What Does Mathematical Mean
Instead of defining a relation and checking its functionality we just write it down as if we knew it was a function and check whether everything makes. In mathematical jargon that developed long before our current understanding of functions as sets of pairs we refer to a relation whose being a function requires a proof as well-defined.
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So what we see is that you certainly can calculate the mean of the means but the mean of the means and the mean of all the raw data dont match.
What does mathematical mean. We can also try a weighted average using BilltheLizards suggestion to use each groups sample size as a weight the weights are indicated with the w argument.
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