Weighted Average and Ratings

Question

Maths isn't my strong point and I'm at a loss here.

Basically, all I need is a simple formula that will give a weighted rating on a scale of 1 to 5. If there are very few votes, they carry less influence and the rating pressess more towards the average (in this case I want it to be 3, not the average of all other ratings).

I've tried a few different bayesian implementations but these haven't worked out. I believe the graphical representation I am looking for could be shown as:

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Cheers

Answer 1

I'd do this this way

1*num(1) + 2*num(2) + 3*num(3) + 4*num(4) + 5*num(5) + A*3
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      num(1) + num(2) + num(3) + num(4) + num(5) + A

Where num(i) is number of votes for i.
A is a parameter. I can't tell You exact value of it. It depends on what do You mean by "few votes". In general high value of A means that You need many votes to get average different than 3, low value of A means You need few votes to get different value than 3.

If You consider 5 as "few votes" then You can take A=5.

In this solution I just assume that each product starts with A votes for 3 instead of no votes.

Hope it helps.