How to calculate participant*hours

Question

I'm trying to calculate the number of "participant*hours" for participation in a program.

I have the following variables/data: 1) Total # of sessions given throughout the program. 2) Average duration (in hours) of each session. 3) Average # of participants in each session.

So, for example, if 84 sessions were given with a duration of 0.75 hours per session, and about 25 participants per session, what would be the proper way of calculating a figure with the units "participant*hours"?

By simple multiplication and unit cancelation, it seems the calculation should be:

Total hours = (84 sessions)*(0.75 hours / session) = 63 hours

Total # of participants = (84 sessions)*(25 participants / session) = 2,100 participants

(2,100 participants)(63 hours) = 132,300 participanthours

Is this the proper way of obtaining "participant*hours"? I ask because the figure seems very high.

Thank you in advance.

Answer 1

After digesting the feedback received and other resources, I believe the calculation that yields the correct units (i.e., "participation*hours") and makes conceptual sense is:

$$[(# participants × # hours) ∕ session]×(total # of sessions)$$

Answer 2

Your calculation of participant hours is reasonable. You don't need to worry about whether the participants in each session are the same or different. If one person comes to five sessions of 0.75 hours each, that is still $5 \cdot 0.75=3.75$ participant hours. Whether that is more or less valuable than five different people coming for $0.75$ hours each is not addressed by this statistic. As long as there were $84$ sessions, all the sessions were $0.75$ hours and the mean number of participants in each session is $25$ you are set. In this case you only have one number that varies-the number of participants. If the sessions vary enough that you care, even though the length averages $0.75$ hours, you could worry that the short sessions were more heavily attended than the long ones. If you have a correlation between length and attendance, you can't multiply the two averages. For a four session example, you might have three sessions of $0.25$ hours each and one of $2.25$ hours. The average is $0.75$ hours. Then you have only four people at the long one and $32$ at each short one. The average attendance is $25$. The number of participant hours is not 4 sessions times 0.75 hours times 25 participants, which would be 75. Instead it is $2.25\cdot 4+0.25\cdot 32=17$ This is extreme, but it shows the problem.