SOLUTION: In a class of 25 students, 24 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 24 exams and found an aver

Question 1132785: In a class of 25 students, 24 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 24 exams and found an average score of 74 points with a standard deviation of 8.9 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?
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?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The total is average*n, so the total for 24 is 74*24=1776
the 25th students's score adds to 1776 to get 1840. Now divide by 25 to get 73.60. The average decreases.
The score for the last student's test is 10 fewer than the average, and still 9.6 fewer than the new average. That will increase the standard deviation.

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