Expert: Chanda Walker - 3/26/2009

Question
I have a series of numbers: 2,5,8,9,9,13,13.  I need to convert them to a scale of 0 to 10, so that 2 becomes 0 and each 13 becomes 10.  How would I do that? (what formula?)

Answer
Well first subtract 2 from the entire list making them:

0 3 6 7 7 11 11

Then multiply by 10/11.

The formula would be (x - 2)10/11.

Let me know if I can help further.

To answer you question about the general formula:

A simple formula is only possible if the bottom of the new range is 0.

If the bottom of the new range is something other than zero you have to do this:

1) scale the data's range to match the new range.
2) shift the range

In my formula, since the minimum was zero I could change the order.

So mathematically . . .

k = range new/range old

After you apply that, you'll have a new data min, let's call that x.
b = x - new min.

So when you know k and x, the formula is:

(data*k)-x

I'll apply this to your data:

range new = 10
range old = 11
k = 10/11

x = 2*10/11 - 0 = 20/11

(data* 10/11)- 20/11

2->0
5->30/11
etc.
13->110/11 = 10

Let me know if I can help you further.