Median Absolute Deviation Calculator

This robust statistic calculator returns the median, raw median absolute deviation, and scaled MAD for a comma-, semicolon-, or space-separated list.

Formula notes

median = middle sorted value or midpoint; MAD = median absolute deviation from the median; scaled MAD = 1.4826 x MAD.

Worked examples

1. Example: 1, 1, 2, 2, 4, 6, 9 has median 2, MAD 1, and scaled MAD about 1.483.
2. For values 3, 5, 7, 9, 11, the median is 7, raw MAD is 2, and scaled MAD is about 2.9652.

How to use it

1. Enter a list of finite numbers.
2. Confirm the split sign or whitespace.
3. Read count, median, raw MAD, and scaled MAD.

Frequently asked questions

Limits and interpretation

• MAD ignores the magnitude of outliers beyond their median distance, which is useful for robustness but not a complete outlier test.
• The scaling factor assumes an approximately normal reference distribution; for heavy-tailed or multimodal data, interpret accordingly.

References

• OpenStax Introductory Statistics 2e