Explanation Let’s consider students A and B , we have to assign marks of six exams such that the mean of both the students remain same. A = { 92 , 85 , 65 , 89 , 96, 71 } B = { 90 , 80 , 6 0 , 80 , 96, 92 } Mean of student A is calculated as shown below: x ¯ = ∑ x n x ¯ = ( 92 + 85+65+89+96+71 ) 5 x ¯ = 498 5 = 83 m e a n of A = 83 Similarly, Mean of student B is calculated as shown below: x ¯ = ∑ x n x ¯ = ( 90 + 80+6 0 + 80+96+92 ) 6 x ¯ = 498 5 = 83 m e a n of B = 83 Now, let’s calculate standard deviation of student A . Scores Square of the deviation from mean x ( x − x ¯ ) 2 92 ( 92 − 83 ) 2 = 9 2 = 81 85 ( 85 − 83 ) 2 = 2 2 = 4 65 ( 65 − 83 ) 2 = − 18 2 = 324 89 ( 89 − 83 ) 2 = 6 2 = 36 96 ( 96 − 83 ) 2 = 13 2 = 169 71

13th Edition

ISBN: 9780357127193

Author: SMITH

Publisher: CENGAGE L

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Chapter 14.2, Problem 6PS

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An example of “two students’ scores in six exams, have the same mean, but one student’s scores have a small standard deviation than the other student”.

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Chapter 14.2, Problem 5PS

Chapter 14.2, Problem 7PS

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To give: An example of “two students’ scores in six exams, have the same mean, but one student’s scores have a small standard deviation than the other student”.

Solution Summary: The author explains that two students' scores in six exams, have the same mean, but one student's scores have a small standard deviation than the other student.