University Physics Volume 1 — Mechanics · Problem 11
Units and Measurement — OpenStax
Physics — University · significant-figures
Problem
(a) What is the relationship between the precision and the uncertainty of a measurement? (b) What is the relationship between the accuracy and the discrepancy of a measurement?Intuitive explanation
Precision and uncertainty are two sides of the same coin: precision describes how repeatable your measurements are (how tightly clustered), while uncertainty quantifies that scatter as a numerical range around your result. High precision means low uncertainty—if your measurements bunch together, you can confidently state a narrow margin of error. Accuracy and discrepancy work similarly but focus on how close you are to the true value: accuracy is your overall success at hitting the target, while discrepancy is the actual distance between your measured value and the accepted value. A measurement can be precise but inaccurate (clustered far from truth) or accurate by luck but imprecise (scattered wildly around the right answer).
Intuitive explanation
Precision and uncertainty are two sides of the same coin: precision describes how repeatable your measurements are (how tightly clustered), while uncertainty quantifies that scatter as a numerical range around your result. High precision means low uncertainty—if your measurements bunch together, you can confidently state a narrow margin of error. Accuracy and discrepancy work similarly but focus on how close you are to the true value: accuracy is your overall success at hitting the target, while discrepancy is the actual distance between your measured value and the accepted value. A measurement can be precise but inaccurate (clustered far from truth) or accurate by luck but imprecise (scattered wildly around the right answer).