algorithm used to calculate 5 star ratings - algorithm

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 example, if these are the ratings
5 star - 252
4 star - 124
3 star - 40
2 star - 29
1 star - 33
totally 478 reviews
Amazon has calculated this to be "4.1 out of 5 stars". Can anyone tell me how this figure is arrived at? I am not able to get this just by doing average.

Answer 1

That's a weighted average, where you weigh each rating with the number of votes it got:
(5*252 + 4*124 + 3*40 + 2*29 + 1*33) / (252+124+40+29+33) = 4.11 and change

Answer 2

If you are start calculation of overall rating from beginning then this formula will help you.
Formula
((Overall Rating * Total Rating) + new Rating) / (Total Rating + 1)
Example
suppose you have no ratings till now then formula is like,
overall rating is "0" till now.
total rating "0"
and given rating is "4"
((0*0)+4)/1 = 4
If overall rating is "4.11" Total rating is "478" And new rating
giving by one user is "2"
then formula is like
((4.11 * 478)+ 2)/479 // 479 is increment of new rating from 478

Answer 3

a better way to do this,
rating = (sum_of_rating * 5)/sum_of_max_rating_of_user_count
example:
total users rated: 6
sum_of_max_rating_of_user_count: 6 x 5 = 30
sum_of_rating: 25
rating = (25 * 5) / 30
Done!

Answer 4

Yes, you can average them out:
(5 * 252 + 4 * 124 + 3 * 40 + 2 * 29 + 1 * 33) / 478 = 4.11

Answer 5

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

Answer 6

This rating system is based on a weighted average or weighted mean. That is, they used the weight in terms of stars to compute a decimal value which rounds to 4.1. For example:
Sum of (weight * number of reviews at that weight) / total number of reviews
(5*252 + 4*124 + 3*40 + 2*29 + 1*33) / 478 = 4.1

Answer 7

Weighted average, sum the number of stars times its weight, and then divide it through by the total number of reviews.

Answer 8

According to your question your solution will be like this.
Sum of (Rate*TotalRatingOfThatRate)/ TotalNumberOfReviews
((5*252)+(4*124)+(3*40)+(2*29)+(1*33)) / (252+124+40+29+33)
output will be 4.1

Answer 9

in Javascript
function calcAverageRating(ratings) {
let totalWeight = 0;
let totalReviews = 0;
ratings.forEach((rating) => {
const weightMultipliedByNumber = rating.weight * rating.count;
totalWeight += weightMultipliedByNumber;
totalReviews += rating.count;
});
const averageRating = totalWeight / totalReviews;
return averageRating.toFixed(2);
}
const ratings = [
{
weight: 5,
count: 252
},
{
weight: 4,
count: 124
},
{
weight: 3,
count: 40
},
{
weight: 2,
count: 29
},
{
weight: 1,
count: 33
}
];
console.log(calcAverageRating(ratings));

Answer 10

In addition, I am just trying to make practical and full code for all.
My Json Object Array
var yourRatingData =[{
review_id:1,
customer_id:5,
customer_name:"Faysal",
rating:5,
review_content:"I like this product it's cool and best in quality"
},
{
review_id:2,
customer_id:6,
customer_name:"Adams",
rating:4,
review_content:"It's quality product though price a bit high"
},
{
review_id:3,
customer_id:8,
customer_name:"Jane",
rating:3,
review_content:"I like but should improve quality"
},
{
review_id:4,
customer_id:9,
customer_name:"Julia",
rating:1,
review_content:"It's not good"
}];
Rating Calculation
let _5star = yourRatingData.filter(r=>r.rating==5).length;
let _4star = yourRatingData.filter(r=>r.rating==4).length;
let _3star = yourRatingData.filter(r=>r.rating==3).length;
let _2star = yourRatingData.filter(r=>r.rating==2).length;
let _1star = yourRatingData.filter(r=>r.rating==1).length;
//Sum of individual star.
let sumOfRating = parseInt( _5star + _4star + _3star + _2star + _1star );
//Total number of rating
let overallRating = parseInt( 5*_5star + 4*_4star + 3*_3star + 2*_2star +1*_1star );
//Average of all rating
let averageRating = parseFloat(overallRating/sumOfRating);
//Percentage of each star rating
let _5starPercentage = parseInt((_5star/totalRating)*100);
let _4starPercentage = parseInt((_4star/totalRating)*100);
let _3starPercentage = parseInt((_3star/totalRating)*100);
let _2starPercentage = parseInt((_2star/totalRating)*100);
let _1starPercentage = parseInt((_1star/totalRating)*100);
I think it's helpful.

Answer 11

This is an example method using flutter,
double starRating = 5.0;
getRating() {
// ! Check Already Accepted by others or Not -----------------------------------
//
int totalof5s = 0;
int totalof4s = 0;
int totalof3s = 0;
int totalof2s = 0;
int totalof1s = 0;
//
FirebaseFirestore.instance
.collection('usersRating')
.where("passengerUid", isEqualTo: "GNblJJJsjicaA2vkXJNJ6XCAiwa2")
.snapshots()
.forEach((querySnapshot) {
if (querySnapshot.size > 0) {
querySnapshot.docs.forEach((element) async {
if (element["rating"] == 5) {
totalof5s++;
} else if (element["rating"] == 4) {
totalof4s++;
} else if (element["rating"] == 3) {
totalof3s++;
} else if (element["rating"] == 2) {
totalof2s++;
} else if (element["rating"] == 1) {
totalof1s++;
}
//
if (this.mounted) {
setState(() {
starRating = (5 * totalof5s +
4 * totalof4s +
3 * totalof3s +
2 * totalof2s +
1 * totalof1s) /
(totalof5s + totalof4s + totalof3s + totalof2s + totalof1s);
});
}
});
} else {
// This is default one in any case these user doesn't have any rating document exists
if (this.mounted) {
setState(() {
starRating = 5.0;
});
}
}
});
}

Answer 12

(Total nunber of star / total number of persons who review * 5 ) * 5
= Answer
Fixed decimals in js to 1.
answer.toFixed(1);
Example the total reviews of 5 person is 20 star.
(20/5*5)*5 = 4.0

Answer 13

I used this way to calculate ratings and it is working perfectly
let one_star = 0;
let two_star = 0;
let three_star = 0;
let four_star = 0;
let five_star = 0;
Object.values(reviews).forEach(({ rating }) => {
switch (rating) {
case 1: one_star++; break;
case 2: two_star++; break;
case 3: three_star++; break;
case 4: four_star++; break;
case 5: five_star++; break;
}
});
let sum = one_star + two_star + three_star + four_star + five_star;
let average = ((5 * five_star) + (4 * four_star) + (3 * three_star) + (2 * two_star) + (1 * one_star)) / (sum);
console.log(average);