Root mean square vs average absolute deviation?

Both Root Mean Square and Average absolute deviation seem like the measures of the magnitude of variability (especially when the variates are both +ve and -ve). What are the rules of thumb to choose one of them over the other?

Answer

In theory, this should be determined by how important different sized errors are to you, or in other words, your loss function.

In the real world, people put ease of use first. So RMS deviations (or the related variances) are easier to combine, and easier to calculate in a single pass, while average absolute deviations are more robust to outliers and exist for more distributions. Basic linear regression and many of its offshoots are based on minimsing RMS errors.

Another point is that the mean will minimise RMS deviations while the median will minimise absolute deviations, and you may prefer one of these.

Attribution
Source : Link , Question Author : Mohit Ranka , Answer Author : Henry

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