Which of these two exams A or B has a better relative positi

Which of these two exams, A or B, has a better relative position? Compute the relative position using a z-score:

A grade of 82 on a test with .

A grade of 56 on a test with .

Solution

A grade of 82 on a test with X=85 and s=6 (Note there is a line over the X)
b. A grade of 56 on a test with X=60 and s=5 ( Note there is a line over the X)
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x-bar is the sample mean; s is the sample standard deviation.
a. A grade of 82 on a test with X=85 and s=6 (Note there is a line over the X)
Meansure the distance 83 is from the mean using s as the unit of measure:
(82-85)/6 = -1/2

This means that 82 is one-half standard deviation below the mean score.
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b. A grade of 56 on a test with X=60 and s=5 ( Note there is a line over the X)
(56-60)/5= -4/5= -0.8
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The grade of 56 is further below the mean of its sample then the 82, so 56
is a worse score; 82 is the better of the two