Question

The Data
A central tenet to being a good instructor, I believe, is to be a reflective practitioner of your craft. From time to time I find it to be necessary to review and reflect on my work as an instructor from a grade perspective. On our moodle page you will find a link to a second word document titled “300 Grades”. This data sheet contains both the alphanumeric grade (page 1) and the numerical equivalent (page 2) for every grade I have given for the last 300 students that have attempted this very course.

After your readings in chapter 7 and examining this 300 grades document, it should be relatively obvious that it is not uncommon to find an individual student that would achieve an A in my class. However, logically, it would be much more difficult to find a FULL CLASS (25 students) that would achieve an A average for my course. This project will help us answer this question… together.

Objective 1 (28 points)
Using excel or statcato, stack all ten columns together into a single column. Once you have all 300 grades in a single column, calculate:

   •   The average numeric grade for all 300 students

   •   The standard deviation for numeric grade for all 300 students

   •   If we were to assume the population of grades was normally distributed (which it certainly isn’t) calculated the probability that an individual would have a final grade higher than a 90.

   •   Again, assuming normality, calculate the probability that an individual was have a final grade higher than 80.

Objective 2 (21 points)
Since we are attempting to examine the behavior of a class of students, the behavior of an individual (as we calculated in objective 1) is really of little concern to us. Assuming that there are 30 students enrolled for a typical class, use the central limit theorem to calculate the following:

   •   What would be the shape of the distribution of the average class grade of these 30 students?

   •   What would be the average class average of these 30 students be?

   •   What would the standard deviation of the class average be for these 30 students?

Objective 3 (3 points)

Watch this video.

Objective 4 (28 points)

After watching the simulation video in objective 3, address the following questions:

   •   What is the probability that a class of 30 students would have a final average grade higher than a 90?

   •   Compare your results from objective 4 question 1 to your answer in objective 1 question 3. At face value, the two questions seem very similar, but you should have quite different responses. Is the probability of the 30 students higher or lower than just the individual? Why?

   •   What is the probability that a class of 30 students would have a final average grade higher than an 80?

   •   Compare your results from objective 4 question 3 to your answer in objective 1 question 4. At face value, the two questions seem very similar, but you should have quite different responses. Is the probability of the 30 students higher or lower than just the individual? Why?

Objective 5 (20 points)
At the beginning of this document I prompted the discussion referring to this activity as a reflection of my teaching. Now that you have calculated two different distributions (one for individual student performance and one for class average performance) which of the two distributions is more appropriate for my reflection as an instructor? Would it benefit me more to discuss the behavior of one of my students with the math coordinator at CCC&TI or to discuss the behavior of my classes? Be descriptive in your answer.

A
A
F
F
B-
B
B-
B
A
F
F
A
B
A
B
C
B
B
A
B+
B-
B+
F
C
A-
C
A
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B+
B
A-
F
B
C-
A
B+
A
C
A-
A-
A
F
F
D
B+
B
C
A
A
B+
B+
B+
B+
B-
C-
F
A
A
A
A
C
A
B-
B-
D-
C
B
A
D-
F
A
B
B
F
B
A-
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A
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F
A
C
A
A-
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B+
A
A-
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B-
B
C
A-
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F
A-
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B
B+
A-
A
A
C
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A-
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A
A
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A
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F
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A
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A
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A
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A-
A
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F
A
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A
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A-
B+
A
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A
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A
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F
B
B
A
B+
B+
B
B
C+
B
B+
D+
C+
B
F
B
A-
A
A
A
C+
F
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C+
D
A
F
A-
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F
A-
A-
A
B+
A
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C+
B
A
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A
B-
B+
B-
A
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A
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A-
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F
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A
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A
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A-
A
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A
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A-
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F
A-
A
A
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A-
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A
A
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A
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A
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D+
A-

95
96
94
58
67
94
89
88
97
76
50
94
61
63
78
90
79
81
98
64
86
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79
89
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65
40
80
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58
88
77
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92
91
61
74
90
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80
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91
80
95
90
85
77
58
98
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100
97
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85
86
71
78
88
94
72
68
97
83
88
62
89
93
42
98
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59
88
79
95
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80
92
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89
86
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93
77
59
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80
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35
68
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86
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87
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68
83
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68
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57
99
79
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77
75
60
87
67
63
84
95
96
91
89
93
95
69
86
61
53

Answer 1

Don't clear about objective 3 & objective 4.

Objective 1.

From excel we have calculated mean and population std. deviation.

Sum of grades	25688
Average Grade	85.63
Population std. dev	12.52