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Informations about the package remainder
Largest Remainder Method ➗
This library provides a simple way to calculate percentages using the Largest Remainder Method. Learn more.
Installation
Usage
In simple terms, the goal of the Largest Remainder Method is to make sure that when calculating the weight of each seat in the data set, the aggregated percentage will not be 99.99 or 100.01.
The first example above is arbitrary and end up rounding up only the
first record so that 0.34 + 0.33 + 0.33 = 1, however not always
the decision is arbitrary.
As we can see, 0.36 + 0.37 + 0.27 = 1, however using standard
rounding, the result would have been different. To demonstrate that,
let's calculate 92 + 93 + 70 = 255. Each value takes the following
percentage of the whole:
| Value | Percentage | Round | Largest Remainder Method |
|---|---|---|---|
| 92 | 0.3607843137 | 0.36 | 0.36 |
| 93 | 0.3647058823 | 0.36 | 0.37 |
| 70 | 0.2745098039 | 0.27 | 0.27 |
As we can see from the table above, standard rounding end up
losing one percentage point because all three numbers round
down. The Largest Remainder Method will scan the values that will
be discarded (0.3607843137, 0.3647058823,
0.2745098039) and prioritize the ones with the largest
contribution. In this case, the 2nd value will discard 47058823,
which is the largest value discarded. That makes it viable for
round up to fill the gap.
The fact that 93 is also the largest value does not necessarily
have a direct connection to the option being rounded up. We can
try the same example again using a much smaller number. Take
92 + 32 + 70 = 194.
| Value | Percentage | Round | Largest Remainder Method |
|---|---|---|---|
| 92 | 0.4742268041 | 0.47 | 0.47 |
| 32 | 0.1649484536 | 0.16 | 0.17 |
| 70 | 0.3608247422 | 0.36 | 0.36 |
