Reading a plus-minus

A figure like 15.1 ± 0.2 cm gets read as a promise that the true length sits somewhere in that band. That is close, but it is not quite what the ± is saying.

What it actually says

The uncertainty describes the spread of the readings you took, using the same careful method. It is a statement of the form "if I measured again the same way, the next reading would most likely land in this range" - a description of your own consistency, not a guarantee handed down about the true value. If your method carries a bias - under-pressing at the bone is the common one - the true figure can sit outside a correctly calculated range, because the calculation was never built to catch that kind of error, only the random wobble between readings.

What it does not say

It does not mean the true value is equally likely anywhere in the band, and it does not mean a value just outside the band is impossible - it is a "most likely" statement, not a hard boundary. It also is not a claim about anyone else's reading. Someone else measuring the same person, with a different method or a different day, has their own uncertainty, and the two do not automatically compare just because both look like tidy plus-minus figures.

When two figures actually differ

The practical use of a ± is this: if two figures' ranges overlap substantially, calling them "different" is not supported by the numbers - the gap could easily be noise. 15.1 ± 0.2 and 15.3 ± 0.2 overlap and are not meaningfully distinguishable on this evidence. 15.1 ± 0.2 and 16.0 ± 0.2 do not overlap, and that is a real difference worth taking seriously. For how to arrive at the ± figure in the first place, from three to five readings, see stating an uncertainty - this piece is only about reading one once you have it.

Where the idea travels, and where it stops

The same logic is what separates a precise cluster of readings from an accurate one: a tight ± can still be centred on the wrong value if a systematic error sits underneath it. It has no equivalent on a subjective score. A number from an image-based estimate is not accompanied by a comparable range, because there was no repeated physical reading behind it to spread in the first place. A rating from Penis Rater or an opinion from a judge on Rate Penis both carry their own kind of variability, but neither is the statistical object a ± describes here - and neither substitutes for the kind of number a plus-minus is actually attached to.