How many votes do i need to changea percentage? I got an app with a 4.4631 rating after 176 reviews. Every user can review it and rate it from 1 to 5 points. How many 5 points reviews do i need to reach 4.6 and then 4.7? 
I've googled about percentage change but I don't understand how it relates to my problem. Please help.
 A: The rating of $4.4631$ is the average of the $176$ individual ratings, so the app must have received a total of about $4.4631\cdot176=785.5056$ points from users. This probably represents an actual total of $785.5$ rating points, the $0.0056$ being the result of rounding $\frac{785.5}{176}$ to four decimal places. There is no way to get $4.4631$ from $176$ users if ratings have to be integers, so it appears that half-point ratings are possible.
Suppose that you now get $n$ $5$-point ratings and nothing lower. You will then have a total of $785.5+5n$ rating points from $176+n$ users, so your average will be
$$\frac{785.5+5n}{176+n}\;,$$
and you want that to be at least $4.6$. Set it equal to $4.6$ and solve for $n$: if
$$\frac{785.5+5n}{176+n}=4.6\;,\tag{1}$$
then 
$$785.5+5n=4.6(176+n)=809.6+4.6n\;,$$
so $0.4n=24.1$, and 
$$n=\frac{24.1}{0.4}=60.25\;.$$
You can’t actually get $60.25$ ratings, so you need $61$ ratings of $5$ with nothing lower in order to reach $4.6$, and that actually gives you
$$\frac{785.5+5\cdot61}{176+61}\approx4.6013\;,$$
rounded to four decimal places. Replacing $4.6$ with $4.7$ in equation $(1)$ and solving in the same way will give you the other desired number.
A: Well, I believe you can't do this unless you can find the exact amount of people that voted each number. Assuming you have access to that, what you could do is:


*

*Assign each rating a numerical point value, so 1 would be 20 points, 2 - 40, 3 - 60, 4 - 80, and 5 - 100

*Then multiply the number of total reviews by 100, so $176*100$, which equals 17,600

*Now, take the amount of each rating and multiply it by the corresponding point value. i.e with 25 ratings of 1, you multiply $25*20$.

*Add all the products from the last step

*Now solve for $x/17600 = y/100$, where $x$ is the sum from step 4, and $y$ is the percent out of 100 that it equals

*Once you have $y$(as a percent), do $y*5$ to get the current 4.xxxx

*Keep adding 100 to $x$ and repeat steps 5&6


I guess this really doesn't answer your question, but I provided how to do it yourself. Hope it helps!
