I've calculate the "mean absolute error" for my predicted data and I want to calculate the standard deviation of an error to find the $\pm$ range from mean absolute error. The question is do I need to take the absolute to every data points because I've using the mean absolute error. So it's gonna be the same assumption.
Although the mean absolute error seems like a natural error measure at first sight, it has the drawback that it is not related to confidence intervals in a natural way. That's why the mean quadratic error (aka the variance) is used instead.
Another interesting property of the variance is that the arithmetic mean minimizes the variance. The mean absolute error is minimized by the median, instead. The variance can thus be considered the natural dispersion measure for a mean value.