# is my concept of averaging averages under this scenario wrong?

I'm confused on the concept of whether or not to average the averages under this scenario, when the data relating to a particular technique are collected 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. ( Fraction is just terms in radiotherapy, you can interpret it as no. of treatment. In the example, patient 1,2 and 3 has a radiotherapy course of 3 fractions , 4 fractions and 5 fractions respectively.) 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?

• What do you mean by "fraction" in this context? – gung - Reinstate Monica Feb 11 '17 at 18:48
• Fraction is just terms in radiotherapy, you can interpret it as no. of treatment. In the example, patient 1,2 and 3 has a radiotherapy course of 3 fractions , 4 fractions and 5 fractions respectively. – stat newbie L Feb 12 '17 at 1:29