Why do we round up 0.5000 to 1 instead of rounding down to 0?
In: 12
5 isn’t the “middle” of 10, it’s half. 0-4 is half, and 5-9 is half.
5 is the first number on the second and higher half, which is why it makes sense to round up.
I do not have any post secondary or academia awards around math and could be completely wrong so feel free to ignore this but thank you anyways for coming out to my cold-soup-in-a-milkcarton swamp ditch Ted talk.
5 isn’t the “middle” of 10, it’s half. 0-4 is half, and 5-9 is half.
5 is the first number on the second and higher half, which is why it makes sense to round up.
I do not have any post secondary or academia awards around math and could be completely wrong so feel free to ignore this but thank you anyways for coming out to my cold-soup-in-a-milkcarton swamp ditch Ted talk.
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.
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.
As others have mentioned, we don’t always round 0.5 up. There’s many different methods of rounding that are more appropriate for some applications than others, it just so happens that rounding 0.5 up is good enough for the vast majority of daily life applications.
There are 9 different numbers (0.1 – 0.9) that need rounding and only 2 options (0, 1) to chose from so it’s impossible to divide it evenly with a straight forward method so we had to randomly-ish chose one.
As others have mentioned, we don’t always round 0.5 up. There’s many different methods of rounding that are more appropriate for some applications than others, it just so happens that rounding 0.5 up is good enough for the vast majority of daily life applications.
There are 9 different numbers (0.1 – 0.9) that need rounding and only 2 options (0, 1) to chose from so it’s impossible to divide it evenly with a straight forward method so we had to randomly-ish chose one.
Well technically there are different rounding-modes to choose from.
But one has to be the default ….
Well technically there are different rounding-modes to choose from.
But one has to be the default ….
1,2,3,4 round down
6,7,8,9 round up
So 5 could go either way. It is just typical convention to decide to round up. However, anything larger than 5 should round up, included if you have additional place values, so if 0.5000001 rounds up then it’s neater to do 5 and up with 5 inclusive than exclusive.
However, there are different conventions; for instance, “bankers rounding” alternates if 5 rounds up or down. Negatives also cause different conventions, some round -0.5 to -1 and other to 0.
1,2,3,4 round down
6,7,8,9 round up
So 5 could go either way. It is just typical convention to decide to round up. However, anything larger than 5 should round up, included if you have additional place values, so if 0.5000001 rounds up then it’s neater to do 5 and up with 5 inclusive than exclusive.
However, there are different conventions; for instance, “bankers rounding” alternates if 5 rounds up or down. Negatives also cause different conventions, some round -0.5 to -1 and other to 0.
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