What is the definition of mean absolute deviation?

Mean absolute deviation (MAD) is defined as the average of the absolute values of the deviations of individual data points from their mean or some expected value. It provides a clear measure of the variability or dispersion within a dataset, focusing solely on the magnitude of errors without considering their direction (whether they are positive or negative). By taking the absolute value of the deviations, MAD ensures that all discrepancies contribute positively to the total deviation, which makes it an effective and straightforward way to assess accuracy in forecasting.

This measure is particularly useful in contexts where understanding the extent of forecast errors is more important than the specific direction of those errors. The simplicity of calculating the average of the absolute deviations helps to convey the overall accuracy of a prediction model in a manner that is intuitive and easy to interpret.

Other options reflect different statistical concepts. For instance, the average of the squared deviations from the mean is known as variance, which encompasses an entirely different approach to error measurement by penalizing larger errors more significantly. Total deviation from forecast values may describe a broader measure of accuracy but lacks the specific focus on average error across all data points. Similarly, while a measure of error distribution may refer to a range of statistical techniques or metrics, it does not specifically define mean absolute deviation as effectively