Two researchers are examining academic performance. They use the same set of 11
ID: 3047998 • Letter: T
Question
Two researchers are examining academic performance. They use the same set of 11 college student participants, but they each measure academic performance differently. Researcher 1 measures academic performance by asking the participants to self-report which letter grade is most typical for them to receive on an assignment on the standard A through F scale. Researcher 2 measures academic performance by accessing the volunteer’s academic record and retrieving their overall grade point average from the college system. The participants’ scores are shown below.
Researcher 1: Letter Grade
Researcher 2: Overall GPA
B
3.25
A
3.31
C
2.45
B
3.09
A
4.00
C
1.90
D
.60
B
2.85
A
2.96
B
3.02
C
1.54
.9. What percentage of the students had an overall GPA of 3.0 or higher? (3 pts) 2.
10.What is the most appropriate measure of central tendency for typical letter grade? Provide an explanation why. (4 pts) 3.
11.What is the most appropriate measure of central tendency for overall GPA? Provide an explanation why. (4 pts) 4. Calculate (2 pts) and interpret (2 pts) the mode for letter grade. 5. Calculate (3 pts) and interpret (3 pts) the median for letter grade. 6. Calculate (3 pts) and interpret (3 pts) the mean for overall GPA. 7. Calculate the sum of squares (SS) for GPA using the definitional formula. (3 pts) 8. Calculate the sum of squares (SS) for GPA using the computational formula. (3 pts) 9. Calculate the variance for GPA, assuming these 11 people are a population. (4 pts) 10. Calculate (4 pts) and interpret (4 pts) the standard deviation for GPA, assuming these 11 people are a population. 11. Calculate (4 pts) and interpret (4 pts) the standard deviation for GPA, assuming these 11 people are a sample. FOR QUESTIONS 20-24: Use the sample mean and standard deviations in your calculations. 12. How many standard deviations away from the mean would someone be who had an overall GPA of 2.25? (3 pts) 13. How many standard deviations away from the mean would someone be who had an overall GPA of 1.50? (3 pts) 14. If someone had a Z-score of 1.85, what would their overall GPA be? (3 pts) 15. If someone had an overall GPA that was 1.60 standard deviations below the mean, what would their raw score be? (3 pts) 16. Would someone with a GPA of 2.25 be considered “extreme” or “typical”? Provide an explanation why with your answer. (3 pts)
Researcher 1: Letter Grade
Researcher 2: Overall GPA
B
3.25
A
3.31
C
2.45
B
3.09
A
4.00
C
1.90
D
.60
B
2.85
A
2.96
B
3.02
C
1.54
Explanation / Answer
9. (4/11)*100% = 0.363636*100 %= 36.3636% students have overall percentage 3.0 or higher.
10. Mode is the most appropriate measure to measure the centrl tendency of letter grade.
Because, we can only find the grade having higher number of frequency.
11. Median is the appropriate measure of central tendency of overall grade. Because median is not affected by outliers.
12.
Mode = B
Letter grade Frequency A 3 B 4 C 3 D 1 Total 11Related Questions
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