Calculating an average of multiple data sets based on priority.

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First and foremost I'm no mathematician, it may be a case of over complication.

What I'm trying to do is that I have 2 sets of data, I want to calculate one average for both sets but I want the first set to have more 'influence' over the average than the second.

I.e I want an outlier in set A to swing the average more than if that outlier was in set B (If that makes any sense).

I would assume I'd need a value to deem how much of an effect each set would have.

I don't expect a specific answer but if someone could get me started/point me in the right direction I'd be grateful.

Cheers.