I have some data and need to know the average commission of all the items. For each row, I calculate the percent of items sent out. If I wanted to know, "What is the average commission", which is correct, $14.96$% or $12.89$%?
Item Cost Revenue Commission
1,000 289 28.90%
2,991 190 6.35%
10,400 1,050 10.10%
20,000 2,900 14.50%
Totals 34,391 4,429 **14.96%**
The $14.96$% is calculated in Excel with:
=AVERAGE(28.90%, 6.35%, 10.10%, 14.50%)
(Is this called an average of percents? Not sure what to call this).
Now, if I do 4429 / 34391 I get $12.88$%. Which average do I "want" to use to answer, "What's the average commission?" I think the SUM(Revenue) / SUM(Item Cost) is what I want, not the average of the percentages calculated, but don't know even what terms to use to look up what the difference is, or when to use one over the other. For the former, AVERAGE(), since that adds the percentages together, then divides by $4$, I don't think that is accurate for my purposes.
12.88. ...but now that I think about it, is there a way to phrase both? This is where my stats semantics fail me, "The overall average commission is 12.88. The average of commissions is 14.96". Does that make sense from a stats/maths point of view? ...let me keep thinking of how to clarify. $\endgroup$