How do I compute a double weighted average? In other words, an average with two weighting factors.

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This might be a simple question...

I was wondering, how does one take a double weighted average? (honestly, don't know if that is what it is called). For example, let's say that we are working with data from the table below:

Cellphone type | # of phones sold | # of hours spent on design | Profit
-------------- ---------------- --------------------------- ------
Iphone 1,000 200 $30K
Samsung 3,000 150 $40K
HTC 7,000 140 $35K

1) I know that the simple average of the profit is: $35K

2) I also know that the average weighed by # of phones sold is: $35.9091K

3) And, that the average weighted by # of hours spent on design is $34.4898K

Now, what is the profit average weighted by # of phones sold and # of hours spent on design? Is it a simple average between 2 and 3?

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1 Answer

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You can't do this without further information. The second weighted average should be weighted with respect to how important the metrics are to you - perhaps you care twice as much about # of hours than # of sales. In that case you would do

$$ave= 2[\text{weighted by hours worked}]+1[\text{weighted by sales}]$$

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