Assume a population of 10 students take an exam resulting in

Assume a population of 10 students take an exam resulting in a high, low, and mean score of 75. What is the standard deviation of final exam grades?   (N= number of students, x = each observed final grade)   Explain.

Solution

Since highest, lowest and mean coincide at point 75, all 10 students must have scored 75. Thus, the deviations from mean are all zero, and finally the standard deviation is zero.