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Thread: 5 star rating

  1. MHB Apprentice

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    #1
    Hello guys I was going to ask a question regarding 5 star ratings its a hard one for me but it could be simple for you guys here it is,

    I've got 1115 ratings ( 5 star max 1 lowest )

    * What I know so far is my total rating is 4.80
    * 696 of these are 5 star ratings
    * some of the 1115 have not rated not sure how many but not too many 100-150 max i'd say

    Questions, how many 5* ratings would I need to get rating up by 0.01 my aim is 4.85 rating or 4.9 to make it easier I just want a estimate to figure out where i'am

    thanks

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    #2
    Quote Originally Posted by loso6699 View Post
    Hello guys I was going to ask a question regarding 5 star ratings its a hard one for me but it could be simple for you guys here it is,

    I've got 1115 ratings ( 5 star max 1 lowest )

    * What I know so far is my total rating is 4.80
    * 696 of these are 5 star ratings
    * some of the 1115 have not rated not sure how many but not too many 100-150 max i'd say

    Questions, how many 5* ratings would I need to get rating up by 0.01 my aim is 4.85 rating or 4.9 to make it easier I just want a estimate to figure out where i'am

    thanks
    Hi loso6699! Welcome to MHB!

    Suppose we have $N$ actual votes $x_i$ where $i=1..N$.
    So $N \le 1115$.
    Then the rating is:
    $$\text{rating} = x_{average} = \frac {\displaystyle\sum_{i=1}^N x_i}N = 4.80$$
    It follows that the sum of all actual votes is:
    $$\sum_{i=1}^N x_i = 4.80 N$$

    Now suppose we add $n$ extra votes of $5$ stars.
    Then the new rating will be:
    $$\frac {\displaystyle\sum_{i=1}^N x_i + 5n}{N+n} = \frac {4.80 N + 5n}{N+n} = 4.81 \quad\Rightarrow\quad
    4.80 N + 5n = 4.81(N+n) \quad\Rightarrow\quad
    (5 - 4.81)n = (4.81-4.80)N $$
    So:
    $$n = \frac{0.01 N}{5-4.81} \le \frac{0.01 \cdot 1115}{5-4.81} = 58.7
    $$
    That means that with 59 extra votes of 5 stars, the rating is guaranteed to go up by 0.01.

    If the actual votes was, say, 100 less, then we can do the same calculation with $1015$ instead of $1115$.
    And if we want to go up by $0.05$, we can replace $0.01$ and $4.81$ by $0.05$ respectively $4.85$.

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