Flag outliers in a list of numbers by z-score, Tukey IQR fences and the MAD modi...

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{ "example": { "anyMethodFlaggedPositions": [ 10 ], "asOf": "2026-10-21T06:18:23.456Z", "degraded": false, "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.", "iqr": { "flaggedPositions": [ 10 ], "flaggedValues": [ 100 ], "iqr": 4.5, "lowerFence": -3.5, "multiplier": 1.5, "q1": 3.25, "q3": 7.75, "upperFence": 14.5 }, "mad": { "flaggedPositions": [ 10 ], "flaggedValues": [ 100 ], "formula": "modified z = 0.6745 (x - median) / MAD", "limit": 3.5, "mad": 2.5, "median": 5.5, "modifiedZ": [ -1.2141, -0.9443 ] }, "method": "all", "n": 10, "notChecked": [ "whether a flagged value is an error or a real event", "seasonality or trend (a normal seasonal peak can look like an outlier)", "…1 more" ], "reasons": [ "z-score: |x - mean| / sample sd above 3. With n points the largest possible |z| is (n-1)/sqrt(n) = 2.846, so small samples cannot reach large limits.", "IQR fences: quartiles by linear interpolation (type 7); flag below Q1 - 1.5 IQR or above Q3 + 1.5 IQR.", "…1 more" ], "source": "computed locally (z-score; Tukey 1977 fences; Iglewicz and Hoaglin 1993 modified z-score)", "summary": "1 of 10 values flagged by at least one method (positions 10).", "verdict": "OUTLIERS_FLAGGED", "zscore": { "flaggedPositions": [], "flaggedValues": [], "limit": 3, "mean": 14.5, "sampleSd": 30.1523907, "zScores": [ -0.447726, -0.414561 ] } }, "type": "json" }