Presenting 5-point Likert scale data as a percentage, rather than an average I'm working on a project that uses mostly descriptive statistics to show how satisfied people who visit police services are with the services at any particular station. The consumers aren't very savvy with statistics, so it's a challenge to present this data (think the police chief of a developing country).
Here I'm limited to descriptive statistics. Now, and in this case usually, I'd just take this 'very satisfied' to 'very dissatisfied' data and show a breakdown bar and the final score of all the data and average it on a 5-point scale (e.g. 4.25/5). However, the company I'm working for has been basically taking that data and putting it on a 100% scale because that's the only scale they've found that the audience can understand. 4.25/5 doesn't make sense to them, but apparently 85% out of 100% does.
My concern is... how they are interpreting this data (are they secretly interpreting it as a school grade because it's a scale they're familiar with?) and part of me wonders if it's valid methodologically to put 1/5 as 0% score and 5/5 as 100%. Any thoughts on these questions?
 A: "Methodologically" it doesn't make a difference, because more or less whatever method is applied to these data will give you equivalent results, whether you code it between 1 and 5 or between 0% and 100%. 
There is some controversy around whether Likert scales can be analysed as quantitative (more precisely: interval scaled) data or whether only methods for ordinal data (such as medians) should be applied, but even then it doesn't make a difference how the levels are coded. If you compute averages of the original values, you have already chosen to treat them as quantitative, so the issue has nothing to do with whether percentage scaling is used.
I think what you really want to know is not a "methodological" issue but rather a psychological one: Will the percentage scale give some people inappropriate ideas about what these values mean? I can't address that because this is really not an issue for a statistician. However, I doubt it will make a big difference.   
A: According to 
https://www.ibm.com/support/pages/node/422073
to transform a score of x on Likert scale for which the minimum is a and the maximum is b to a Likert scale with min=A and Max=B, we should use the formula
Y = (B - A) * (x - a) / (b - a) + A
In your example, x = 4.5, a = 1, b = 5, A = 0, B = 100.
Thus 4.5 corresponds to 
Y = 0 + (100-0)(4.5-1)/(5-1) = 350/4 = 87.5 
