# Mean absolute error

## Statistical error measure / From Wikipedia, the free encyclopedia

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In statistics, **mean absolute error** (**MAE**) is a measure of errors between paired observations expressing the same phenomenon. Examples of *Y* versus *X* include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the **sum of absolute errors** divided by the sample size:[1]

It is thus an arithmetic average of the absolute errors $|e_{i}|=|y_{i}-x_{i}|$, where $y_{i}$ is the prediction and $x_{i}$ 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.

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