Assume that there two people working in a call centre: PersonA and PersonB.
They are both waiting for calls in separate locations.
I want to calculate the average amount of time spent waiting overall.
The scenario is this:
PersonA spends 50 minutes out of 100 (50.00%) waiting for calls to come in (the other 50 minutes were spent on calls).
PersonB spends 900 minutes out of 1000 (90.00%) waiting for calls to come in (the other 100 minutes were spent on calls).
My question is this: what is the correct way to calculate the average waiting time across both people?
Should I take an average of their respective time-spent-waiting percentages or should I take into account their collective total available time when working this out?
I have tried taking the average of PersonA's and PersonB's time-spent-waiting percentages, which seems plausible:
AVERAGE(0.5, 0.9) = 0.7 (70.00%)
I understand this to mean that, on average, the time spent waiting was 70.00% across both people.
But then, taking into consideration PersonA and PersonB's total available times when calculating this also seems plausible:
950 minutes (waiting) / 1100 minutes (total available time) = 86.36%
Which I understand to mean that, out of 1100 minutes of total availability, the average amount of time spent waiting across both people was 86.36%.
What is the difference, and which is the correct way to calculate this in this scenario (and why)?
You need to average over the same time interval. Take the time interval to be 1000 minutes. A spends 50% of that, 500 minutes, waiting. B spends 90% of that, 900 minutes, waiting. They spend a total of 500+ 900= 1400 minutes waiting out of a total of 2000 minutes. Together they average 1400/2000= .7 or 70% of their time waiting. That is, of course, exactly the same as (50+ 90)/2= 70 since the "base" in both cases is the same- time. Your second calculation is wrong because you used different time intervals.