Precision and Accuracy

Precision describes how close repeated measurements are to each other. Precise readings have a small spread. Poor precision is caused by random errors.Accuracy describes how close a measurement is to the true value. Poor accuracy is caused by systematic errors, which shift readings away from the true value in one direction.The two are independent. Think of darts on a board: darts grouped tightly but away from the bullseye are precise but not accurate; darts spread widely around the bullseye are accurate on average but not precise; a tight group on the bullseye is both.Worked example: The true value of g is 9.81 m s⁻².
• Set A: 9.52, 9.54 and 9.53 m s⁻². The spread is tiny, so the set is precise, but every value is well below 9.81, so it is not accurate (probably a systematic error).
• Set B: 9.70, 9.95 and 9.78 m s⁻². The mean is 29.43 ÷ 3 = 9.81 m s⁻², equal to the true value, so the mean is accurate, but the large spread means the set is not precise.Accuracy can be judged using the percentage difference between the experimental and accepted values:percentage difference = (|experimental − accepted| ÷ accepted) × 100%For set A: (9.81 − 9.53) ÷ 9.81 × 100% = 2.9%.To improve precision, reduce random errors (repeat readings, use better techniques). To improve accuracy, find and remove systematic errors (check zero readings and calibrate instruments).