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$\begingroup$ Re: bias, that's the reason for the "banker's rounding" (round to nearest even) strategy; when you're faced with only (or at least primarily) positive numbers, the "away from zero" bias can add up over time. "Round to nearest even" avoids introducing bias even if all your values are positive, as long as they're distributed equally ...
1. The maths question below is asking me to find the number of people. I have found the answer to be 57553.0834 57553.0834, but obviously there can't be 0.0834 0.0834 of a human. The mark scheme states the answer is 57553 57553 as it's been rounded to the nearest integer.
For floor rounding we eliminate the decimal part by subtracting the decimal part of the divided number from the divided results. For ceiling rounding we figure out the number that, when added to the divided results, will increase it to the next whole number.
22. WE do this because when you round, generally it is with decimals that are rational or long. When there is 5.000000000000000001, it is better to round up. So, lets say you have the square root of 26 (5.09901951359) It's close to 6 than to 4. When rounding, you can't have 5.090919534243123 whatever to round down because decimals cant go down.
1. There is no intrinsic reason to round at all. Even though all your samples have a whole number of people the mean may well not. Just report 4.3 4.3 or 4.7 4.7 or whatever you get. If you are going to round it, the usual rounding rules apply, so 4.3 4.3 would round to 4 4 and 4.7 4.7 would round to 5 5 if you wanted a whole number. Share. Cite.
$\begingroup$ @JérémyBlanc There are many different conventions for what to do when rounding from an exact midpoint value - I would say that the most 'common', particularly in computer sciences, is to round so as to make the last digit even - so 8.645 would round to 8.64, while 8.655 would round to 8.66. $\endgroup$
2 Answers. Sorted by: 3. Rounding is to take the nearest number with a given number of digits. To approximate is to give any number nearby, not necessarily with a finite number of digits. For example, x =2.4564 is rounded to 2.46 with two decimal places, and 211 90 = 2.455555... 211 90 = 2.455555... is an approximation of x within 0.2%.
Also, if you were supposed to round 2.89 2.89 to 2.9 2.9, then I would consider 2.90 2.90 as wrong, since that 0 0 implies more acuracy than you have. If 2.89 is correct to two decimal points, 2.90 is correct only to one. OTOH if the answer was 2.898, then to two decimal points the correct answer would be 2.90.
If you want to round to the nearest 10, you can then do. 10⌊ x 10 + 1 2⌋ 10 ⌊ x 10 + 1 2 ⌋. which rounds x 10 x 10 to the nearest integer, then multiplies by 10 again. Replacing the 10 with something else such as 17 will round to the nearest multiple of 17 or whatever; in particular. 1 10⌊10x + 1 2⌋ 1 10 ⌊ 10 x + 1 2 ⌋.
Like lets say 412 to 425 or 400 (if the multiples are 25) or 516 to 550 or 500 (if the multiples are 50). I don't know this is not rounding but how would this go?