i am looking for a theorem to state if exists any for the following problem.
I have 4 different groups of different sizes with smokers and non smokers and I have calcualted relative frequencies for smokers in each group.
I combined four groups into one and calculated relative frequencies.
Now the question: are the average of realtive frequencies of 1 and relative frequenices of 2 the same?
If yes, which theorem explains that?