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=AVERAGEIF(range, criteria, [average_range])
In terms of range and criteria for OSU's average number of hot dogs ate per participant in cell F4, once again they'll be the same as COUNTIF and SUMIF:
=AVERAGEIF(B2:B11, "OSU", [average_range])
To compute [average_range]...
To determine your [average_range], ask yourself where the values are that you're wanting to average are.
In our case, that's once again the values in cells C2:C11!
=AVERAGEIF(B2:B11, "OSU", C2:C11)
When we plug this into cell F4, we learn that OSU participants ate an average of 16 hot dogs.

To copy this over to G4 for Michigan participants, we just need to replace "OSU" with "Michigan".
=AVERAGEIF(B2:B11, "Michigan", C2:C11)

This shows us that Michigan participants ate on average 15.5 hot dogs.