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Basic Math/Average Annual Rate?

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Question
Ok, I am a librarian and I like to run analysis of the print books in my library annually to determine what sections are being used well and what sections may need improvement. One of the things I look at is Average Annual Circulation as opposed to just looking at “raw” absolute total circulation. The average annual circulation is the number of circulations (i.e., checkouts) that a given item or collection averages per year.

Here is an example of what I mean:

Book A has circulated 20 times (raw circulation) in ten years on the shelf. Which means it has an Average Annual Circulation of 2 (20 circs/ 10 years).

Now where I run into trouble is doing this calculation for items that have been on the shelf for less than a complete year.

Book B has circulated 3 times in a quarter of a year on the shelf. When I run the same calculation for Book B for Average Annual Circulation I get 16 (4 circs/ .25 years).

Now how can the average be higher than the absolute total? What am I missing here? Any assistance would be greatly appreciated.

Thanks,
Carl  

Answer
I think there is a typo in your book b calculations, but the reason the average is higher than the absolute is because you're extrapolating the data to fill in the full year.  Taking the average assumes that you will continue to have 3 (or 4) checkouts per quarter.  In reality, based on the first quarter, without extrapolation, the average is 3/1 because that's all the data you have.

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Lynn Houston

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