Lower Fence Calculator
Calculate lower fence for outlier detection using quartiles and IQR
Enter Your Data
Higher values make outlier detection less strict
Note: At least 4 data points are required to calculate quartiles and fences. Currently you have 0 valid numbers.
Example: Simple Dataset
Data: 1, 2, 3, 4, 5
Q1: 2
Q3: 4
IQR: 4 - 2 = 2
Lower Fence Calculation
Lower Fence = Q1 - 1.5 × IQR
Lower Fence = 2 - 1.5 × 2 = -1
Result: -1
1.5 IQR Rule
Standard method for outlier detection
Values below Q1 - 1.5×IQR are outliers
Values above Q3 + 1.5×IQR are outliers
Adjustable multiplier for different sensitivities
Understanding Lower Fence and Outlier Detection
What is the Lower Fence?
The lower fence is a statistical boundary used to identify outliers in a dataset. Any data point below the lower fence is considered an outlier - an unusually small value that deviates significantly from the rest of the data.
How it Works
- Find the first quartile (Q1) and third quartile (Q3)
- Calculate the interquartile range (IQR = Q3 - Q1)
- Apply the formula: Lower Fence = Q1 - k × IQR
- Identify outliers below the lower fence
Lower Fence Formula
Lower Fence = Q1 - k × IQR
where k is typically 1.5 (standard) or 2-3 (more lenient)
Multiplier Guidelines
- • k = 1.5: Standard rule, moderate outlier detection
- • k = 2.0: More conservative, fewer outliers
- • k = 3.0: Very conservative, only extreme outliers
Applications and Uses
Quality Control
Identify defective products or unusual measurements in manufacturing
Data Cleaning
Remove or flag suspicious data points before analysis
Statistical Analysis
Ensure robust statistical models by handling outliers appropriately