How to make rounded percentages add up to 100%
algorithm, math, percentage, rounding
Solution
Since none of the answers here seem to solve it properly, here's my semi-obfuscated version using underscorejs:
function foo(l, target) {
var off = target - _.reduce(l, function(acc, x) { return acc + Math.round(x) }, 0);
return _.chain(l).
sortBy(function(x) { return Math.round(x) - x }).
map(function(x, i) { return Math.round(x) + (off > i) - (i >= (l.length + off)) }).
value();
}
foo([13.626332, 47.989636, 9.596008, 28.788024], 100) // => [48, 29, 14, 9]
foo([16.666, 16.666, 16.666, 16.666, 16.666, 16.666], 100) // => [17, 17, 17, 17, 16, 16]
foo([33.333, 33.333, 33.333], 100) // => [34, 33, 33]
foo([33.3, 33.3, 33.3, 0.1], 100) // => [34, 33, 33, 0]
Problem
Consider the four percentages below, represented as `float` numbers: ``` 13.626332% 47.989636% 9.596008% 28.788024% ----------- 100.000000% ``` I need to represent these percentages as whole numbers. If I simply use `Math.round()`, I end up with a total of 101%. ``` 14 + 48 + 10 + 29 = 101 ``` If I use `parseInt()`, I end up with a total of 97%. ``` 13 + 47 + 9 + 28 = 97 ``` What's a good algorithm to represent any number of percentages as whole numbers while still maintaining a total of 100%? Edit: After reading some of the comments and answers, there are clearly many ways to go about solving this. In my mind, to remain true to the numbers, the "right" result is the one that minimizes the overall error, defined by how much error rounding would introduce relative to the actual value: ``` value rounded error decision ---------------------------------------------------- 13.626332 14 2.7% round up (14) 47.989636 48 0.0% round up (48) 9.596008 10 4.0% don't round up (9) 28.788024 29 2.7% round up (29) ``` In case of a tie (3.33, 3.33, 3.33) an arbitrary decision can be made (e.g. 3, 4, 3).