A method for centring an error or uncertainty, if two signed bounds for the error are known.
Suppose you have an approximation M{\displaystyle M} for a certain quantity, with a lower bound on the error of α{\displaystyle \alpha } and an upper bound of β{\displaystyle \beta }.  Then, the true value lies somewhere in between M+α{\displaystyle M+\alpha } and M+β{\displaystyle M+\beta }. We can centre the error by picking the midpoint, M+β+α2{\displaystyle M+{\frac {\beta +\alpha }{2}}}; now our error is ±β−α2{\displaystyle \pm {\frac {\beta -\alpha }{2}}}. Therefore, the approximation can be written as (M+β+α2)±β−α2{\displaystyle \left(M+{\frac {\beta +\alpha }{2}}\right)\pm {\frac {\beta -\alpha }{2}}}.

Concept from Bluman, George W. (1984)       Problem Book for First Year Calculus  .
Own work
Eviatar Bach