First: your calculation (which is un average or just average) has a typo: you have 19562 '4' ratings, but you must have 1562 . Fixing this gives ~ 8.17, which is rounded to the same value as the average value of IMDB arithmetic.
Then, if you want a weighted average, you need to weigh something! So, for example, if users have a βreputationβ or similar (at least the duration of the time registration), you can use this as a multiplier for the weight of your rating. At the end, divide by the sum of the weights, not the total number of votes, and you have a weighted average.
It will probably take some kind of scaling factor for the weight - for example, if SO did something similar, it might be a little unfair to John Skeet to carry two hundred thousand times the weight of the registered new user opinion :)
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