This is a good example of how in the real world, everything is correlated with everything. Understanding this principle, I would <i>expect</i> uneven birth times and birth dates. I may not be able to guess what will cause it to be uneven (though in this particular case I would have gotten pretty close), or by how much it will deviate from uniformly random (I would have gotten this wrong to the low side), but it's sure to be something.<p>To put it another way intuitively, in a complicated world with so many things impacting so many other things, to have a totally uniformly random birth times or dates would essentially require some <i>active force</i> to smooth the times and dates out, because it is beyond implausible that <i>absolutely nothing</i> would have an impact. From diurnal hormone cycles, traffic cycles, preferences about surgery times, and probably another dozen things you could think of that <i>could</i> impact the times, it is implausible to expect that they would all be completely wrong or that they would all precisely cancel.<p>Uniform randomness is a very convenient mathematical fiction for making Statistics 101 problems easy enough for students to do. This is a necessary thing and it's hard to imagine how to avoid it. But in reality almost nothing is ever truly uniformly random. There's always <i>something</i> out there that's going to correlate it with something. It is a sad side effect of this need to simplify problems enough to be tractable by students that we end up teaching that uniform randomness is somehow the "default" distribution and the others are exceptions or something.