Average Rating Calculator

The average rating calculator takes a number of votes for each rating (1 star, 2 stars, 3 stars, 4 stars, 5 stars) and gives you the mean rating. This is an example of taking the weighted average, where the number of votes for each category are weighted by their score (i.e., 3 votes for 5 stars have a weight of 15, 6 votes for 4 stars have a weight of 24, etc.).

Keep reading to learn what is the star rating system, the difference between a star classification and an average star rating, and how to calculate the star rating for any combination of votes.

The star system is a classification method that uses glyphs and symbols such as stars to visualize in a quick and intuitive way the ranking of many things, from services to purchased items, usually where a certain degree of interaction with the customers is present.

There are two principal types of star classification:

• Star rating, where a given number of stars is assigned, and the higher the number, the higher the quality. Think of the Michelin star for restaurants or hotel classifications.
• Star "voting", where many votes expressed as a number of stars are tallied to return a final rating that takes into account the opinion of many people.

We are mostly interested in the latter: in the next section, we will learn how a star rating calculator system works and how to calculate the average rating in such systems. For now, let's explore these systems a bit more!

Assigning an increasing number of symbols to describe the quality of something apparently appeared the first time in guidebooks in the first half of the 19th century (though a monk traveling in Italy in the 12th century already classified a wine as Est! Est Est!). Rather quickly, stars became the preferred symbol. By the beginning of the 20th century, hotels started receiving official star ratings.

With the onset of the internet, it became possible to gather the opinion of many customers in a quick and efficient way, which led to the popularity of average star rating systems. In these systems, the user is tasked with assigning a certain number of stars to a good or service. Once enough votes are gathered, we can show future customers the result: a number of stars that reflects the opinion of the previous customers.

But how do we calculate the average rating in such systems?

To calculate the average rating in a star rating system, we follow some simple steps:

1. We count the number of votes for each star number (number of votes for one star, number of votes for two stars, etc.).
2. We multiply the number of votes by the matching star number: this means that the number of votes for a three-star rating gets multiplied by 3.
3. We sum all these products.
4. We divide the result of the previous step by the total number of votes.

This returns a weighted average according to the formula:

where:

• $\mathrm{rating}$ — Average rating; and
• $r_1$, $r_2$, $r_3$, ... — Number of votes for each number of stars.

The formula for the average 5-star rating reads:

average rating = (5r₅ + 4r₄ + 3r₃ + 2r₂ + r₁) / (r₅ + r₄ + r₃ + r₂ + r₁)

where r_i is the number of i stars responses for i = 1, ..., 5.

To determine the average 5-star rating, you need to:

1. Gather the data: write down how many five stars you got, how many four stars, etc.

2. Add together all numbers from Step 1. This is the total number of responses.

3. Multiply the number of five stars by 5, the number of four stars by 4, etc.

4. Add together all numbers from Step 3. This is your total rating.

5. Divide the number from Step 4 by that from Step 2. This is your average rating!