Math  /  Data & Statistics

Question5 6 8 9 10 12 13 14\checkmark 14 15\checkmark 15 16\checkmark 16
At most colleges and universities, weighted means are used to compute students' grade point averages (GPAs). At one college, the grades AFA-F are assigned numerical values as follows. A=4.0C=2.0B+=3.5D+=1.5B=3.0D=1.0C+=2.5F=0.0\begin{array}{ll} A=4.0 & C=2.0 \\ B+=3.5 & D+=1.5 \\ B=3.0 & D=1.0 \\ C+=2.5 & F=0.0 \end{array}
Grade point average is a weighted mean where the "weights" for each grade are the number of credit-hours for that class. Compute the GPA for the following 'grades. Round to the nearest hundredth. \begin{tabular}{|l|c|c|} \hline Course & Grade & Number of Credit-Hours (Weights) \\ \hline Intermediate Algebra & BB & 1 \\ \hline Theater & B+B+ & 4 \\ \hline Music Appreciation & C+C+ & 5 \\ \hline World History & FF & 2 \\ \hline \end{tabular}
The GPA for these grades is \square .

Studdy Solution

STEP 1

1. The grades are assigned numerical values as follows: A=4.0,B+=3.5,B=3.0,C+=2.5,C=2.0,D+=1.5,D=1.0,F=0.0 A = 4.0, B+ = 3.5, B = 3.0, C+ = 2.5, C = 2.0, D+ = 1.5, D = 1.0, F = 0.0 .
2. The GPA is calculated as a weighted mean where the weights are the credit-hours for each course.

STEP 2

1. Assign numerical values to each grade.
2. Calculate the total weighted grade points.
3. Calculate the total number of credit-hours.
4. Compute the GPA by dividing the total weighted grade points by the total number of credit-hours.
5. Round the GPA to the nearest hundredth.

STEP 3

Assign numerical values to each grade based on the table:
- Intermediate Algebra: B=3.0 B = 3.0 - Theater: B+=3.5 B+ = 3.5 - Music Appreciation: C+=2.5 C+ = 2.5 - World History: F=0.0 F = 0.0

STEP 4

Calculate the total weighted grade points by multiplying each grade's numerical value by its credit-hours:
- Intermediate Algebra: 3.0×1=3.0 3.0 \times 1 = 3.0 - Theater: 3.5×4=14.0 3.5 \times 4 = 14.0 - Music Appreciation: 2.5×5=12.5 2.5 \times 5 = 12.5 - World History: 0.0×2=0.0 0.0 \times 2 = 0.0
Total weighted grade points:
3.0+14.0+12.5+0.0=29.5 3.0 + 14.0 + 12.5 + 0.0 = 29.5

STEP 5

Calculate the total number of credit-hours:
1+4+5+2=12 1 + 4 + 5 + 2 = 12

STEP 6

Compute the GPA by dividing the total weighted grade points by the total number of credit-hours:
GPA=29.512=2.4583 \text{GPA} = \frac{29.5}{12} = 2.4583\ldots

STEP 7

Round the GPA to the nearest hundredth:
GPA2.46 \text{GPA} \approx 2.46
The GPA for these grades is:
2.46 \boxed{2.46}

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