1. What Are Lower and Upper Fences?

Lower and upper fences are values used in statistics to identify potential outliers in a dataset. The lower fence is the boundary below which data points are considered outliers, while the upper fence is the boundary above which data points are considered outliers.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

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

Explanation: The fences are typically set at 1.5 times the IQR below Q1 and above Q3. Data points outside these fences are often considered potential outliers.

3. Importance of Fences in Statistics

Details: Fences are crucial in box plot analysis and outlier detection. They help identify unusual observations that may warrant further investigation or indicate data quality issues.

4. Using the Calculator

Tips: Enter the Q1, Q3, and IQR values. The calculator will compute the lower and upper fences. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why 1.5 × IQR for fences?
A: This is a common convention that identifies moderate outliers. Some use 3 × IQR for extreme outliers.

Q2: Are points outside the fences always outliers?
A: Not necessarily. They should be investigated but may represent valid extreme values in some distributions.

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

Q4: What if my IQR is zero?
A: This suggests no variability in the middle 50% of data. Fences will equal Q1 and Q3 in this case.

Q5: Can I use different multipliers than 1.5?
A: Yes, some analyses use 2.2 or 3.0 for more conservative outlier detection.