The MAPE preference

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In the theory section, we mention how MAPE is known to treat overestimation and underestimation unequally.

Let's consider the following scenario. We have two sets of true targets and predictions:

Case1:Y={90},Y^=70Case2:Y={70},Y^=90\text{Case}_1: Y = \{90\}, \, \hat{Y} = {70} \\ \text{Case}_2: Y = \{70\}, \, \hat{Y} = {90}

Calculate the MAPE for the two cases above and answer the following question: which case showed worse score?

Your answer function looks like this:

Answer={MAPE1,if  Case1showed worse performanceMAPE2,otherwise\text{Answer}= \begin{cases} \text{MAPE}_1, & \text{if }\ \text{Case}_1\, \text{showed worse performance} \\ \text{MAPE}_2, & \text{otherwise} \end{cases}

Round the answer up to the third decimal.

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