CODEWITHSUNDEEP
phpalgorithmstatistics
nickf
nickf

Reputation: 546075

How to calculate a weighted mean?

My language is PHP, but the algorithm should be fairly universal.

I have an associative array of (let's say) ratings and number of times that rating has been given.

$ratings = array(
    1 => 1,
    2 => 3,
    3 => 6,
    4 => 3,
    5 => 3
);

This is the equivalent of: [1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5], but given the numbers I'm working with, it would be quite inefficient to convert from the first form to the second.

What would be the algorithm to calculate the mean of the above numbers?

Upvotes: 4

Views: 6332

Answers (3)

Sparr
Sparr

Reputation: 7712

Doubt I can beat the accepted answer, but I find that built in looping functions run faster than scripted loops. Not sure how well the calls to $multiply are going to be optimized. If this is really slow then I expect someone will point it out in a comment.

function multiply( $k , $v ) { return $k * $v; }
return array_sum( array_map( 'multiply' , array_keys($ratings) , $ratings ) ) / array_sum( $ratings );

Upvotes: 3

Sasha
Sasha

Reputation: 1190

Wouldn't this work?

$total = 0;
$sum = 0;
foreach ($ratings as $k => $v) {
  $total += $k * $v;
  $sum += $v;
}
echo $total / $sum;

EDIT: Well, I look silly, since someone beat me to it. Oh well.

Upvotes: 10

Ray Hidayat
Ray Hidayat

Reputation: 16249

Try this:

$total = 0;
$count = 0;
foreach($ratings as $number=>$frequency) {
  $total += $number * $frequency;
  $count += $frequency;
}
return $total / $count;

Upvotes: 17

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