do I need?
- Enter at least four so the quartiles and fences are meaningful.
- When should I use a z-score instead of the IQR rule?
- Use z-scores when the data is roughly normal and you want a threshold in standard deviations, typically beyond ±3. The IQR rule is safer for skewed data, because outliers inflate the standard deviation and can hide themselves from a z-score test.