Uncertainty in Measurement: Accuracy and Precision

Scientists make repeated measurements of a quantity during experimentation to ensure that their results are accurate and precise.

The accuracy of a measurement is the degree of closeness of the results to the true or accepted value.

Consider two students, A and B, who repeatedly weighed a gold bar known to have a true mass of 10 grams. Student A reported three values － 9.5 grams, 10 grams, and 10.5 grams, while student B reported masses of 8.5 grams, 8.6 grams, and 8.5 grams. Student A reported values closer to the true mass of the bar compared to student B. Thus measurements by student A were, therefore, more “accurate”.

Precision, on the other hand, is the measure of how closely the results agree with each other, or how reproducible they are. A measurement is said to be precise if it gives highly similar results when repeated under the same conditions. For instance, the values for the mass of the gold bar reported by student B were very similar to one another, as compared to student A. That is “precision”.

Accuracy and precision are two distinct qualities of measurement which are independent of each other. Thus, a particular set of measurements can be either accurate, or precise, or neither, or both.

The measurements for the mass of the gold bar by student A were more accurate, close to the true value of 10 grams, but not precise, as they were not close to each other. On the contrary, the measurements by student B were precise, but not accurate.

Highly accurate values tend to be precise too. Like a weighing balance showing true or close to true masses for all the objects, repeatedly. However, highly precise measurements may not necessarily be accurate; if the same balance is improperly calibrated, it may give precise but inaccurate readings. This may lead to scientific errors. 

Errors in the measurement process is a common problem. Such errors may fall into two categories － random and systematic. 

Random errors are the result of inconsistency in the measuring process or variations in the quantity being measured. These result in fluctuations, too high or too low, around the true value. Consider a scientist measuring the length of an earthworm using a caliper. Inconsistency of the scientist to read the scales correctly, or continuous body movement of the earthworm during the measurement, may result in incorrect length measurements. Random error cannot be avoided, however, it can be averaged out with repeated trials.

Systematic errors are the results of a persistent issue and lead to a consistent discrepancy in measurement. These errors tend to be either all too high or all too low compared to the true value. For instance, weights being measured using an improperly calibrated weighing balance. These are predictable and mostly instrument-related. However, unlike random error, it cannot be averaged out with repeated measurement.