Likert scale categories and composite scores I have used the following Likert scale for a series of questions in a survey:


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*$0=$ Not Important 

*$1=$ Slightly Important 

*$2=$ Moderately Important 

*$3=$ Very Important 

*$4=$ Extremely Important


As I understand it, this is a 5-point Likert scale. (Unsure, though!)
I have then used a weighting formula that has resulted in final (composite) scores as follows: $0.2, 1.4, 2.3, 3.4, 4.6$, etc.
Example: If a person has indicated "moderately important" to three questions, it is $2+2+2=6$. I have then multiplied $6$ by a constant, e.g. $6\times.33=1.98$. The constant is derived from theory and represents percentage contribution of a variable.
Questions: 


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*How do I represent the composite scores on the above Likert scale (i.e. what does a score of $1.98$ mean?)

*Is it possible for composite scores to be greater than the last category, e.g. if a person has chosen "extremely important" for four questions, is it $(4 + 4 + 4 + 4 = 16)\times.33=5.28$?

*When we talk about a 5-point Likert scale, do we mean the distance between the response categories (e.g. between $0$ and $1$ or $1$ and $2$ on the above scale), or just the category numbers (e.g. $0, 1, 2, 3, 4$)?

 A: Regarding your question about the composite score being greater than the last category, I think it is important to differentiate between the outcome space of your items (in this case 0 to 4) and your "scale".
In the case of your example, the procedure for aggregating the scores is producing a 'scale' that goes from 0 (when a person answers the four questions as 0,0,0,0) and 5.28 (when the answers to the questions are 4,4,4,4). [Note: I noticed that your questions indicates that you are aggregating answers across persons. I am not sure about the context of your analysis, but usually Likert scales are aggregated within subjects.]
In sum, the outcomes in the questions need not coincide with the scale that is created by aggregating them, however, this might make the interpretation of the aggregated scale more difficult. As a final note, it is worth considering that you are assuming that there is an equal spacing between the response categories, not a trivial assumption, and the aggregation method that you are using assumes this interval scale in the response categories.
