Measurements that are widely spread apart have a large standard deviation. That is, if the standard deviation is very small, it might take only a handful of measurements before the mean gives a very good estimate of the true value. When the standard deviation is large, many more measurements must be taken before the mean gives as good an estimate of the true value. Two related concepts, defined below, are precision and accuracy. In the figures which follow, imagine that the center of the target represents the true value of some observable that interests us, and that the crosses are individual measurements of that observable.
Precision refers to how closely multiple measurements of the same quantity cluster to one another.
Accuracy refers to how closely multiple measurements of the same quantity cluster around the true value. Neither precise nor accurate. Large standard deviation. Precise, but not accurate. Small standard deviation.