Outlier Detection Calculator

This calculator runs a single Data Value through three independent outlier tests, each built on a different assumption about your data's distribution. The IQR test compares Data Value against fences built from Q1 and Q3: IQR Lower Bound = Q1 − Threshold × IQR and IQR Upper Bound = Q3 + Threshold × IQR (lines 12-13), so those two bounds respond only to Q1, Q3, and the Threshold Multiplier — Data Value, Mean, and Standard Deviation never enter their formulas at all. The Z-Score test instead measures how many standard deviations Data Value sits from Mean (line 16) and is completely unaffected by Q1 or Q3.

The Modified Z-Score test approximates the median with the Mean input, but for the denominator it does not approximate the Median Absolute Deviation at all — mad = iqr * 0.7413 (line 22) is the standard IQR-to-standard-deviation conversion (for a normal distribution IQR ≈ 1.349σ, so IQR × 0.7413 ≈ σ), not an IQR-to-MAD one; a genuine MAD approximation from IQR would instead be roughly IQR × 0.5. Because the test effectively divides by an estimated σ rather than the true MAD, the reported Modified Z-Score runs about 1.48x smaller than a textbook Modified Z-Score would against the same fixed 3.5 cutoff (line 24) — and that cutoff is hard-coded, so the Threshold Multiplier field has zero effect on this third test no matter what you set it to. Because all three summary statistics are entered by hand rather than derived from a raw dataset, this calculator cannot detect whether your Mean, Q1, and Q3 are mutually inconsistent — for example a Mean sitting outside the Q1–Q3 range — it will still run all three tests on whatever numbers you provide.