How Many Will Raise the Rating?

Probability Level 3

A manga series that I enjoy has a rating of 7.5 on a site called MyAnimeList. If 2796 users have rated it, what is the minimum number of additional people who need to rate it, in order to get an average rating of at least 8?

Note: The maximum rating one can give is 10. The minimum rating one can give is 1 .

The answer is 699.

1 solution

Feathery Studio
Jul 1, 2015

Let $x$ represent the sum of all the user ratings. Then $\frac{x}{2796} = 7.5$ , $x = 20970$ . If we want the minimum amount of people, then each person must give the highest rating possible, which is $10$ . Now, let $n$ represent the number of users who rated the series $10$ . Then $\frac{20970 + 10n}{2796 + n} = 8$ . Solving the equation... we find $n = \boxed{699}$ .

Awesome! That's how I did it too.

Mohammad Saleem - 5 years, 11 months ago

I used an excell spreadsheet to calculate the average rating rounding to the nearest .1 (which is how the algorithm would work on the site itself,) to determine a minimum value of 615.

Jonathan Sciance - 5 years, 9 months ago

I thought: "Hmm, the best way to get to 8 with the least amount of people is probably for them to rate a 10 right?" So I decided that we just need to go backwards. How I Did It Note that this is basically a "How to Calculate Average" question.

Mohammad Saleem - 5 years, 8 months ago

How Many Will Raise the Rating?

The answer is 699.

1 solution

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