16. Below are the GPAs (in standard deviation units or z-scores) for three students in last year’s class of master’s students. The average GPA was 3.5 and the standard deviation of the GPAs for the class is .5. For each of the three students, transform the GPA into a Z-score, then indicate the approximate class rank of the student (i.e., percent of students scoring below the student).
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Student 1 |
Student 2 |
Student 3 |
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GPA |
4.0 |
3.7 |
3.0 |
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GPA in z-score units |
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Class rank (percent of students scoring below) |
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17. Use the following numbers to calculate the range, the mean, the median, the mode, and the standard deviation. Do the calculations by hand, showing your work. Replicate the calculations using Excel to check your work – you do not need to turn in the Excel spreadsheet.
Data = 5, 7, 10, 12, 14, 18, 19, 19, 20, 21, 25
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Range |
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Mean |
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Mode |
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Median |
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Standard Deviation |
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18. John took two nationally normed, standardized tests and scored 700 on both tests. The following are the results of the test for the national norming sample of students:
Mean Standard Deviation
Test 1 1000 300
Test 2 800 200
John’s Results
Test 1 700
Test 2 700
John needs to submit results of only one of the two tests to Penn in support of his college application. Which would you advise him to submit and why?
19. Students in your school have been labeled “gifted” on the basis of their scores on standardized tests. Knowing this, would you expect the correlation between achievement test scores and school grades to be higher among the gifted 12 year-olds in your school or among the entire population of 12 year olds in the school? Why?
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