weighted averages in groups with common range

First post so here goes...

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.

Group | Question | Weight | Low Score | High Score | Low End | High End | Group Low | Group High |

A | 1 | 1.1 | 1 | 5 | 1.1 | 5.5 | | |

| 2 | 0.9 | 1 | 5 | 0.09 | 4.5 | 1.00 | 5.00 |

B | 3 | 1.5 | 1 | 5 | 1.5 | 7.5 | | |

| 4 | 1.4 | 1 | 5 | 1.4 | 7 | 1.45 | 7.25 |

C | 5 | 1.7 | 1 | 5 | 1.7 | 8.5 | | |

| 6 | 2.1 | 1 | 5 | 2.1 | 10.5 | 1.90 | 9.50 |

| | | | | | | | |

| | | | | | TOTAL AVG | 1.45 | 7.25 |

The answers are a range of 1-5 (likert scale). So as you can see above, 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?

Re: weighted averages in groups with common range

I just had a thought. Would it work if I made all of the weights in the category equal 1 (100%)?

Re: weighted averages in groups with common range