Answer :
Answer:
grade point average (GPA) as a weighted mean = 3.14
Yes, student makes the Dean's list.
Step-by-step explanation:
Since the data is not given I will explain the question with a relevant example:
For example
Data:
Students grades are: A, C, B, A, D
The corresponding number of credit hours: 3, 3, 3, 4, 1
The grading system assigns quality points to letter grades as:
A = 4
B = 3
C = 2
D = 1
F = 0
To find:
grade point average (GPA) as a weighted mean
If the Dean's list requires a GPA of 3.00 or greater, did this student make the Dean's list?
Solution:
Weighted Mean = Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex]
Here
Using the earned grades of A, C, B, A, D and corresponding quality points to these letter grades we get:
A = 4
C = 2
B = 3
A = 4
D = 1
So the values in x[tex]_{i}[/tex] are:
x
4
2
3
4
1
Now the number of credit hours are represented as weights w[tex]_{i}[/tex] :
w
3
3
3
4
1
In order to calculate weighted mean first multiply x[tex]_{i}[/tex] with w[tex]_{i}[/tex]
x[tex]_{i}[/tex] w[tex]_{i}[/tex]
4 * 3 = 12
2 * 3 = 6
3 * 3 = 9
4 * 4 = 16
1 * 1 = 1
The sum of x[tex]_{i}[/tex] w[tex]_{i}[/tex] is :
Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] = 12 + 6 + 9 + 16 + 1 = 44
Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] = 44
Now compute the sum of w[tex]_{i}[/tex]
Σw[tex]_{i}[/tex] = 3 + 3 + 3 + 4 + 1 = 14
Σw[tex]_{i}[/tex] = 14
Putting the values in the weighted mean formula:
Weighted Mean = Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex]
= 44 / 14
= 3.1429
Weighted Mean = Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex] = 3.14
Since the Dean's list requires a GPA of 3.00 or greater and the grade point average (GPA) as a weighted mean of the student is 3.14 so the student makes the Dean's list because his/her GPA is higher than 3.00