Accuracy vs Precision

Mr. Murray's Physics

Accuracy vs. Precision

Accuracy is how close you get to an actual, correct number.

Precision is how well an instrument can reproduce the same numbers.

A graduated cylinder is precise. A beaker is not. If you need to know the volume of a liquid you would want to use the graduated cylinder. Five different people will get different numbers if reading from a beaker, since a small change of water does not change the level in the beaker: it is too wide. Each of the five people could be off by 10 or 25 mL of each other. With a graduated cylinder, all five people will get within 1 mL of each other. If they all know how to read a meniscus, they will probably all read the same volume. The graduated cylinder is thin enough that a couple of drops of water will raise the level significantly. The graduated cylinder is precise because the numbers can be reproduced by different people.

If I give you these sets of numbers: 11.232 cm; 11.231 cm; 11.234 cm, you can see that they are precise, since they are exactly the same up to the hundredth of a cm. You cannot, however, determine if they are accurate unless there is a given or known number with which to compare. If your known number was 11.236 cm, you can say that your measurements are both precise and accurate (missing by only .003 or .004 cm). If your given number was 11.854, you would say your measurements are precise, but inaccurate. In this second case you wouldn't fret much, because a precise measuring instrument can be recalibrated to then become accurate. An imprecise instrument cannot be recalibrated to be precise.

Many books tell us that with a precise instrument you will get the same number every time you measure with it. The problem with this way of describing precision is that a particular person will guess the same number every time. Each person tends to make the same assumptions when reading from an imprecise instrument. The above method of discussing precision is better: with a precise instrument different people will get the same number. This is the most important reason for precise instruments in science: so that results can be reproduced and verified by other scientists. An experiment that is not reproducible, it is not proven.

Given 4.3 mL (this is the right number found by using a precise and calibrated instrument, so we know it is accurate).

Data set a) 4.1 mL; 4.6 mL; 4.5 mL

Data set b) 4.12 mL; 4.11 mL; 4.13 mL

Data set a) is not very precise, but it is accurate. All numbers are around the "bull's eye".

Data set b) is very precise, but not accurate. Once this instrument is calibrated, it should be even more accurate and precise than the one that gave the given number.