Upper and Lower Fence Calculator
Enter numeric data to calculate quartiles, IQR, and the fences used for outlier detection.
1.5 for mild outliers, 3.0 for extreme outliers.
Lower fence
0.0000
Q1 (18.0000) − 1.5 × IQR (12.0000)
Upper fence
48.0000
Q3 (30.0000) + 1.5 × IQR (12.0000)
How to Use This Calculator
- Enter your dataset in the left input area.
- Select a multiplier (1.5 by default) to adjust sensitivity.
- Review the computed quartiles, IQR, and the resulting fences.
- Values outside the fences can be investigated as potential outliers.
Formula
IQR = Q3 − Q1
Lower fence = Q1 − multiplier × IQR
Upper fence = Q3 + multiplier × IQR
Fences provide cutoffs for detecting potential outliers in box plot analysis.
Full Description
Upper and lower fences define thresholds beyond the interquartile range for identifying anomalous observations. Adjusting the multiplier allows analysts to control sensitivity to outliers depending on context.
Frequently Asked Questions
When should I use 3.0 instead of 1.5?
Use 3.0 to identify extreme outliers while ignoring mild deviations.
Do fences depend on normality?
No. They rely on ranks and percentiles, so they work for skewed distributions.
What if all values are identical?
IQR equals zero, and both fences equal the value itself, indicating no outliers.
Are fence violations always errors?
Not necessarily. Use domain knowledge to decide whether flagged points are valid or problematic.