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 third quartile (Q3) values from the dataset.

2. How Does the Calculator Work?

The calculator uses the lower fence formula:

Where:

• \( Q1 \) — First quartile (25th percentile)
• \( Q3 \) — Third quartile (75th percentile)
• \( Q3 - Q1 \) — Interquartile range (IQR)

Explanation: The formula calculates a threshold below which data points are considered potential outliers. The multiplier of 1.5 is a standard convention in statistics.

3. Importance of Lower Fence Calculation

Details: The lower fence helps identify unusually low values in a dataset that may need further investigation. It's commonly used in box plot visualizations to detect outliers.

4. Using the Calculator

Tips: Enter the Q1 and Q3 values from your dataset. Q3 must be greater than Q1 for a valid calculation. The result shows the lower boundary for potential outliers.

5. Frequently Asked Questions (FAQ)

Q1: Why 1.5 × IQR?
A: The 1.5 multiplier is a standard convention that identifies mild outliers. Some analyses use 3 × IQR for extreme outliers.

Q2: What if my data point is below the lower fence?
A: Points below the lower fence are potential outliers that may warrant further investigation, but they're not automatically errors.

Q3: How do I find Q1 and Q3?
A: Q1 is the median of the first half of your data, Q3 is the median of the second half when data is ordered.

Q4: Is there an upper fence too?
A: Yes, the upper fence is calculated as Q3 + 1.5 × IQR and identifies potential high outliers.

Q5: Can I use different multipliers?
A: Yes, some fields use different multipliers based on the nature of their data, but 1.5 is standard.