Question

Is the mean (in a data set where each number is an error) more representatieve if you take the absolute values or the negative and positive values. I feel that if I take the negative and positive values the mean could be 0 even if error in both directions is very high.

Answer 1

Deviation is a measure of difference between the observed value of a variable and some other value, is nothing but variable's Average, that is its Mean. The sign of the deviation (positive or negative), tells us the direction of that difference (the deviation is positive when the observed value is greater than the reference value). The magnitude of the value shows the size of the difference.

The absolute deviation of an element of a data set is the absolute difference between that element and a given point. So the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the mean of the data set.

Maxwell, Herschell and others derived an appropriate probability distribution from the simple assumptions that the expectation about the errors is symmetric (positive and negative errors of the same absolute size are expected with the same probability). The result of this derivation is the normal distribution. So we should use the median to describe the center of the data, and we should use the mean if our aim is to model such a common center for which our expectations about the errors are in accordance to the two above given assumptions.