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I have two ways to calculate the average starting price of an auction item compared to it's actual value.

Starting Value    Actual Value    Percent
--------------    ------------    -------
1                 2               50%
2                 3               66%
3                 4               75%
4                 5               80%
5                 6               83%
6                 7               86%
7                 8               88%
8                 9               89%
9                 10              90%

My question: which is the average starting price of the items as a percent?

SUM(start_values) / SUM(actual_values)

or

AVG(percent_value)

In this case, the difference is between 85% and 79%, which is sizable.

Which calculation will be most useful way to express the average starting price of all items, expressed as a percentage? We're having some debate here at work on the matter, and would like someone to set the record straight for us.

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1  
Both are things you can calculate. Neither is in and of itself more or less correct than the other. The pertinent question is not which of the calculations is "mathematically correct", but which calculation will be most useful for whatever it is your eventual purpose is. –  Henning Makholm Jun 28 '12 at 13:53
    
I'll edit the question. –  Droogans Jun 28 '12 at 13:54

1 Answer 1

Henning Makholm's point is that useful is in the eye of the beholder. What use are you going to make of the number? It sounds like you want to estimate the final selling price based on the starting value. There might be dependences you are ignoring so far. For example, the percentage between starting price and selling price might depend upon the starting price. Maybe things which start at $1$ end up at $3 \pm 1$, while those that start at $10$ end at $17 \pm 2$. Or maybe the relationship depends on the day of the week the auction starts. If that is the purpose, you need to collect and study the data, make your model (which may involve this sort of averaging), and (preferably) test against new data.

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