Science Puzzle
The Dartboard and the Clock
Thrower A puts four darts in a tight cluster, all in the same spot near the edge of the board. Thrower B scatters four darts widely, but they sit evenly around the bullseye and average out to its centre.
A laboratory has two thermometers behaving the same way. One reads 22.4, 22.4, 22.5, 22.4 in a room that is actually 19 degrees. The other reads 17, 21, 20, 18 in the same room. Which is precise, which is accurate, and which is the more useful instrument?
The Answer
Precision is how closely repeated measurements agree with each other. Accuracy is how close they are to the true value. They are independent, and confusing them is one of the most common errors in practical science.
The first thermometer is precise but inaccurate: it agrees with itself beautifully and is wrong by about 3.4 degrees every time. The second is accurate but imprecise: its readings average close to 19, but any single reading could be out by two degrees.
The first instrument is the more useful one, which is the part people find surprising. A consistent offset is a systematic error, and systematic errors can be measured once and subtracted. Calibrate it against a known standard, discover it reads 3.4 too high, and from then on subtract 3.4. You now have an instrument that is both precise and accurate.
Random scatter cannot be fixed that way, because there is nothing consistent to correct. You can only beat it down by taking many readings and averaging, and that improvement is slow: to halve the uncertainty you need roughly four times as many measurements. The scatter is a property of the instrument and it does not go away.
The deeper lesson is that repeatability is not correctness. Four readings that agree to one decimal place look authoritative and reassuring, and they tell you absolutely nothing about whether the instrument is calibrated. That reassurance is exactly why systematic errors are so dangerous: they hide inside data that looks tidy.
The principle: Precision versus accuracy. Precision is agreement between repeated measurements; accuracy is closeness to the true value. A systematic error can be calibrated out; random scatter cannot, and can only be reduced slowly by averaging.