G-up (or down?) [Basicmetrology]

There is on old joke among metrologists that a measurement should only be made once, for if it is repeated the result is bound to differ. Then, all is lost because a third measurement must be made to decide between the first two, and then a fourth, and so on to eternity. What follows is a prime example. All masses attract one another, be it ever so slightly. The force F between two isolated masses, M₁ and M₂ that are a distance r apart is G M₁M₂/r² where G is the universal gravitational constant, equal to about 6.67x10^-11m³s-2kg^-1. One unfortunate fact about G is that no present theory connects it with any other physics and another lies in the word about. It would be nice to have a more accurate value of G for astronomical calculations, and metrologists have been trying hard for the past two centuries to measure one. The results of eleven attempts in ascending order from 1996 onwards are shown in the diagram in Fig. 1. The traditional one-standard-deviation error bars have been replaced by Gaussian probability distribution curves whose height at the corresponding value of G is the likelihood of that value of G being correct according to that particular measurement. Clearly, no vertical line through one value can be drawn which is at all likely to be the actual correct value - the results are all over the place.