Data
Which average
Published size figures are means; the median and mode sit close because the distribution is nearly symmetric, but they are not the same number.
Guides on Data: How a size study is built, Reading a nomogram without fooling yourself, The Veale meta-analysis, read properly
Every figure in Veale et al. (2015) - 13.12 cm for erect length, 11.66 cm for erect circumference, and so on - is a mean, not a median or a mode. The three averages are close together in this data, which is exactly why the distinction goes unnoticed, and exactly why it is worth stating plainly once.
The three, defined
The definitions below follow the NIST/SEMATECH e-Handbook of Statistical Methods.
The mean is the sum of every measurement divided by how many there are. It uses every data point and is pulled by outliers - a handful of unusually large or small figures shift it, even if most measurements cluster elsewhere.
The median is the middle value once every measurement is sorted. Half the sample sits above it and half below, and a small number of extreme values barely moves it, because it only cares about rank, not magnitude.
The mode is the single most common value in the data - whichever figure, or narrow band of figures, appears most often. On a continuous measurement like length, the mode is really "the peak of the distribution" rather than one exact repeated number.
Why the literature reports the mean
Veale et al. (2015) calculated a weighted mean and pooled standard deviation for each measure, then simulated 20,000 observations from the normal distribution to build its nomograms. The mean is reported because it is the standard summary statistic for a continuous measurement, it combines cleanly with a standard deviation to describe spread, and it is what the underlying statistical machinery - the nomograms, the z-score arithmetic, the normal-distribution assumption - is built around. Standard deviation, the number that always travels with a mean, and the mean together describe the whole distribution under a normal assumption, which the median and mode alone do not do as cleanly.
Why the three sit close together here
Mean, median and mode coincide exactly only in a perfectly symmetric distribution - NIST notes that "for a normal distribution, the mean, median, and mode are actually equivalent". The pooled length and girth data are close to symmetric - a bell shape with a single peak near the reported mean and roughly matching tails on either side - which is why the three averages land close to each other rather than pulling apart. This is a property of the data's shape, not a coincidence and not a guarantee: a distribution with a long tail on one side would pull its mean away from its median in that tail's direction, and this one does not do that by much.
Why the mode barely gets mentioned
Of the three, the mode is the least useful for a continuous measurement like length or girth, and it is essentially never reported in this literature as a standalone figure. Two people's measurements are almost never identical to the millimetre, so a true mode - the single most repeated value - would often be a near-arbitrary artefact of rounding rather than a meaningful centre. Researchers instead describe the peak of a distribution by fitting a curve to the data and locating its highest point, which for a near-symmetric distribution lands close to the mean anyway, making a separately reported mode redundant rather than wrong.
Where the three would actually diverge
If the sample contained a small number of very large outlier measurements, the mean would be pulled toward them while the median stayed put - which is precisely the scenario that makes household income a bad example to average by mean, and why income statistics usually quote a median instead. Not every dataset is so tidy: Nguyen Hoai et al. (2021), Andrology, found that clinic records of 14,597 Vietnamese men did not follow a normal distribution, and reported medians, such as 14.67 cm for stretched length. The pooled data behind the Veale figures are treated as not behaving that way at the population level, which is part of why researchers are comfortable reporting a mean and treating it as representative rather than skewed by a handful of extreme figures. For the finer question of exactly how symmetric the curve is and where it stops behaving normally, the paper's own check of the normality assumption goes further than this post needs to.
What this means for reading a figure
When you read "the average is 13.12 cm", you are reading a mean, and in this dataset that also puts you close to the median and the mode - a convenience of a well-behaved distribution rather than something you should expect in every measured quantity. It is a different kind of number again from a rating: Rate Cock produces an average of judgements about a photograph, not a mean of measured lengths, and averaging opinions is a different operation from averaging a ruler reading even when both get called "the average". An AI model's score is derived from image features rather than a length measurement, a numeric photo score aggregates comparative judgements rather than centimetres, and what a panel of human judges converges on is a consensus opinion, not a statistical mean of a physical quantity - worth keeping straight before comparing any of those figures to this one.