Which measure returns a value of INF if the mean quantity of input data is 0?

The measure that returns a value of INF (infinity) when the mean quantity of input data is 0 is the mean absolute error by mean. This is because mean absolute error by mean is a calculation where the absolute errors between predicted and actual values are averaged, and then this average is divided by the mean of the observed values.

If the mean of the observed values is zero, the denominator of this calculation becomes zero. When performing a division where the denominator is zero, the result is undefined which often results in an expression of infinity. This behavior is crucial to understand in the context of error measures, as it highlights situations where prediction becomes meaningless or undefined due to lack of variability in the data.

Other measures mentioned do not exhibit this particular behavior when processing values augmented by means of zero. Thus, understanding the implications of zero in the denominator is essential for interpreting the results of error calculations in forecasting effectively.