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Let's say we're given a set of 10 length and width measurements (with slight variance due to uncertainties), and we want to find the area. Should we

  1. Take the average of the length and multiply it with the average of the width

or

  1. Calculate the area 10 times and take the average of the area?

I have a feeling that it might be option 1, since it gives the best estimate of the length and width. But I do not know how to disprove option 2.

Thanks in advance!

Example Measurements: Length (cm): 10.02, 10.11, 10.08, 9.98, 9.99, 10.02, 10.11, 10.08, 9.98, 9.99

Width (cm): 4.97, 5.10, 5.06, 4.99, 4.99, 4.97, 5.10, 5.06, 4.99, 4.99

Type Definition
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1 Answers1

1

If you have 10 length measurements and 10 width measurements, and you cannot match up specific lengths with specific widths, you cannot justify preferring any particular 10 combinations out of the 100 possible combinations. So you average the 100 possible products, which is the same as multiplying the average length and the average width.

Peter
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