Some information on the variations in measurements:
http://alignment.hep.brandeis.edu/Lab/Measurement.html
Resolution
The resolution of a measurement is how well it can distinguish between two values of the measured physical quantity. The precision of our MRT is 1.4°C. If one end of the table is 0.1°C warmer than the other, the probability of our MRT being right when it says which end is warmer will be close to 50%, because our stochastic error is much larger than the difference we are trying to observe.
When a stochastic error is gaussian, which is most of the time, there is a 68% chance that the magnitude of the error will be less than one standard deviation of the distribution. If we measure the temperature at both ends of our table, and the far end measurement is one standard deviation higher than the near end, it is 68% likely that the MRT measurement of the far end will be higher than the MRT measurement of the near end. In other words, it's 68% likely that our MRT will be correct in telling us which end is warmer, provided that the warmer end is one standard deviation warmer than the other end.
That's how we arrive at our definition of resolution. The resolution of a measurement is the amount by which the measured quantity must change for it to be 68% likely that our measurement will be correct in saying whether the change was up or down.
Because almost all stochastic errors are gaussian, the resolution of a measurement is almost always equal to its precision.
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