Why do we round up 0.5000 to 1 instead of rounding down to 0?

Question

Why do we round up 0.5000 to 1 instead of rounding down to 0?

In: 12

Answer 1

We don’t. We round to the even to avoid biasing the mean in a sample or population.

Let’s say we had 4 numbers: 1.5, 2.5, 3.5 and 4.5. Rounding them all up gives us 2, 3, 4 ,5. The mean of these is (2+3+4+5)/4 = 14/4 = 3.5 whereas (1.5 + 2.5 + 3.5 + 4.5)/4 = 12/4 = 3, so we can see that consistently rounding up will artificially inflate the mean.

Instead we round to the even so 1.5 and 2.5 BOTH round to 2 and 3.5, 4.5 both round to 4. Now taking the mean of the rounded numbers (2 + 2 + 4 + 4) = 12/4 = 3 so the mean is unchanged.

Rounding to the even thus helps to avoid biasing the mean in a data set.