Dear Dr. Jochen and Behnam,

Thank you so much for the advice.

Thank you

In this case (sum = 4, mean = 1), if you don't allow negative numbers, your sd will be constrained. It could be 0, for (1, 1, 1, 1) or up to 2, for (0, 0, 0, 4).

If you allow for negative numbers, then sd be as large as you want.

Dear Prof. Salvatore and Dr. Jochen,

Thank you so much. Dear Prof. Salvatore, if the SD is zero than the scoring gets zero when i put into the formula that i have for scoring system. What could be done to have less effect on the scores or how to avoid scoring zero when SD is zero.

Thank you

Of course, I don't know your scoring system formula, so I don't know how to answer the question. 

Knowing only the mean and sum --- and putting additional constraints, like that the numbers can't be negative --- I think the best you could do is put the high and low values for sd in to the formula, and report a range of results.  E.g. "sd=0 gives a score of 0, while sd=2 gives a score of X."