Putting a plus-minus on it

A single figure without a range around it claims more certainty than a handful of readings can support. The fix takes one extra line of arithmetic, not a statistics course.

The method

With three readings, use the median as your central value and half the spread (the largest reading minus the smallest, divided by two) as your uncertainty. With five or more, the standard deviation is a better-behaved estimate of spread, and either the mean or the median works as the central value. Report the result as value ± uncertainty, and round the uncertainty to the same resolution as the reading itself.

Three readings is the practical minimum for this - one reading gives you a number and nothing about how much to trust it. More than five readings in one session rarely buys much extra: the estimate tightens a little, but the time spent is better used checking technique than chasing a smaller decimal. Two readings is not enough to compute either version of this honestly - with only two numbers, "spread" and "difference" are the same thing, and there is no way to tell a wobble from a trend.

A worked example (illustrative numbers, not a real measurement)

Say three length readings, bone-pressed, come out as 15.1, 15.0 and 15.3 cm.

The median is 15.1 cm. The spread is 15.3 minus 15.0, which is 0.3 cm; half of that is 0.15 cm. Rounded to the resolution the ruler can actually support, that is 15.1 ± 0.2 cm.

With five readings - 15.1, 15.0, 15.3, 15.1, 14.9 cm - the arithmetic changes slightly. The mean is 15.08 cm, which rounds to 15.1 cm. The standard deviation of that set works out to about 0.15 cm, giving 15.1 ± 0.2 cm again in this case - the two methods often land close together, which is expected when the readings themselves are well behaved.

Why half-range for three, and SD for five or more

Half-range is crude but honest with very few data points: it does not pretend to know the shape of the underlying spread, it just reports how far apart your extremes landed. With only three numbers, a standard deviation formula does not have enough data behind it to be more informative than that, so there is little point reaching for it. Once you have five or more readings, the standard deviation starts to use the information in every reading rather than just the two extremes, and becomes the better estimate. This mirrors the same reasoning behind choosing the mean or the median for repeats - the right summary depends on how much data you actually have.

What the number does and does not promise

A ± range describes how consistent your own readings were; it is not a guarantee that the true value sits inside it, and it does not mean what people often assume it means. It also only ever describes random spread among your readings - if your method has a systematic error, for instance from under-pressing at the bone, the true value can sit outside a perfectly calculated interval, because the interval was never trying to catch that kind of error in the first place. Recording the raw readings that went into the calculation, not just the final ± figure, is what lets you or anyone else check the arithmetic later - see keeping a measurement log for where that record lives.

Where this stops

This is about stating a range on your own reading, not about what that range means placed against a population of other men - that is a separate question, answered with the published data and a percentile calculation, not with anything covered here. It also has no equivalent for a photo-based estimate, since there are no repeated readings behind a single inference from an image - an app assessing a photograph is doing something else entirely and has no spread to report. A numeric score from a service like Penis Rater carries its own kind of range in the sense of a position among other photographs, which is not the same statistical object as a ± on a physical reading. And a person's opinion, the sort you'd get from a judge, does not come with an uncertainty at all in this sense - it is one impression, not a set of readings to spread around a centre.