Table of Contents
What Is the Upper Fence?
The upper fence is a boundary used in the IQR (Interquartile Range) method for outlier detection. It is calculated as Q3 + 1.5 * IQR, where Q3 is the third quartile and IQR = Q3 - Q1. Any data point above the upper fence is flagged as a potential outlier. This method was popularized by John Tukey as part of his box-and-whisker plot methodology.
The 1.5 multiplier is a convention that works well for approximately normal distributions. For a perfect normal distribution, about 0.7% of data points would fall beyond the fences, making it a reasonable threshold for identifying unusual values without excessive false alarms.
Formula
Inner vs Outer Fences
| Fence Type | Formula | Classification |
|---|---|---|
| Inner Upper Fence | Q3 + 1.5 × IQR | Mild outlier |
| Outer Upper Fence | Q3 + 3.0 × IQR | Extreme outlier |
| Inner Lower Fence | Q1 - 1.5 × IQR | Mild outlier |
| Outer Lower Fence | Q1 - 3.0 × IQR | Extreme outlier |
Frequently Asked Questions
Why 1.5 times the IQR?
Tukey chose the 1.5 multiplier empirically. For normally distributed data, it identifies approximately the most extreme 0.7% of values as outliers, which provides a good balance between sensitivity and specificity for outlier detection across many types of data distributions.
Should I always remove outliers?
No. Outliers can be legitimate data points that contain important information. Always investigate outliers before removing them. They might indicate measurement errors (remove), data entry mistakes (correct), or genuine extreme values (keep and consider robust methods).