Rolling Z-Score & MAD Outlier Detection
A robust MAD score that finds the outliers an ordinary z-score hides inside its own standard deviation, and separates level shifts from errors.
Rolling Z-Score & MAD Outlier Detection is a free Excel workbook: 6 sheets, 1,428 live formulas and realistic sample data throughout, 31 KB as .xlsx.
The formulas are printed on this page, unedited, so you can check the method before downloading anything. Swap in your own numbers and the whole file recalculates — which is the part no chat window can hand you. Opens in Excel, Google Sheets, Numbers and LibreOffice; no add-in and no macro.
A look inside
This is a real slice of the Detection sheet from the actual file — not a screenshot, and not a mock-up. Cells shown in violet are live formulas, exactly as they arrive.
| # | Date | Value | Roll mean | Roll SD | Z | Roll median | MAD |
|---|---|---|---|---|---|---|---|
| 2 | =Series!A2 | =Series!B2 | =AVERAGE(Series!$B$2:$B$12) | =STDEV.S(Series!$B$2:$B$12) | =IFERROR((B2-C2)/D2,0) | =MEDIAN(Series!$B$2:$B$12) | =MEDIAN(ABS(Series!$B$2:$B$12-F2)) |
| 3 | =Series!A3 | =Series!B3 | =AVERAGE(Series!$B$2:$B$13) | =STDEV.S(Series!$B$2:$B$13) | =IFERROR((B3-C3)/D3,0) | =MEDIAN(Series!$B$2:$B$13) | =MEDIAN(ABS(Series!$B$2:$B$13-F3)) |
| 4 | =Series!A4 | =Series!B4 | =AVERAGE(Series!$B$2:$B$14) | =STDEV.S(Series!$B$2:$B$14) | =IFERROR((B4-C4)/D4,0) | =MEDIAN(Series!$B$2:$B$14) | =MEDIAN(ABS(Series!$B$2:$B$14-F4)) |
| 5 | =Series!A5 | =Series!B5 | =AVERAGE(Series!$B$2:$B$15) | =STDEV.S(Series!$B$2:$B$15) | =IFERROR((B5-C5)/D5,0) | =MEDIAN(Series!$B$2:$B$15) | =MEDIAN(ABS(Series!$B$2:$B$15-F5)) |
| 6 | =Series!A6 | =Series!B6 | =AVERAGE(Series!$B$2:$B$16) | =STDEV.S(Series!$B$2:$B$16) | =IFERROR((B6-C6)/D6,0) | =MEDIAN(Series!$B$2:$B$16) | =MEDIAN(ABS(Series!$B$2:$B$16-F6)) |
| 7 | =Series!A7 | =Series!B7 | =AVERAGE(Series!$B$2:$B$17) | =STDEV.S(Series!$B$2:$B$17) | =IFERROR((B7-C7)/D7,0) | =MEDIAN(Series!$B$2:$B$17) | =MEDIAN(ABS(Series!$B$2:$B$17-F7)) |
| 8 | =Series!A8 | =Series!B8 | =AVERAGE(Series!$B$2:$B$18) | =STDEV.S(Series!$B$2:$B$18) | =IFERROR((B8-C8)/D8,0) | =MEDIAN(Series!$B$2:$B$18) | =MEDIAN(ABS(Series!$B$2:$B$18-F8)) |
| 9 | =Series!A9 | =Series!B9 | =AVERAGE(Series!$B$2:$B$19) | =STDEV.S(Series!$B$2:$B$19) | =IFERROR((B9-C9)/D9,0) | =MEDIAN(Series!$B$2:$B$19) | =MEDIAN(ABS(Series!$B$2:$B$19-F9)) |
What’s in the file
What it explains
- Why the ordinary z-score fails
- The robust alternative
- An outlier is not an error
Download it
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Related templates
Learn the method
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