Computing weighted average from a set of values

weighted_average.php

function weighted_average($values) {
    $sum = 0;
    foreach ($values as $i => $value) {
        $sum += $value;
    }
    
    $avg = $sum / count($values);

    $error = array();
    
    $max_error = 0;
    
    foreach ($values as $i => $value) {
        $error[$i] = abs($avg - $value);
        $max_error = max($error[$i], $max_error);
    }
    
    $total_weight = 0;
    $weighted_sum = 0;
    
    foreach ($values as $i => $value) {
        $weight = 1 - ($error[$i] / $max_error);
        $weight = $weight * $weight; // square
        $total_weight += $weight;
        $weighted_sum += $weight * $value;
    }
    
    $weighted_average = $weighted_sum / $total_weight;
    
    return $weighted_average;
}

Weighted average is great for weeding out "erroneous" readings in a data set - for example:

var_dump(weighted_average(array(7,8,6,9,7,8,8,5,99))); // => ~ 7.29

Notice how the 99 has very little impact on the result - great for calculating average scores, ratings, prices, etc.