Why do we round up 0.5000 to 1 instead of rounding down to 0?
In: 12
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.
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.
Because 0,1,2,3, and 4 are the first half. 5,6,7,8, and 9 are the second.
.5 is closer to the next higher integer than the lower. If only by the smallest of margins. There are exactly as many numbers between 0-.4999 as there are from .5-.9999. (Obviously, I don’t mean infinity)
Because 0,1,2,3, and 4 are the first half. 5,6,7,8, and 9 are the second.
.5 is closer to the next higher integer than the lower. If only by the smallest of margins. There are exactly as many numbers between 0-.4999 as there are from .5-.9999. (Obviously, I don’t mean infinity)
If there was half a pizza on the table, it’s more accurate to say there is a pizza instead of there is no pizza.
I remember learning this example from my teacher in second grade.
Imagine that you’re on a journey but the weather is getting bad. You need to travel from mile marker 1 to mile marker 2. At mile 1.4 you decide the weather is too bad, and it’s quicker to go back to market 1 than risk it to mile 2. But what if you made it to 1.5? It’s equally distant to both. You might as well keep going to 2 that’s where you need to go.
If there was half a pizza on the table, it’s more accurate to say there is a pizza instead of there is no pizza.
I remember learning this example from my teacher in second grade.
Imagine that you’re on a journey but the weather is getting bad. You need to travel from mile marker 1 to mile marker 2. At mile 1.4 you decide the weather is too bad, and it’s quicker to go back to market 1 than risk it to mile 2. But what if you made it to 1.5? It’s equally distant to both. You might as well keep going to 2 that’s where you need to go.
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