Question

A section of an Introduction to Psychology class took an exam under a set of unusual circumstances. The class took the exam in the usual classroom, but heavy construction noise was present throughout the exam. For all previous exams using the same format and same questions, student scores were normally distributed with a mean of µ = 75.00 and a population standard deviation (sigma) = 10.50. To understand the possible effects of the construction noise, you have been asked to perform a number of statistical procedures for the following sample of exam scores obtained during the construction noise:

Construction Noise Exam Scores

57 58 59 60 61 64 65 66 66 67 67 68

68 69 69 70 70 70 70 71 72 72 72 72

72 73 75 77 78 81 82 83 84 88 96 100

What is the sum of squared deviations (SS) of the sample?

Answer 1

$\bar x$ = (57 + 58 + 59 + 60 + 61 + 64 + 65 + 66 + 66 + 67 + 67 + 68 + 68 + 69 + 69 + 70 + 70 + 70 + 70 + 71 + 72 + 72 + 72 + 72 + 72 + 73 + 75 + 77 + 78 + 81 + 82 + 83 + 84 + 88 + 96 + 100)/36 = 72

SS = (57 - 72)^2 + (58 - 72)^2 + (59 - 72)^2 + (60 - 72)^2 + (61 - 72)^2 + (64 - 72)^2 + (65 - 72)^2 + (66 - 72)^2 + (66 - 72)^2 + (67 - 72)^2 + (67 - 72)^2 + (68 - 72)^2 + (68 - 72)^2 + (69 - 72)^2 + (69 - 72)^2 + (70 - 72)^2 + (70 - 72)^2 + (70 - 72)^2 + (70 - 72)^2 + (71 - 72)^2 + (72 - 72)^2 + (72 - 72)^2 + (72 - 72)^2 + (72 - 72)^2 + (72 - 72)^2 + (73 - 72)^2 + (75 - 72)^2 + (77 - 72)^2 + (78 - 72)^2 + (81 - 72)^2 + (82 - 72)^2 + (83 - 72)^2 + (84 - 72)^2 + (88 - 72)^2 + (96 - 72)^2 + (100 - 72)^2 = 3290