## weighted averages in groups with common range

I am doing a survey of questions grouped into categories. Each question has a weight applied to it. I want to then total and average each category. Lastly, I want to total and average all the categories together. Here's the challenge: I want all of categories and the total average to have the same range somehow.

See attachment (png file) for a pic of the data I mocked up to describe my situation.

The answers are a range of 1-5 (likert scale). So as you can see in the picture, the group ranges are 1-5, 1.45-7.25, and 1.90-9.50 respectively. However, the group is a completely different range 1.45-7.25. This is naturally happening because of the different weights on the questions. My end goal here is to give an average score for each category and the total score at the end similar to a FICO score. So the ranges must be the same for them to have the same effect. How can I do this with these weights in the mix?
Attached Thumbnails

 I just had a thought. Would it work if I made all of the weights in the category equal 1 (100%)?
 Scratch that, not it.

Recognitions:
Homework Help
 This seems to work pretty well. However, it does not seem to scale if I change the range. Is there a way to make the "grade" the same based on the range? Range = 1000-200 CategoryA Score = 504.2 Percentage Grade = 59.9% Range = 850-300 CategoryA Score = 509.14 Percentage Grade = 50.4% Excel formula =((AVERAGE(J6:J16)-D17)*($B$1-$B$2)/(E17-D17)+$B$2) 504.20=(2.7273-1.0667)*(1000-200)/(5.4091-1.0667)+200 509.14=(2.7273-1.0667)*(850-300)/(5.4091-1.0667)+300 Entry Weight Score 1 1.2 1.2 2 1.3 2.6 3 1 3 4 1 4 5 1 5 1 1 1 2 1.1 2.2 3 1 3 4 1.2 4.8 1 1 1 2 1.1 2.2