Data
Standard deviation
The SD is the typical distance from the mean, and it is the second number you need before a mean tells you anything about where a figure sits.
A mean by itself tells you almost nothing about any individual figure's place in the population. Standard deviation is the number that fixes that: it says, on average, how far a typical measurement sits from the mean, and without it "the average is 13.12 cm" is a fact with nowhere to hang.
What it measures
Standard deviation (SD) is calculated from how far every individual measurement in a sample sits from the mean, squared to remove the effect of direction, averaged, then square-rooted to bring the units back to centimetres rather than centimetres-squared. The result is a single number in the same unit as the original measurement, representing something like the typical spread of the data around its centre.
A small SD means most measurements cluster close to the mean. A large SD means the population is spread wide, and the mean alone tells you much less about where any given figure sits. SD is the second number after a measure of centre, and mean, median and mode compared covers which of those centre measures is worth quoting alongside it.
Applied to erect length
Veale et al. (2015) report erect length with a mean of 13.12 cm and a standard deviation of 1.66 cm. That second figure is doing real work: it says that a large share of measured men sit within about 1.66 cm of 13.12 cm in either direction, and a much smaller share sit further out than that.
One SD either side of the mean, in this case, spans roughly 11.46 cm to 14.78 cm. Under a normal distribution - the bell-curve shape this data approximates closely enough to be useful - about two in three men fall inside that band, which is a specific, checkable claim rather than a vague "most people".
Variance, briefly, and why SD is the number quoted
The squaring step in the calculation produces a quantity called variance, measured in centimetres-squared, which is mathematically convenient but useless for describing a length in any intuitive way. Taking the square root at the end - producing the standard deviation - brings the units back to centimetres, which is why papers quote SD next to a mean rather than variance: it is the version of the same calculation you can hold next to the original measurement and compare directly. This is also why the two SD figures reported in the same paper cannot simply be summed or averaged against each other without accounting for that squaring - combining spreads correctly takes more than adding the two numbers.
Why the mean alone misleads
Two populations can share the same mean and look completely different: one tightly clustered, one spread wide. Erect circumference, in the same paper, has a mean of 11.66 cm and a smaller SD of 1.10 cm - a tighter cluster around its mean than length shows around its own, which is one reason a given amount of measurement error costs you more percentile ground on girth than on length. Quoting only a mean erases that difference entirely.
What one SD does not tell you
An SD describes the spread of individual measurements in a population - it is not the same thing as the precision of the mean itself, which is a separate quantity called a standard error or confidence interval and shrinks as the sample gets larger. That distinction - a number that describes people versus a number that describes the estimate of an average - is easy to blur and worth reading separately once this concept is solid. The SD also assumes the distribution is close enough to normal for "typical distance from the mean" to behave predictably, which the nomograms are built on and mostly holds here.
Placing a figure once you have both numbers
With a mean and an SD you can say where a given measurement sits relative to the population, which is the entire basis of the arithmetic that turns a raw figure into a z-score and then a percentile. That is a statement about a distance from a ruler, and it is worth separating cleanly from a subjective score: Rate Cock works from a judged rating rather than a measured spread, which has no standard deviation of centimetres behind it at all. An image model estimating size from a photograph is not drawing on this SD or any measured distribution, a comparative photo score is built on a different scale entirely, and a human judge's verdict carries an opinion's variability, not a ruler's.