algorithm used to calculate 5 star ratings

Question

I need to calculate 5-star ratings like the one on Amazon website. I have done enough search to find what is the best algorithm, but I am not able to get a proper answer. For ex

Answer 1

Super helpful reply by Blindy, here's the PHP code that's based on it. Some may find useful. The results will be 4.11 as per OP's example:

$ratings = array(
5 => 252,
4 => 124,
3 => 40,
2 => 29,
1 => 33
);

function calcAverageRating($ratings) {

$totalWeight = 0;
$totalReviews = 0;

foreach ($ratings as $weight => $numberofReviews) {
    $WeightMultipliedByNumber = $weight * $numberofReviews;
    $totalWeight += $WeightMultipliedByNumber;
    $totalReviews += $numberofReviews;
}

//divide the total weight by total number of reviews
$averageRating = $totalWeight / $totalReviews;

return $averageRating;
}

How to build the above $ratings array

Example pseudo code, but which should work that explains how to build the $ratings array when info is stored in DB assuming you have a table called "ratings" and a column called "rating". In this case it's 1 join, you would need to do 4 joins to get all ratings, but this should get you started:

SELECT count(c1.rating) as one_star, count(c2.rating) as two_star  
FROM ratings c1 
LEFT OUTER JOIN
ratings c2
ON
c1.id = c2.id
WHERE
c1.rating = 1
AND
c2.rating = 2

another approach suggested in comments

SELECT SUM(rating = 1) AS one_s ,SUM(rating = 2) AS two_s ,SUM(rating = 3) as three_s FROM reviews where product_id = 9