A professor of a business school course has been struggling to motivate students to put some effort into the course. Frustrated, he offers them a 5 point bonus in the Final exam if they all attend a Marketing presentation to be given in school. All students attended. When entering the Final exam grades, the professor did not use separate columns for the exam result and bonus for each student. The final exam mean he gets, as a measure of average student knowledge, is inflated because of the bonus. Now, if the professor really wants to assess how much the students knew in the final exam through the average score and the actual exam average was 78, how must the actual final exam average score be adjusted to account for the bonus given to all students? 

If Xi is what each student got in the exam without the bonus then, accounting for the bonus, the mean Final score was Y̅ = Σⁿ _{i =1}(X_i + 5)/n .)