On average, how far is each value from the average? Sounds circular — but it's a perfectly good (and very intuitive) measure of spread, and it dodges the squaring that makes standard deviation feel like magic.
The mean (absolute) deviation is the average of how far each value is from the mean — using absolute distances, so positives and negatives don't cancel.
An intuitive spread measure for teaching, and (with the median) a robust alternative to standard deviation. Used in forecasting accuracy (MAD — mean absolute deviation).
Take each value's distance from the mean (always positive), average them. Bigger MD = more spread.
Data: 10, 12, 14, 16, 18. Find the mean deviation.
Why does mean deviation use |x − x̄| and not (x − x̄)?
Without the absolute value, the deviations always sum to zero (that's a defining property of the mean). The absolute value strips the signs so distances actually add up.
Mean deviation ≠ standard deviation. SD squares the deviations (then square-roots), which weights big departures more heavily. MD treats all distances equally. SD is far more common, but MD is more intuitive.
In forecasting, MAD (mean absolute deviation) of the forecast errors is a standard accuracy metric — closely related, just measuring distance from the prediction instead of from the mean.
- MD = average distance of values from the mean (using absolute values).
- Absolute values are essential — raw deviations sum to zero.
- More intuitive than SD; SD (which squares) is more widely used.