How to use this calculator
- Enter or choose numbers.
- The median absolute deviation (raw) updates as you type. Use Copy result or Share to keep it.
Method
MAD = median(|xᵢ − median(x)|); scaled MAD = 1.4826 × MAD; modified z = 0.6745 × (xᵢ − median) ÷ MAD
- xᵢ
- each value
- 1.4826
- 1 ÷ Φ⁻¹(0.75), which makes MAD estimate σ for normal data
- 3.5
- Iglewicz–Hoaglin outlier cut-off for modified z
Worked example
- Median of the sorted data = (4 + 5) ÷ 2 = 4.5.
- Absolute deviations: 2.5, 0.5, 0.5, 0.5, 0.5, 0.5, 2.5, 4.5; their median is 0.5.
- Scaled MAD = 1.4826 × 0.5 ≈ 0.7413 (R’s mad() default).
The MAD is 0.5, or 0.7413 scaled to the standard-deviation scale.
What the result means
Compare the scaled MAD with the standard deviation: if the SD is much larger, a few extreme values are inflating it. Values with a modified z-score above 3.5 deserve a closer look.
Assumptions and limits
- The scale factor 1.4826 assumes the bulk of the data is roughly normal.
- Outliers are flagged with the Iglewicz–Hoaglin modified z-score rule.
- If more than half the values are identical, MAD is 0 and modified z-scores cannot be computed.
Questions
Is MAD the same as mean absolute deviation?
No. Median absolute deviation uses medians throughout and resists outliers; mean absolute deviation averages distances from the mean. Both are shown.
Which software matches this?
R’s mad(x) returns the scaled value; mad(x, constant = 1) returns the raw MAD. Excel has no built-in MAD.