Slightly more efficient, I suspect:

f[n_]:=Mean /@ Partition[RandomChoice[data, 7 n], 7]

Also note (!) the distinction that this needs to be RandomChoice rather than RandomSample. RandomChoice allows random selection from the list of data without using any of the data more than once. RandomSample allows for choosing a random datum more than once. I assume that this is actually what you want.

If you actually want RandomSample then the original approach posted above by Melvyn would be better, but the lenght of data must be greater than or equal to 7.

Thank you!

Right you are! I think the coffee hadn't kicked in yet. But the code is right ;-) (I an often code in Mathematica before I can speak sensibly....)

See my comment below about the difference between RandomSample and RandomChoice... it's an important distinction that you need to make to be sure you are calculating what you intend.