Suppose we have a test consisting of 30 questions, and 10 people take this test. The mean test score of these 10 people is 17, and the standard deviation of all the scores in the sample is 4. When reporting the descriptive statistics at school, we use these raw scores and write (M=17, SD=4); but in some cases I have the feeling that reporting percentages would be better. Because I think that we have a more intuitive grasp of what it means to score 56.7 over 100 than to score 17 over 30 (probably because we are accustomed to the decimal system).
So, for the example given above, would it be possible to report the mean and standard deviation as (M=56.7%, SD=13.3%)?
Does it make sense to say that the exam scores in a sample have the standard deviation of 13.3%?
These percentages are the arithmetic equivalent of the raw scores I made up and given above, but I am not sure whether it is good practice to directly convert them into percentages like that.