Question

2.27 Make-up exam: In a class of 27 students, 26 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 26 exams and found an average score of 84 points with a standard deviation of 7 points. The student who took the make-up the following day scored 64 points on the exam.

a) Does the new student's score increase or decrease the average?

• Increases
• Decreases

b) The new average is: ____  (round to two decimal places)
c) Does the new student's score increase or decrease the standard deviation of the scores?

• Decreases
• Increases

Answer 1

Solution:
Total no. of student in class = 27
Average score for 26 students = 84
One student receives score in make up exam = 64 points
Solution(a)
New Student score will decrease the avearge of the class. becasue make up exam student score is less than the average of 26 students. So this will decrease the average of the class.
Solution(b)
the new average can be calcualted as
Total scores of 26 student = 26*84 = 2184
Score of new student = 64
So new average = (2184+64)/27 = 2248/27 = 83.26
Solution(c)
the new student score is 20 points fewer than the average while 19.26 fewer than the new average so that will increase the standard deviation.