 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

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

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.

 28  48  76.

4



Let’s see how we can complete the calculations we did in the previous slide using a spreadsheet.

B

2

3

4

Weighting Factor

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

Let’s update the information given in the previous spreadsheet.

B

4

5

2

6

7

Weighting Factor

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,

Scale

Letter

Homework 15 [93, 100]

[90, 93)

A

A-

Quizzes 15

Exams 30

[87, 90)

[83, 87)

[80, 83)

B+

B

B-

[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

7

Let’s modify the previous worksheet by integrating the new information.

2

3

B

Homework

6

7

4

5

8

Quizzes

9

10

11

12

13

Exams

Weight

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

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

4

Quizzes

10

11

12

13

Exams

14

15 Weight

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

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

4

5

2

3

B

Homework

10

11

12

13

8

9

6

7

Quizzes

Exams

Points Earned

Points Available

14

15

Score

16

17

18

Weight

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

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

19 Weighted Contribution

0

60

63

67

70

73

77

C

Homework

0.15

88.67

13.3

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

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

Lookup value.

which is stored in the cell G19.

13

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

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

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!

101 you calculated the weighting factor for each grade component. What is the equivalent weighting factor in the GPA calculation?

14

1.

2.

Homework

Quizzes

Midterm Exams

Final Exam

Percentage

20

20

30

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

### End of Module Assignments

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

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