Out of a class of 25 students, 24 took an exam in class and got a mean of 74 points and a standard deviation of 6.9 points. a) What would the last student have to get on the exam to raise the mean to 75 points? If the last student scored a 64, would you expect the mean to increase or decrease (without computing). Explain. b) c) If the last student scored a 64, would you expect the standard deviation to increase or decrease (without computing). Explain. d) If the last student scored a 64, what is the new mean?

Given: Total number of students, n = 25

           Number of students who gave the test, n' = 24

           Mean score of 24 students, M' = 74

          SD of 24 students, s' = 6.9

          Total score of 24 students, T' = n'$\times$M' = 24$\times$74 = 1776

Part a:  Let x be the last student's score such that the mean score of 25 students become, M = 75. Then

           The total score of 25 students = Total score of 24 students + x

=>                                           n$\times$M   = n'$\times$M' + x

=>                                          25$\times$75 = 1776 + x

=>                                                    x = 1875 - 1776

=>                                                    x = 99

Therefore, the last student must score 99 points so that the mean score increase to 75.

Part b: If the last student scored 64, then the mean score may decrease because 64 is quite a low score as compared to 99, required to increase the mean score.

Part c: If the last student score 64, the standard deviation may decrease or may remain the same because the number of observations will increase and the sum of the squares of the deviations will increase.