Passage: Standard deviation may serve as a measure of uncertainty.  In physical science, for example, the reported standard deviation of a group of repeated measurements gives the precision of those measurements.  When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance:  if the mean of the measurements is too far away from the prediction (with the distance measured in standard deviations), then the theory being tested probably needs to be revised. This makes sense since they fall outside the range of values that could reasonably be expected to occur, if the prediction were correct and the standard deviation appropriately quantified.  See prediction interval.

Question: What is a very important part of deciding whether measurements agree or not with theoretical predictions?
the standard deviation of those measurements