Determining the error from a list of individual errors

Question

I have a list of values each with a corresponding error. I can determine the average/mean of the list, but I'm not sure how to best calculate the error over the entire population.

e.g.

107 +/- 0.2
120 +/- 0.1
184 +/- 0.4
44  +/- 0.3

Average is simply 113.75, but what is the error?

Answer 1

If errors can be either negative or positive it does not make sense to average them because positive errors cancel negative error. That is why statisticians use variance (average squared error) or the mean absolute error to summarize the magnitude of the errors.