# Mean absolute error

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${\displaystyle \mathrm {MAE} ={\frac {\sum _{i=1}^{n}\left|y_{i}-x_{i}\right|}{n}}={\frac {\sum _{i=1}^{n}\left|e_{i}\right|}{n}}.}$
It is thus an arithmetic average of the absolute errors ${\displaystyle |e_{i}|=|y_{i}-x_{i}|}$, where ${\displaystyle y_{i}}$ is the prediction and ${\displaystyle x_{i}}$ the true value. Alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between predicted values that use different scales.[2] The mean absolute error is a common measure of forecast error in time series analysis,[3] sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally.