Table of Contents
Understanding Upper and Lower Fences
Upper and lower fences are boundaries used in exploratory data analysis to identify potential outliers on both sides of a distribution. The lower fence catches unusually small values, while the upper fence catches unusually large values. Together they form the complete fence system used in Tukey's box-and-whisker plots.
Values between the inner and outer fences are considered mild outliers, while values beyond the outer fences are extreme outliers. This two-tier system helps distinguish between moderately unusual values and truly extreme observations that warrant special attention.
Formulas
Box Plot Connection
In a standard box plot, the whiskers extend to the most extreme data point that falls within the fences. Points beyond the fences are plotted individually as outliers (dots or asterisks). The box spans from Q1 to Q3, with the median shown as a line inside the box.
- The box contains the middle 50% of data (the IQR)
- Whiskers extend to the last data points within the fences
- Individual dots represent mild outliers (beyond 1.5 IQR)
- Asterisks or double dots represent extreme outliers (beyond 3.0 IQR)
Frequently Asked Questions
Can data have no outliers?
Yes. If all data points fall within the fences, there are no outliers by the IQR definition. This is common in well-controlled processes and normally distributed data with moderate sample sizes. Approximately 99.3% of normally distributed data falls within the inner fences.
Does this method work for skewed data?
The IQR method works reasonably well for skewed data because it is based on quartiles, which are resistant to skewness. However, for highly skewed distributions, the adjusted boxplot method (using the medcouple) may provide better outlier detection.