How do you spread a set of numbers out proportionally from the mean?

Question

I graded my students' listening test, but all the scores are too close to each other. How do I spread them out proportionally to accurately reflect the difference between the better and worse students? Please give me the math I need to use. Thank you.

Answer 1

You can spread the results out but it won't change anything. The results have no way of knowing what the actual difference between your best and worst students is.

I see lots of graphs where the origin has been shifted to emphasise small differences. The graphs can be quite dramatic and show a 'clear' winner, but in reality the difference might be between 990, 987, and 992 which is no difference at all!

Why don't you list the anonymous scores?

Answer 2

If the data are so close that you cannot separate them into 10 intervals, grading "on the curve" may well be inappropriate. For instance, if top score is 100 and you can make 10 intervals with μ = 95, and σ ≈ 1.35, all or 95% of your students would deserve an A, even with a "perfect " bell curve distribution.

The usual way of setting up your histogram is to take (max value - min value) / 10 = interval

Answer 3

If you have EXCEL it will be easy!
Put each score in a column
In the next column subtract the mean from each
Looking at the largest differences, what would you like them to be?
Say at the moment it is 6 and you would like it to be 10 (say this is col B)
Go to the largest one in the 3rd column and type '= Col B/6 *10 and you will see your largest one now says 10 in col C
Repeat the above formula for all scores
In next col add back in the mean and you are there!