One and two standard deviations

A mean on its own tells you where the middle sits. It says nothing about how spread out everyone else is, and "everyone else" is what a reader actually wants to know when they compare a measurement to a published figure. The 68-95 rule is the shortest route from a mean and a standard deviation to an actual range of people.

The rule itself

For a normal distribution, roughly 68 percent of individual values fall within one standard deviation of the mean, on either side. Roughly 95 percent fall within two standard deviations. Roughly 99.7 percent fall within three. It is a property of the normal curve's shape, not of any particular dataset - it holds for anything that is approximately normally distributed, and length data of this kind is close enough to normal for the approximation to be useful.

Applying it to erect length

Veale et al. (2015), pooling measurements taken by health professionals across 15,521 men, reports a mean bone-pressed erect length of 13.12 cm with a standard deviation of 1.66 cm.

Apply the rule directly:

Read that plainly: about two-thirds of measured men in the pooled sample fall between roughly 11.5 cm and 14.8 cm. About 19 in 20 fall between roughly 9.8 cm and 16.4 cm. The remaining one in twenty is split between the two tails, so about one in forty falls above 16.44 cm and about one in forty falls below 9.80 cm.

What this range is doing

It is not a claim that anyone outside it is unusual in some meaningful sense. It is arithmetic describing where the mass of a distribution sits, given a mean and a spread that were themselves measured with their own uncertainty. Standard deviation itself is worth understanding on its own terms before leaning on a rule that uses it, and the ranges above assume the underlying figures are the ones you get from the full table of Veale means and spreads by state, which is worth checking before comparing anything to them.

Where the approximation strains

Two things limit how far this can be pushed. First, "normal" is an approximation, and approximations are least reliable in the tails - the 99th percentile, in particular, is a case where the normal assumption and the real data are more likely to diverge, which is a separate calculation worth doing carefully rather than skimmed off this one. Second, the standard deviation itself carries sampling uncertainty; a pooled figure from 15,521 men is precise about the mean, but the reported SD is still an estimate, not a fixed constant, so the boundaries above are themselves approximate rather than exact.

Applying it to a second row

The same arithmetic runs identically against any other row in the reference table of Veale means and SDs by state. Flaccid length, mean 9.16 cm and SD 1.57 cm, gives a one-SD range of 7.59 cm to 10.73 cm and a two-SD range of 6.02 cm to 12.30 cm. Erect girth, mean 11.66 cm and SD 1.10 cm, gives a one-SD range of 10.56 cm to 12.76 cm and a two-SD range of 9.46 cm to 13.86 cm - visibly tighter, in absolute terms, than the length ranges above, because girth's standard deviation is smaller relative to its mean. The mechanics never change: take the mean, add and subtract one SD for the middle two-thirds, add and subtract two SDs for the middle 95 percent.

Why this beats a single number

A single mean invites the reader to ask "am I above or below it" and stop there, which is not a very informative question - roughly half of any distribution is below its mean by definition. A range with a stated coverage - 68 percent, 95 percent - answers a more useful question: how far from typical is this, and by how much. That is a genuinely different kind of statement from a subjective rating, which describes an impression of a photograph rather than a position in a measured distribution - Rate Cock produces the second kind of number, and a rated-photo score should not be read as interchangeable with a percentile. If what you want instead is a person's opinion rather than either kind of number, that is its own separate category with its own site, and it is also worth being clear that an AI image estimate is neither a measurement nor a rating in this statistical sense - it is an inference from pixels, not from a ruler or a distribution.