Human body density is approximately 1 kg/l (same as fresh water) - which is not surprising (at first) given that we are 70% water, and is surprising (on a second thought), given that the other 30% can be just about anything (from the air in the lungs to the relatively heavy bones).
How remarkable is that?
Consider other mammalian species. For each species, compute the average body density of an adult. Thus, for each species we have the number - the mean body density. How are these numbers distributed? Mostly heavier than water? Lighter?
It is unlikely that this kind of research has been done, so I would settle for something simpler: what are the densest/lightest mammals? (or, in general, vertebrae)
PS. As you can guess, I am a mathematician, not a biologist :-)
PPS. Given abundance of water of Earth's surface (70%, same as above!), it makes a lot of sense to be as dense as water: not heavier (to avoid drowning), not lighter (to be able to dive for food), so natural selection should favor the density of 1. Are there exceptions?