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Let's say that I have a model that counts target objects in images. In the first image, I have success $1/2$ and in the second image is $1/5.$

First image: Absolute error = $1$, percent error = $50\%$

Second Image: Absolute error = $4$, percent error = $80\%$

I want to calculate the average percent error for both of the images. Should I go with the total absolute errors and divide it by the total number of targets or should I calculate the avg of the two percent errors?

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Mean percentage error (MPE) would be average of the two percentage errors. However, percentage error is not defined if the number of target objects in an image is zero. You can circumvent this by doing what you suggest and it sounds reasonable but I don't know what the statistic should be called (I would myself like to know it, too).

You can compare this to the mean absolute percentage error (MAPE), where you ignore the sign of the error. It is usually defined as the mean of absolute percentage errors, but due to this zero division problem, it is often estimated by dividing the sum of absolute errors by the sum of actual values times 100%. According to wikipedia https://en.wikipedia.org/wiki/Mean_absolute_percentage_error it is sometimes called WAPE (weighted absolute percentage error). I have also seen the name "volume-weighed MAPE".

So, analogically, we could call your option 1 as weighted percentage error.

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