I'd draw the table more like this

  Metric       Weight  Percent   Score  Weighted_score
Leadership       40      40%       2      0.8
Punctuality      20      20%       2      0.4
Cleanliness      30      30%       2      0.6
Responsiveness   10      10%       2      0.2
Total           100     100%              2.0
[download]

Then remove one item and you don't have to change any weights, just calculate the new percentages and weighted scores:

  Metric       Weight  Percent   Score  Weighted_score
Leadership       40     50%        2      1.0
Punctuality      --     --%       N/A     ---
Cleanliness      30     37.5%      2      0.75
Responsiveness   10     12.5%      2      0.25
    Total        80    100%               2.0
[download]

A percentage is just a type of weight but weights don't have to add up to 100 while percentages do. So dealing in weights that aren't (necessarily) percentages is more flexible and easier to understand when you have a problem like this.

Precisely the sort of thing I was suggesting, but made more clear. The absolute weights and scores can then be used to calculate percentages and weighted scores. I'd probably list the percentages after the scores, though, unless there's some specific reason that, for viewing purposes, they should be listed first.


- apotheon
CopyWrite Chad Perrin

my @metrics = (  # Weights don't need to add up to anything specific.
   [ 'Leadership',     0.40 ],
   [ 'Punctuality',    0.20 ],
   [ 'Cleanliness',    0.30 ],
   [ 'Responsiveness', 0.10 ],
);

my @scores = (2, undef, 2, 2);



my $total_weight = 0;

foreach (0..$#metrics) {
   $total_weight += $metrics[$_][1]
      if (defined($scores[$_]));
}



my $total = 0;

foreach (0..$#metrics) {
   if (defined($scores[$_])) {
      my $metric   = $metrics[$_][0];
      my $score    = $scores[$_];
      my $weight   = $metrics[$_][1] / $total_weight;
      my $weighted = $score * $weight;

      $total += $weighted;

      printf("%-20s %d %5.3f %5.3f$/", $metric, $score, $weight, $weig
+hted);
   }
   else
   {
      my $metric = $metrics[$_][0];
      printf("%-20s - ----- -----$/", $metric);
   }
}

printf("%-20s - ----- %5.3f$/", 'Total', $total);

output
======
Leadership           2 0.500 1.000
Punctuality          - ----- -----
Cleanliness          2 0.375 0.750
Responsiveness       2 0.125 0.250
Total                - ----- 2.000
[download]

Simple, just distribute that 20% among the rest three according to their ratio 8:6:2. This should result the same as if you re-distribute the original 100% among those 3 according to this same ratio 8:6:2. Either way, the end result would be 50%, 37.5%, 12.5%.

That's pretty similar to how I see it, though I do it a different way..

Metric         Weight     Score  Weighted Score
Leadership     40%        2      .8
Punctuality    20%        2      .4
Cleanliness    30%        2      .6
Responsiveness 10%        2      .2
Total          100%              2
[download]

Basically, all the weights apply to a total... in this case, it's 100%

When you eliminate the Punctuality column, you're left with a total of 80%... So just figure out what percentage of 80 the remaining weights are:

Leadership     40/80 =  50%
Cleanliness    30/80 =  37.5%
Responsiveness 10/80 =  12.5%
Total             80%  100%
[download]

So the recalculated weighted score becomes:

Metric         Weight     Score  Weighted Score
Leadership     50%        2      1
Cleanliness    37.5%      2      .75
Responsiveness 12.5%      2      .25
Total          100%              2
[download]

Trek

Edit: Added recalculated table.

The remaining percentages will add up to a certain other percentage. Multiply every number left (raw score as well as percentage) by 100/(sum of remaining percentages). This will give you the new weighted score as well as the percentage of the whole that each represents.