If you consider the definition of mean for a continuous variable you can see that you can indeed break up the operations into different partitions of the data t

If you consider the definition of mean for a continuous variable you can see that you can indeed break up the operations into different partitions of the data then add them up. The weight in continuous case is explicit while for discrete case it is sometimes implicit (1/N). When I think Simpson’s paradox I think of regressions. It is indeed true that if you do regression on half your data and then regression on the other half, you won’t get the same result as doing regression on the full data.