This seems like something I should be able to do but I can not for the life of me figure it out. I'm writing a program to calculate an average score; let's say that my data looks like this.
x = number of votes
y = current rating
z = new rating
Is there a way for me to calculate in the new rating, without needing the scores of each individual vote?
So say that an item has a total of two scores, the data would look like this:
x = 2
y = 90
and then a new rating is introduced (let's say someone scored a 50%):
z = 50
I need to calculate how the z would influence the 90%, without having a record of each individual rating.
Help is greatly appreciated!
Suppose that $x$ votes lead to rating of $y$. Then $xy$ is the current total score (the sum of the scores of the $x$ people). Add the new score $z$, and divide by the new number of people. So the new average is $$\frac{xy+z}{x+1}.$$
In your numerical example, we have $x=2$ and the average score is $90$. So the scores of the $2$ people add up to $(2)(90)=180$. Add the new score $50$. We get $230$. Finally, divide by $3$.
Remark: The letters $x$, $y$, and $z$ are perhaps not ideal for your problem. I would call the current number of people something like $n$ instead of $x$.