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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.

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    $\begingroup$ Welcome to Cross Validated! What do you want to know? What do you want to learn from this calculation? How will you use this calculation? The answers to questions like those will guide you toward the correct calculation. Under most circumstances, I would go with the $12.88\%,$ but maybe there is a reason to go with $14.96\%.$ $\endgroup$ Commented Feb 14, 2024 at 20:51
  • $\begingroup$ @Dave - I'm not trying to be thick/difficult, but it's just to answer the question "What is the average commission". Since we are curious from a business standpoint what our average commission is, I think I want the 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. $\endgroup$ Commented Feb 14, 2024 at 21:46
  • $\begingroup$ But why do you want to know that number? $\endgroup$ Commented Feb 14, 2024 at 21:54

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