First of all I must state that I am not a mathematician, so please correct me if I use wrong terminology.
I am building a web application which needs to calculate the rating for each entity based on both the quantity and score of the reviews for that entity.
In other words, I don't want to just calculate the rating based on the average score as that would make an entity with one hundred 9 score (review score can be from 0 to 10) reviews rate lower than an entity with only one 9.5 score review.
I need an algorithm to calculate rating and add rating "weight" to the final rating based on how many reviews the entity has, so that for instance in the above example the entity with 100 9 score reviews would get a rating that is higher than the entity with only one 9.5 score review. In other words, the final entity rating score will be based on the "relationship" between quality and quantity.
There is another important thing to note: an entity can not have a rating higher than 10, so the rating "weight" added by the quantity can not be linear.
In the algorithm we can use any data about the reviews/rating, that is individual review score, total number of reviews, sum of all reviews, number of good reviews (score 8 or higher) so far, etc, in each iteration of the rating calculation process.
Any kind of help or info regarding this would be appreciated. Thank you.