Lower Fence Calculator
Enter data and choose a multiplier to calculate the lower fence (Q1 − k × IQR) for identifying potential outliers.
Default 1.5 for Tukey fences; 3.0 for extreme outliers.
Q1: 15.7500
Q3: 29.2500
IQR: 13.5000
Lower fence: -4.5000
Values below fence: None detected
How to Use This Calculator
- Enter your dataset values.
- Select an outlier multiplier k (1.5 for standard fences).
- Review the computed quartiles, IQR, and lower fence.
- Investigate any data points flagged as below the lower fence.
Formula
Q1 = 25th percentile
Q3 = 75th percentile
IQR = Q3 − Q1
Lower fence = Q1 − k × IQR
Full Description
Boxplot fences help flag potential outliers in numerical data. The lower fence marks the threshold below which values may be considered unusually low, aiding exploratory data analysis and quality control procedures.
Frequently Asked Questions
What multiplier should I use?
k = 1.5 is common for mild outliers. k = 3 identifies extreme outliers.
Does the method depend on data distribution?
No. Boxplot fences are non-parametric and apply to any distribution, though interpretation depends on context.
How are quartiles computed?
The calculator uses an inclusive method with linear interpolation to handle fractional positions.
Are flagged points always errors?
Not necessarily. Outliers may be legitimate observations. Investigate them rather than automatically removing them.