| Observation | Value | Comment |
|---|---|---|
| 1 | 12 | Typical lower-tail observation |
| 2 | 15 | Near central cluster |
| 3 | 16 | Near median |
| 4 | 21 | Upper-side but still plausible |
| 5 | 55 | Potential extreme high outlier |
This example shows how resistant methods can separate a stable central cluster from a tail value that deserves a closer review.
1) Median
The median is the middle value of the ordered dataset. It is less sensitive than the mean when a few observations are unusually large or small.
2) Median Absolute Deviation
MAD = median(|xi − median(x)|)
MAD measures typical distance from the median. Because it uses medians twice, it remains stable when the sample includes extreme values.
3) Modified Z-Score
Modified Z = 0.6745 × (xi − median) / MAD
A common resistant cutoff is |Modified Z| ≥ 3.5. The constant 0.6745 aligns MAD-based scaling with a standard normal reference.
4) Interquartile Range
IQR = Q3 − Q1
Lower Fence = Q1 − k × IQR
Upper Fence = Q3 + k × IQR
The usual choice is k = 1.5. Observations beyond these fences are treated as outliers by Tukey-style rules.
5) Robust Sigma Estimate
Robust Sigma = 1.4826 × MAD
This estimate converts MAD into a scale that is easier to compare with standard deviation-like interpretations while keeping resistant behavior.
- Enter a dataset label to personalize the report.
- Paste numeric values into the dataset field, using commas, spaces, or new lines.
- Choose the screening method: MAD, IQR, Union, or Intersection.
- Select whether you want both tails, only high values, or only low values reviewed.
- Adjust the Modified Z threshold and IQR multiplier if your domain requires stricter or looser screening.
- Set the decimal precision and optional trimmed-mean preview percentage.
- Press Calculate Robust Outliers to show results above the form.
- Review the cards, the threshold notes, the Plotly graph, and the detailed table.
- Download the detailed table as CSV or export a PDF summary for documentation.
1) Why use resistant methods instead of the mean and standard deviation?
Resistant methods stay more stable when a few values are extreme. That makes them useful for screening messy datasets before modeling, reporting, or cleaning.
2) What is the difference between MAD and IQR methods?
MAD measures distance from the median. IQR focuses on the middle fifty percent and builds quartile fences. Using both can improve confidence.
3) When should I use the union option?
Use union when you want a broad screening pass. It flags any point caught by either MAD or IQR, so it is more sensitive.
4) When should I use the intersection option?
Use intersection when you want stricter agreement. A point must violate both rules, which reduces false positives in some datasets.
5) Does every flagged value need to be removed?
No. A flagged point is a review signal, not an automatic deletion command. Check source quality, domain context, and model sensitivity first.
6) What does the trimmed mean preview tell me?
It shows the average after trimming equal percentages from both tails. This helps you compare the raw mean with a more resistant summary.
7) Why can MAD become zero?
MAD becomes zero when most observations sit exactly at the median. In that case, any different value may stand out sharply.
8) Can I use this for business, lab, or survey data?
Yes. It works well for many numeric datasets, especially when measurement errors, rare events, or entry mistakes may distort ordinary summaries.