SSAC2006.LB3051.SKB1.2
Core Quantitative Issue
Weighted Averages
Supporting Quantitative Concepts
Percentages
Averages
Prepared for SSAC by
Semra Kilic-Bahi, Colby-Sawyer College, New London NH
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006 1

Background and Overview
Mean (Average) and Weighted Mean x , x ,..., x mean (average) of the data set is x
1
 x
2

,...,
 x
N
N
If different data points are worth more or less than the other data points we should take this into account when we are calculating the mean. If the numbers in a data x
1
, x
2
,..., x
N respectively, then the weighted mean of the data set is
N, w
1 x
1 w

1
 w
2 w x
2
2


...

w
...

w
N
N x
N
Slides 2-3 Introduces the problem and gives the main formulas needed
Slides 4-12 Use four different grading policies as examples to demonstrate the use of spreadsheets in calculating grades
Slides 13-14 Introduces the LOOKUP function in determining letter grade and calculating grade point average
Slides 15-16 Gives problems to practice the skills introduced and developed in the module
2

Problem
It is almost the end of the semester. You are getting ready for the final exam in your Foundation 101 course. The acceptance requirements for your intended major are:
1) A minimum grade of B- in Foundation 101 class
2) A minimum cumulative GPA of 2.50
Your minimum expected grades for the other courses you are taken are:
2
B
Course
3 Writing 101
4 Mathematics 101
5 Sociology 101
C
Credit Hours
3.00
3.00
3.00
D
Your Grade
C+
A
D+
If you receive 80 out of 100 on your final exam in Foundation
101 class, will you meet the requirements for this major?
3

Example A
Suppose your Foundation 101 course has only a midterm and a final exam. The midterm is 40% and the final exam is 60% of the grade. You got a 70 out of 100 on the midterm and a 80 out of 100 on the final exam. What's your overall grade for this course?
1. The first step in determining your grade is to calculate the weighted contribution of each of your exams.
• The midterm is worth 40% (40/100=0.40) of the final grade and your midterm exam score is 70. To determine the weighted contribution, you multiply your score by the weighting factor, 0.4.
70  0.40
 28
• The final is worth 60% of your total grade (weighting factor = 0.6). Multiply your score by the weighting factor.

80  0.60
 48
2.
To determine your overall grade you add the two weighted contributions from your midterm and final.
 28  48  76.
4


Example A Using a spreadsheet
Let’s see how we can complete the calculations we did in the previous slide using a spreadsheet.
B
2
3
4
Weighting Factor
Your Grades
5 Weighted Contribution
= Cell with a number in it
C D
Midterm Exam Final Exam
0.4
70
28
0.6
80
48
=C3*C4 =D3*D4
= Cell with a formula in it
First you find the weighted contribution of each exam by multiplying the grade by the weighting factor.
E
Total
1
76
= C5+D5
Note that the sum of weighting factors when the weights are expressed in percentages must always be equal to 1 (100%)!
Then you calculate the sum of the two weighted contributions to determine your overall class grade.
5

Example B
Now suppose you had two exams and your final exam. Your first exam score was 80 and the second was 74. If your exam grade average was still 40 percent of your overall grade, what grade do you expect to receive for the course?
Let’s update the information given in the previous spreadsheet.
B
4
5
2
3 Your Grades
6
7
Weighting Factor
Your Grades
8 Weighted Contribution
C
Exam 1
80
D
Exam 2
74
Midterm Exam Final Exam
0.4
77
30.8
0.6
80
48
E
Exam Average
77
Total
1
78.8
=E3
First find the average of your two exam grades. Then link to that average in cell C7.
=(C3+D3)/2
OR
=AVE(C3:D3)
6

Example C
Suppose you are given the following grading policy and grading scale for the course,
Grading Policy Percentage
Grading
Scale
Letter
Grade
Homework 15 [93, 100]
[90, 93)
A
A-
Quizzes 15
Exams 30
[87, 90)
[83, 87)
[80, 83)
B+
B
B-
Final Exam 40 and your grades are:
[77, 80)
[73, 77)
[70, 73)
C+
C
C-
Homework 85 89
Quizzes 86 75
90
81
87 75
79 87
[67, 70)
[63, 67)
[60, 63)
[0, 60)
D+
D
D-
F
Exams 79 82
Final Exam 80
69
What is your expected course grade?
7

Example C Using a Spreadsheet
Let’s modify the previous worksheet by integrating the new information.
2
3
B
Homework
Grade
6
7
4
5
8
Quizzes
Grade
9
10
11
12
13
Exams
Grade
Weight
Grade
14 Weighted Contribution
C
HW #1
85
Quiz #1
86
Exam 1
79
D
HW#2
89
Quiz #2
75
Exam 2
82
E
HW#3
90
Quiz #3
81
Exam 3
69
F
HW#4
87
Quiz #4
79
G
HW#5
75
Quiz #5
87
Homework Quizzes Exams Final Exam Total
0.15
0.15
0.3
0.4
1
85.2
81.6
76.7
80
12.8
12.2
23 32 80.0
H
HW Average
85.2
Quiz Average
81.6
Exam Average
76.7
=H3 =H6 =H9
It is in the
B- range
8

Example C Modification (Omitting the Two Lowest Homework Grades)
After you read the syllabus carefully, you realized that two lowest homework grades will be omitted. How will this information affect your grade?
Let’s modify our spreadsheet by identifying and omitting the two lowest homework grades as follows:
4
5
6
2
3
B
Homework
Grade
Lowest Grade
Second Lowest Grade
C
HW #1
85
75
85
D
HW#2
89
E
HW#3
90
=SMALL(C3:G3, 2)
=SMALL(C3:G3, 1)
F
HW#4
87
G
HW#5
75
H
HW Average
88.67
=(SUM(C3:G3)-C5-C6)/3
9

Example C Modification Using a Spreadsheet
Let’s modify our grade calculation worksheet by integrating the new information related to omitting two lowest homework grades.
7
8
9
2
3
B
Homework
Grade
4
5 Lowest Grade
6 Second Lowest Grade
Quizzes
Grade
10
11
12
13
Exams
Grade
14
15 Weight
16 Grade
17 Weighted Contribution
C
HW #1
85
75
85
Quiz #1
86
Exam 1
79
D
HW#2
89
Quiz #2
75
Exam 2
82
E
HW#3
90
Quiz #3
81
Exam 3
69
F
HW#4
87
Quiz #4
79
G
HW#5
75
Quiz #5
87
Homework Quizzes Exams Final Exam Total
0.15
88.67
0.15
81.6
0.3
76.7
0.4
80
1
13.3
12.2
23 32 80.5
H
HW Average
88.67
Quiz Average
81.6
Exam Average
76.7
=H3
It is still in the
B- range
10

Example D Midterm Exams with Different Total Points
Suppose you had three exams. You got 170 out of 200 on the first exam,
135 out of 250 on the second exam, and a 280 out of 300 on the third exam. If all the exams have an equal weight and your exam average is still
30 percent of your grade, what is your overall course grade.
First calculate each of your exam grades by dividing the number of points you earned by the number of points available. Then use these scores to calculate your exam average.
2
3
B
Exams
C D E
Exam #1 Exam #2 Exam #3
Points Earned 170
4 Points Available 200
5 Score 85
135
250
54
280
300
93.33
F
Exam Average
77.44
=(C3/C4)*100
=(D3/D4)*100
=AVERAGE(C4:E4)
11

Example D Using a Spreadsheet
Now insert the spreadsheet on the previous slide into your grade calculation spreadsheet on Slide 9.
4
5
2
3
B
Homework
Grade
10
11
12
13
8
9
6
7
Lowest Grade
Second Lowest Grade
Quizzes
Grade
Exams
Points Earned
Points Available
14
15
Score
16
17
18
Weight
Grade
19 Weighted Contribution
C
HW #1
85
75
85
Quiz #1
86
Exam #1
170
200
85
D
HW#2
89
Quiz #2
75
Exam #2
135
250
54
E
HW#3
90
Quiz #3
81
Exam #3
280
300
93.33
Homework Quizzes Exams
0.15
0.15
0.30
88.67
13.3
81.6
12.2
77.4
23.23
F
HW#4
87
Quiz #4
79
Exam Average
77.44
Final Exam
0.40
80
32
G
HW#5
75
Total
1
80.8
H
HW Average
88.67
Quiz #5 Quiz Average
87 81.6
You can simply look at the grading scale table from slide 6 to figure out that your grade is still in the B- range or you can use an Excel feature to determine your letter grade automatically (See the next slide).
12

Determining your letter grade using Excel
You can use the “LOOKUP” function in Excel to determine your letter grade.
29
30
31
32
33
16
17
20
21
22
23
24
25
26
27
28
B
Weight
18 Grade
19 Weighted Contribution
Numeric Grade Range
0
60
63
67
70
73
77
C
Homework
0.15
88.67
13.3
Letter Grade
F
D-
D
D+
C-
C
C+
D
Quizzes
0.15
81.6
12.2
E
Exams
0.30
77.4
23.23
80
83
87
90
93
B-
B
B+
A-
A
F
Final Exam
0.40
80
32
G
Total
1
Numeric Grade Letter Grade
80.8
B-
= LOOKUP(G19, B$21:C$33)
Lookup value
The Lookup value is a
Array
H
An array is a range of cells that contain value that the function number or text
The “LOOKUP” function will be very helpful in the next searches for in an array.
It can be a number or that you want to compare with slide when we calculate your text. In this setting, it is
“overall numberic grade”
Lookup value.
grade point average.
which is stored in the cell G19.
13

Calculating your Grade Point Average (GPA)
Your GPA is calculated as follows:
1.
Multiply the quality point value for your grade in each course by the number of credit hours that the course is worth. This gives you your earned quality points.
2.
Find the total number of credit hours you have completed and the total number of earned quality points.
3.
Divide the total earned quality points by the total number of credit hours to determine your GPA.
14
15
16
17
18
19
20
21
2
3
B
Course
Writing 101
4 Mathematics 101
5 Sociology 101
8
9
6 Foundation 101
7 Total
10
11
Grade
A
12
13
A-
B+
B
B-
C+
C
C-
D+
D
D-
F
C
Credit Hours
3
3
3
4
13
Quality Point Value
4.0
3.7
3.3
3.0
2.7
2.3
2.0
1.7
1.3
1.0
0.7
0.0
D E
Your Grade Earned Quality Points
C+
A
D+
B-
6.9
12
3.9
14.8
GPA
37.6
2.89
= LOOKUP(D3,
B$10:C$21) * C3
GPA= E7/C7
So, if you receive 80 out of 100 on your final exam you will get a B- in the course and earn a GPA of
2.58, thereby meeting both of the requirements for acceptance into your major!
When determining your course grade in Foundation
101 you calculated the weighting factor for each grade component. What is the equivalent weighting factor in the GPA calculation?
14

1.
2.
Recreate the spreadsheet in Slide 5, then answer the following questions by updating the information in your spreadsheet.
a) If you only change your midterm grades to 65 and 92, what would be your expected b) grade?
If your midterm grades were 65 and 92, but now your midterm grades contributes only
30 percent towards your grade, what would be your expected grade?
Recreate the spreadsheet in Slide 7, then answer the following questions by updating the information in your spreadsheet. a) If you were given the following grading policy, what would be your expected grade?
Grading Policy
Homework
Quizzes
Midterm Exams
Final Exam
Percentage
20
20
30
30 b) Suppose you were given the following grading policy and your scores were as follows, what would be your expected grade?
Grading Policy
Homework
Quizzes
Projects
Class Activities
Midterm Exams
Final Exam
Percentage
10
15
15
20
30
10
Homework
Quizzes
Class Activities
Projects
Midterm Exams
Final Exam
75
83
82
75
68
80
69
76
91
86
81
90
85
78
89
87
79
0
79
83
15

3.
Recreate the worksheet in Slide 9, and then update the worksheet if two lowest quiz grades were omitted in the calculation of quiz grades in addition to the omission of two lowest homework grades. What would be your expected letter grade?
4.
Recreate the worksheet in Slide 11. If you need B+ instead of B- in this course, what is the minimum grade
(whole number) you need in the final exam?
5.
By using the information in Slide 13, calculate your grade point average (GPA), if you have taken the following courses and grades.
Course
WRT101
PHI 101
BIO 101
HIS101
SOC 101
Credit Hours
4
3
3
3
3
Grades
C+
B
A
B+
C-
6.
You have created your own blend of coffee, by mixing 3 pounds of Coffee Brand A which costs $4 a pound, 4 pounds of Coffee Brand B which costs $7 a pound, 2 pounds Coffee Brand C which costs $3 a pound. What is the average price of this blend of coffee?
7.
Two sections of Liberal Arts Mathematics class take a test. The average is 76 in one section and the average is
84 in the other section. Under which circumstance, the average for both sections together is 80?
16