Calculator Inputs
Example Data Table
| Observation | Input Value | Median | MAD | Modified Z Score | Status at 3.5 |
|---|---|---|---|---|---|
| 1 | 10 | 12 | 1 | -1.3490 | Within range |
| 2 | 12 | 12 | 1 | 0.0000 | Within range |
| 3 | 12 | 12 | 1 | 0.0000 | Within range |
| 4 | 13 | 12 | 1 | 0.6745 | Within range |
| 5 | 12 | 12 | 1 | 0.0000 | Within range |
| 6 | 11 | 12 | 1 | -0.6745 | Within range |
| 7 | 14 | 12 | 1 | 1.3490 | Within range |
| 8 | 300 | 12 | 1 | 194.2560 | Outlier |
This example shows how the modified z score isolates a strong outlier while keeping central values stable.
Formula Used
Median: Sort the dataset and take the middle value, or the average of the two middle values.
MAD: Median of the absolute deviations from the median.
Modified Z Score: Mi = c × (xi − median) / MAD
Default constant: c = 0.6745. This scales the robust score to resemble a standard normal z score under normal conditions.
A common rule flags an observation as an outlier when the absolute modified z score is greater than 3.5.
Because the method relies on the median and MAD, it resists distortion from extreme values better than mean-based z scores.
How to Use This Calculator
- Enter at least three numeric observations in the data box.
- Choose the outlier threshold, or keep the common value of 3.5.
- Leave the scaling constant at 0.6745 unless your workflow uses a different robust convention.
- Set decimal precision and choose the output sort order.
- Submit the form to display the summary metrics and detailed score table above the inputs.
- Export the resulting table as CSV or PDF for reporting, validation, or model review.
Frequently Asked Questions
1. What does the modified z score measure?
It measures how far each observation sits from the median in units of MAD. Large absolute scores suggest unusually distant values that may deserve review.
2. Why use this instead of a regular z score?
Regular z scores rely on the mean and standard deviation, which can shift heavily with extreme values. Modified z scores stay more stable because they use robust statistics.
3. Is 3.5 always the correct threshold?
No. A threshold of 3.5 is common, but some workflows use tighter or looser cutoffs depending on domain risk, data quality, and tolerance for false positives.
4. What happens if MAD equals zero?
If all values are identical, every score becomes zero. If MAD is zero while values differ, the robust score cannot be computed reliably because the denominator vanishes.
5. Can I use decimals and negative values?
Yes. The calculator accepts positive numbers, negative numbers, integers, and decimals, as long as the values are entered as valid numeric observations.
6. Does sorting change the statistics?
No. Sorting only changes the display order of the result rows. The median, MAD, thresholds, and flags remain based on the original input values.
7. Should flagged values be removed automatically?
Not automatically. A flagged point might be a data error, a rare valid event, or a meaningful signal. Review context before deciding to exclude it.
8. Is this suitable for machine learning preprocessing?
Yes. It is useful during anomaly screening, feature review, and data cleaning, especially when outliers can distort scaling, model fitting, or summary statistics.