So, inspired by by this, here's a thing I think quite a few people may have not noticed in #rstats (and other programming languages). When I first saw this i was like what the heck R is broken someone pls help. 
https://twitter.com/CovinoKristen/status/1362247676322934784
R does something called bankers rounding. If you have a lot of n.5 numbers in a vector and you were to do your normal rounding where 0.5 rounds up then that would increase the mean of your sample. By rounding .5 to the nearest even number R avoids this bias.
Moments pause as I crashed my computer generating a huge vector because I am a fool.
You can have this issue even with normal distributions - illustrated here. With a dataset which had lots of n.5s the drift in the mean would be much greater.
There was probably a more elegant way of doing this so do excuse my slapdash code. If I add 0.5 to all my rounded numbers, then take the mean of the vector, rounded normally (as opposed to bakers rounding) you get this, where the mean has shifted by nearly 1:
My favourite bit about this was that I told R to generate me a vector of 10,000 numbers with a mean of 1000 and then proceeded to check the mean XD
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