So a game gets ratings like this:
5 star............9 reviews
4 star............1 review
3 star............1 review
2 star............2 review
1 star............5 reviews


GoG considers this as an average rating of 4.5 stars..................can anyone explain me what kind of math is GoG using?

The one that doesn't ignore ratings.

You can rate a game you own without writing a review, thus ratings =/= reviews.

You can even rate a game that you don't own, and Lord knows many people rate (and sometimes "review") games which they've never played.

lol look at the 'review' by johnathanamz on Offworld Trading Company, and the one on Tempest by a random who is just criticising GOG.
If people take reviews and ratings seriously, then they need help.