is my concept of averaging averages under this scenario wrong?

#1
hi all, I'm confused on the concept of whether or not to average the averages under this scenario, when the data collected are from different individuals:

say there are 3 patients all having radiotherapy treatment technique A. Each of them have different no. of fractions in their treatment courses. One fraction is delivered per day. Their treatment room occupancy are as follows:

patient 1: Day 1: 15 mins; Day 2 :13 mins; Day 3: 10 mins ( avg = 12.7 mins)
patient 2: Day1: 8 mins; Day2: 7 mins; Day3: 8 mins; Day4: 6 mins (avg=7.25mins)
patient 3: Day1: 12 mins; Day2: 10 mins; Day3: 8 mins; Day4: 8 mins; Day5: 9 mins (avg=9.4mins)

if i want to conclude the average treatment room occupancy per fraction of those patients receiving technique A, should i do like averaging the daily treatment room occupancy per patient and then average their averages i.e. (12.7+7.3+9.4) / 3 = 9.8 mins per fraction?

or the right way should be ignoring the fractions are from different patients and just sum all the fraction time up and get an average as a whole, getting 114mins/12fractions, so as to conclude that the average treatment room occupancy for patient using technique A is 9.5 mins per fraction?
 
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