Six students in a small class took an exam. The average of their grades was . The seventh student in the class was ill that day and took the exam another day. When this student’s score was included, the class average rose to . What was the seventh student’s score?
Source: NCTM Mathematics Teacher, February 2006
Imagine without loss of generality that the six students’ scores are near the average of , that is, some scores are below and some above but they don’t deviate too much from it. Let’s further assume that the six scores area as follows with the amount above or below shown in parentheses
By a property of average, the amounts above and below the average sum to zero
When the seventh student took the exam, the average shoots up to . The seven students’ scores are listed again below but now compared to the new average
, the seventh student score
The amounts above and below the average sum to zero
Score of seventh student equals .