1. What is the Lower Fence?

The Lower Fence is a statistical boundary used to identify potential outliers in a dataset. It is calculated using the first quartile (Q1) and the interquartile range (IQR). Values below the Lower Fence are considered potential outliers.

2. How Does the Calculator Work?

The calculator uses the Lower Fence formula:

Where:

• \( Q1 \) — First quartile (25th percentile) of the dataset
• \( IQR \) — Interquartile range (Q3 - Q1)
• 1.5 — Standard multiplier for identifying mild outliers

Explanation: The Lower Fence establishes a boundary below which data points are considered statistically unusual and potentially erroneous or significant outliers.

3. Importance of Lower Fence Calculation

Details: Calculating the Lower Fence helps in data cleaning, identifying measurement errors, detecting unusual cases, and understanding data distribution in statistical analysis.

4. Using the Calculator

Tips: Enter the Q1 and IQR values. Both values must be valid numbers (IQR should be non-negative). The calculator will compute the Lower Fence boundary.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Lower Fence and Upper Fence?
A: The Lower Fence identifies potential outliers below Q1, while the Upper Fence (Q3 + 1.5×IQR) identifies outliers above Q3.

Q2: Why 1.5×IQR as the multiplier?
A: 1.5 is a conventional threshold that identifies mild outliers. For extreme outliers, 3×IQR is sometimes used.

Q3: Are points below Lower Fence always errors?
A: Not necessarily. They should be investigated as they're statistically unusual, but they might represent valid extreme values.

Q4: How do I find Q1 and IQR for my data?
A: Q1 is the 25th percentile, Q3 the 75th percentile, and IQR = Q3 - Q1. These can be calculated using statistical software or spreadsheet functions.

Q5: Can I use different multipliers?
A: Yes, the 1.5 multiplier is conventional but can be adjusted based on your specific needs and data characteristics.