I would like to calculate an average rating score based on knowing example the final score is 9.2/10 and rated by 286 people ( example: https://foursquare.com/v/coffee-project/56054685498e21a5e4c9d5b2 ). In the example I know 286 people voted and what the final rating is, but what I want to figure out is what was the average rating of given to achieve 9.2/10?
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1$\begingroup$ If the final rating is 9.2, doesn't this imply that 9.2 is the average as well? $\endgroup$– cool.coolcoolcoolCommented Dec 29, 2016 at 20:00
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$\begingroup$ I was thinking the same thing, but some how seems too simple :/ $\endgroup$– BedfordCommented Dec 29, 2016 at 20:11
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$\begingroup$ Unless the website documents how they compute the final score you have no hope. They could just assign a random number between $0$ and $10$. Certainly an easy thing for them to do is to assign the average as a final score. What would you rather they do? The only good reason for doing something else is that you get a more "accurate" (however you define that) value and their potential customers perceive and appreciate it, so they buy from this website instead of another. It could be the taste of the programmer. $\endgroup$– Ross MillikanCommented Jul 8 at 2:12
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In most rating systems, the final score is the average of all the ratings, so in your example, I would assume that the average rating is $9.2/10$.
It is possible that a rating system uses a different measure of central tendency. If you can identify the measure of central tendency that is being used and you have enough information, it may be possible to calculate or estimate the average rating.
Sometimes, we use even more complicated rating systems, like the Elo rating system that predicts the outcome of chess matches, but I doubt foursquare is using anything like that.
