Identify outliers using box plot methodology. Calculate inner and outer fences to detect mild and extreme outliers.
Last updated: March 2026
Min 4 values. Enter numbers separated by commas or spaces.
Mild outliers fall outside these limits
Extreme outliers fall outside these limits
Extreme Outliers:
50.00
Fences are boundaries used in box plot analysis to identify outliers—observations that deviate significantly from the main data distribution. There are two fence types corresponding to two levels of outlier severity.
Inner Fences are at Q1 − 1.5×IQR and Q3 + 1.5×IQR. Values outside these but within outer fences are mild outliers. Outer Fences are at Q1 − 3×IQR and Q3 + 3×IQR. Values beyond outer fences are extreme outliers—highly suspicious and warrant immediate investigation.
The multipliers (1.5 and 3) are empirically chosen based on normal distribution theory: 1.5×IQR ≈ ±2.7σ, and 3×IQR ≈ ±5.4σ. This method doesn't assume normality, making it robust for any distribution shape.
The IQR method is distribution-free (no normality assumption), making it robust for any data shape. Unlike Z-scores which assume normality, fence-based outlier detection works well for skewed, multimodal, or heavy-tailed distributions.
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No. Always investigate first. Outliers may be measurement errors (fix and keep), legitimate extreme values (keep for robustness), or indicate special conditions (analyze separately). Blind removal biases results.
Based on normal distribution theory: 1.5×IQR ≈ ±2.7σ (99.5% within), 3×IQR ≈ ±5.4σ (extreme). These are conventional thresholds that work well empirically, though other values are valid.
At least 4–5 points to calculate meaningful quartiles. For reliable IQR estimation, 20+ observations are better. With small samples, quartiles are unstable.
Yes, it's distribution-free. Unlike Z-scores (which assume normality), the IQR fence method is robust for skewed, multimodal, or any other distribution shape.
Calculate fences separately for each group. Applying global fences to grouped data can misidentify group differences as outliers. Context matters—understand your data's structure.
IQR is distribution-free and robust to skewness. Z-score assumes normality and can misbehave with outliers (they inflate SD). For general use, IQR is often more reliable.
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