# What is the correct way of calculating the average percentage in this scenario?

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)?

• This isn't really a math question. Both averages make sense, but they measure different things. If you are interested in getting a base line on employee efficiency, you should average the two averages. If, on the other hand, you want to get a baseline on how much wait time is involved in a call, you should look at each call. – lulu Oct 3 '18 at 12:13
• That makes sense. Also, I wondered if this belonged here or on a Stats SE site, so opted for here. – SnookerFan Oct 3 '18 at 12:15
• Oh, I think this is a fine place for it. – lulu Oct 3 '18 at 12:15
• Great. So assuming that each employee is available for a different amount of time, then is the first calculation (average of averages) the correct one to use? If so, why? – SnookerFan Oct 3 '18 at 12:34
• As I say, "correct" depends on what you are trying to measure. If I have a lot of students taking Calculus, with a lot of tests, I can compare the averages of two students, even if they have taken different numbers of tests (or different tests). Makes perfect sense. Or, if I am trying to assess how difficult my tests are, I can look at the scores on each test and average them. This also makes perfect sense, though the two averages are different. – lulu Oct 3 '18 at 12:37

## 1 Answer

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.

• So how do I get the average if the time intervals are different, like in the example? Or is this the correct way to do it (by scaling both PersonA and PersonB's available times to match)? – SnookerFan Oct 3 '18 at 12:27