Statistical Outlier Visualizer
Flag extremes with IQR, Z-score, or modified Z-score—and see them on a chart.
Statistical Outlier Visualizer
Detect and analyze statistical outliers using multiple methods
Outlier Detection Settings
Configure the outlier detection method and parameters
IQR multiplier (typically 1.5-3.0)
Three detection methods
IQR
Lower = Q1 − 1.5×IQR, upper = Q3 + 1.5×IQR. Solid default for skewed data. Raise the multiplier (e.g. 3.0) if 1.5 flags too many points.
Z-score
Z = (x − mean) / σ. Flag when |Z| exceeds your cutoff (often 3). Assumes roughly normal data. Extremes already in the set inflate σ, so other outliers can look milder than they are.
Modified Z-score
Uses median and MAD: 0.6745 × (x − median) / MAD. Common cutoff ≈ 3.5. Prefer this when the sample may already contain extremes.
Worked example
Scores: [72, 78, 82, 85, 87, 89, 90, 92, 94, 150]
IQR
Q1 ≈ 82, Q3 ≈ 92, IQR = 10 → fences about 67 and 107. 150 is out.
Z-score
Mean ≈ 91.9, SD ≈ 22.7 → Z for 150 ≈ 2.56. Under a |Z| > 3 rule it might not flag—exactly why one method alone is shaky when the outlier itself widens the SD.
Practical notes
- Compare methods; do not delete on a single automatic rule
- Plot before and after any cleanup
- Domain knowledge beats a default threshold
- If > ~10% of points flag, suspect bad thresholds or mixed populations
- Univariate rules miss weird combinations across variables—use Mahalanobis / LOF / isolation forest for that
Typical uses: QC measurements, odd transactions (flags are leads, not proof), lab values that look wrong, and pre-model data hygiene. This page is educational, not a clinical or fraud system.
Frequently Asked Questions
Which method should I use?
IQR for skew or unknown shape. Classic Z for roughly normal data. Modified Z when extremes may already be present. Running more than one is cheap insurance.
Should I always remove outliers?
No. Investigate first. In fraud or anomaly hunting, extremes are the prize.
What thresholds are common?
IQR ×1.5 (or ×3), |Z| > 3 (or 2.5 / 2), modified Z > 3.5. Tune for your false-positive tolerance—there is no universal correct value.
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