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Words Of Wisdom said:

Do games for each console need to have the same average score for the source to not be biased?

Not at all. A source appears biased when it's scores are badly out of synch with all other reviewers.

If  Magazine A rates PS3 games higher than the average of all other reviwers 90% of the time and the Wii lower 90% that would tend to show a bias.

If the magazine was Playstation Fanatic then that's acceptable. When it's essentially an advertisement for the largest game retailer, it is not acceptable.