How to use this calculator
- Enter or choose numbers.
- Enter or choose fence multiplier k.
- Enter or choose quartile method.
- The outliers found updates as you type. Use Copy result or Share to keep it.
Method
IQR = Q3 − Q1; lower fence = Q1 − k × IQR; upper fence = Q3 + k × IQR; outlier if x < lower or x > upper
- Q1, Q3
- first and third quartiles
- k
- multiplier: 1.5 (outlier) or 3 (far out)
Worked example
- Q1 = 4 and Q3 = 7 (inclusive method), so IQR = 3.
- Fences: 4 − 1.5 × 3 = −0.5 and 7 + 1.5 × 3 = 11.5.
- Only 30 lies outside; it is also beyond 7 + 3 × 3 = 16, so it is far out.
One outlier, 30, lies above the upper fence of 11.5.
What the result means
A flagged value is a prompt to investigate, not to delete: check for data-entry errors, unit mix-ups or a genuinely different case before deciding what to do.
Assumptions and limits
- Tukey’s fences make no normality assumption; for normal data about 0.7% of values fall outside the 1.5 × IQR fences by chance.
- In small or heavily skewed samples the rule may flag legitimate values; the quartile method also shifts the fences slightly.
Questions
Why 1.5?
Tukey chose it as a practical compromise: for normal data the fences sit about 2.7 standard deviations from the mean.
Should I remove outliers?
Only with a reason, such as a proven measurement error. Otherwise report results with and without them, or use robust statistics like the median.