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I have N orders. Each order consist of x units and I know the total cost of each order. If I would like to determine the mean cost per unit do I use approach 1 or 2 listed as follows:

(1) Determine total number of orders X and total cost of all orders Y. Then divide Y by X to determine the cost per unit.

(2) For each order divide the order cost by the number of units of the order resulting in X1. Then take the mean of X1.

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  • $\begingroup$ Why not decide yourself? For instance, suppose you have just two orders: one for one unit at $\$100$ and another for $100$ units at $\$100$. You have thereby sold $101$ units for $\$200$. Do you want to use the average cost per unit of $(100/1+100/100)/2=\$50.5$ or $200/101 \approx \$2$? They are both perfectly fine but they mean different things. $\endgroup$
    – whuber
    Jan 7, 2016 at 21:44
  • $\begingroup$ Sorry but what's the difference in meaning? I would like to know how much I have to pay on average per unit given all orders/samples. $\endgroup$
    – cs0815
    Jan 7, 2016 at 21:58
  • $\begingroup$ I constructed this hypothetical scenario to help make the answer obvious: would you have paid $\$50$ per unit or $\$2$ per unit on average? $\endgroup$
    – whuber
    Jan 7, 2016 at 22:28
  • $\begingroup$ I understand. Your example is more an outlier situation. I think 2 is more appropriated for my scenario as i would like to know how much a unit costs per order on average. See also answer by Dirk Horsten $\endgroup$
    – cs0815
    Jan 7, 2016 at 22:49

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Only the first calculation gives you the mean cost per unit. The second gives you the the mean unit cost per order. That is a completely different question.

Let me explain this further. Suppose you buy lettuce for a grocery chain. You have always had two suppliers from which you bought equal quantities, but now you want to keep only one in the future: the cheapest one. You can expect the price AND consumption of lettuces to vary next year as it did last year, so seasonal variations will play the same roll in the future. Then you need the the average price per lettuce, i.e. your first calculation.

On the other hand, suppose you plan opening a furniture studio that will need a tons of wood per day and you want to forecast what you will pay on wood. Suppose in the past you accidentally bought some wood, sometimes more sometimes less, and you know there were some seasonal differences in the price. Now you are not interested in the average price you have paid. If you were lucky to have bought your largest quantity when wood was cheep, this should not bring your estimate down. So now you average the unit price over the orders. That's your second approach.

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  • $\begingroup$ Great answer! Just shows that my question makes sense! $\endgroup$
    – cs0815
    Jan 8, 2016 at 7:01

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