Calculator Inputs
Example Data Table
This sample shows how an unusually high value can stand apart from the main distribution.
| Position | Sample Value | Comment |
|---|---|---|
| 1 | 10 | Typical low-end observation |
| 2 | 12 | Within normal spread |
| 3 | 12 | Within normal spread |
| 4 | 13 | Within normal spread |
| 5 | 14 | Within normal spread |
| 6 | 15 | Near center of the dataset |
| 7 | 16 | Within normal spread |
| 8 | 17 | Within normal spread |
| 9 | 18 | Within normal spread |
| 10 | 19 | Upper range, still plausible |
| 11 | 25 | Borderline high value |
| 12 | 150 | Likely outlier under several methods |
Formula Used
IQR Method
First calculate Q1 and Q3, then find IQR = Q3 − Q1. Lower threshold = Q1 − k × IQR. Upper threshold = Q3 + k × IQR.
Z-Score Method
Compute mean and sample standard deviation. Lower threshold = mean − z × standard deviation. Upper threshold = mean + z × standard deviation.
MAD Method
Find the median, then MAD = median of |x − median|. Robust sigma ≈ 1.4826 × MAD. Thresholds = median ± modified z limit × robust sigma.
Interpretation
IQR is robust for skewed data. Z-score works best for near-normal distributions. MAD is highly resistant to extreme contamination and small outlier clusters.
How to Use This Calculator
- Paste numeric values into the dataset field using commas, spaces, or line breaks.
- Select the main threshold method you want to emphasize.
- Choose whether to inspect both tails, the upper tail, or the lower tail.
- Adjust the IQR multiplier, Z-score limit, or modified Z limit.
- Click Calculate Thresholds to display results above the form.
- Review the comparison table, flagged values, and Plotly chart.
- Export your results with the CSV or PDF buttons when needed.
Frequently Asked Questions
1. Which method should I choose first?
Start with IQR for general exploratory work. Choose Z-score when your data is roughly normal. Choose MAD when you expect skewness, heavy tails, or strong outliers.
2. Why do methods return different thresholds?
Each method measures spread differently. IQR focuses on quartiles, Z-score depends on mean and standard deviation, and MAD uses robust median-based deviation.
3. What does both-tail analysis mean?
Both-tail analysis checks for unusually small and unusually large values. Upper-tail mode only flags high anomalies, while lower-tail mode only flags low anomalies.
4. Is a flagged point always a bad record?
No. A flagged point is only statistically unusual. It may be a data error, a rare but valid event, or an important signal worth deeper investigation.
5. What happens if my values are identical?
The spread measures can become zero. In that case, Z-score or MAD thresholds may be unavailable because the dataset has no dispersion.
6. Should I remove all detected outliers?
Not automatically. First verify collection quality, business context, and model purpose. Some outliers should be corrected, while others should remain because they carry meaning.
7. Can I use this for small datasets?
Yes, but use caution. Very small samples make thresholds more sensitive to individual values, so interpretation should rely on both statistical and domain judgment.
8. What does the chart help me see?
The chart shows how each value sits relative to the active thresholds. It helps you quickly spot separation, clustering, and unusual points.