Explanation Given information: The table provided is as follows: A B C 1 Student Exam 1 ( % ) Exam 2 ( % ) 2 Michael 80 89 3 Andy 77 93 4 Pam 68 84 5 Jim 81 88 6 Dwight 96 91 7 Stanley 54 75 8 Phyllis 75 54 9 Kevin 81 86 10 Creed 71 0 11 Darryl 89 83 12 Gabe 56 64 13 Toby 81 65 14 Holly 92 73 Formula used: The mean of n quantities is evaluated as follows: Mean = x 1 + x 2 + x 3 + x 4 + ...... + x n n Where, x n is the value of the n th quantity. The standard deviation is evaluated as follows: Standard deviation = ∑ ( Score − Mean ) 2 n Calculation: Consider the table provided in the question. Evaluate the mean and standard deviation for exam 1 as follows: Mean = 80 + 77 + 68 + 81 + 96 + 54 + 75 + 81 + 71 + 89 + 56 + 81 + 92 13 = 1001 13 = 77 The mean is 77 . Calculate ( Score − Mean ) 2 as follows: When the score is 80 , ( Score − Mean ) 2 = ( 80 − 77 ) 2 = 3 2 = 9 When the score is 77 , ( Score − Mean ) 2 = ( 77 − 77 ) 2 = 0 When the score is 68 , ( Score − Mean ) 2 = ( 68 − 77 ) 2 = ( − 9 ) 2 = 81 When the score is 81 , ( Score − Mean ) 2 = ( 81 − 77 ) 2 = 4 2 = 16 When the score is 96 , ( Score − Mean ) 2 = ( 96 − 77 ) 2 = 19 2 = 361 When the score is 54 , ( Score − Mean ) 2 = ( 54 − 77 ) 2 = ( − 23 ) 2 = 529 When the score is 75 , ( Score − Mean ) 2 = ( 75 − 77 ) 2 = ( − 2 ) 2 = 4 When the score is 81 , ( Score − Mean ) 2 = ( 81 − 77 ) 2 = 4 2 = 16 When the score is 71 , ( Score − Mean ) 2 = ( 71 − 77 ) 2 = ( − 6 ) 2 = 36 When the score is 89 , ( Score − Mean ) 2 = ( 89 − 77 ) 2 = 12 2 = 144 When the score is 56 , ( Score − Mean ) 2 = ( 56 − 77 ) 2 = ( − 21 ) 2 = 441 When the score is 81 , ( Score − Mean ) 2 = ( 81 − 77 ) 2 = 4 2 = 16 When the score is 92 , ( Score − Mean ) 2 = ( 92 − 77 ) 2 = 15 2 = 225 Calculate the sum of all the values obtained as follows: ∑ ( Score − Mean ) 2 = 9 + 0 + 81 + 16 + 361 + 529 + 4 + 16 + 36 + 144 + 441 + 16 + 225 = 1878 Divide the sum obtained with the total number of values as follows: ∑ ( Score − Mean ) 2 n = 1878 13 Calculate the standard deviation by taking square root of the value obtained above: Standard Deviation = 1878 13 = 144

1st Edition

ISBN: 9781259218859

Author: David Sobecki Professor, Brian A. Mercer

Publisher: McGraw-Hill Education

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Chapter 4.1, Problem 1A

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To calculate: The standard deviation of the scores in the provided table and then to explain what the mean and the standard deviation convey about the data.

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Chapter 4.1, Problem 4R

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The standard deviation of the scores in the provided table and then to explain what the mean and the standard deviation convey about the data.

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Chapter 4 Solutions