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I have two sets of ranked data which are ranked on different scales, one fixed and one variable, and I would like to convert one of the data sets ranking values to match the other.

Set 1 is ranked 10 - 1 with 10 being the highest rank. Set 2 is ranked 1 - x with 1 being the highest rank and x being the number of items in the set.

Is it possible to convert the ranking of set 2 to fit into set 1?

Thanks, Phil

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Not everything involving sets is set-theory, just like not everything that has the capital letter K involved is K-theory. – Asaf Karagila Jan 18 '11 at 14:52
This isn't my subject area so didn't really know which category this fit into. Apologies if it caused confusion. – philb0 Jan 18 '11 at 16:24

You can take the rank of an item of rank $r_1$ in set 1 and set $r_2=\frac{(x-1)(10-r_1)}{9}+1$. This will linearly map the set 1 ranks into the range of set 2. Is this what you are looking for?

This presumes that the items in the two sets should be "evenly mixed", which may not be what you want. Maybe all the items of set 1 should be ranked above all the items in set 2. It also runs the risk of having two items with the same rank, particularly 1 and x.

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