Weighted Mean Michael has just completed his first semester in college. He earned an A in his five-hour calculus course, a B in his four-hour chemistry course, an A in his three-hour speech course, and a C in his three-hour psychology course. Assuming an A equals 4 points, a B equals 3 points, and a C equals 2 points, determine Michael’s grade-point average if grades are weighted by class hours.

Verified step by step guidance

1. Identify the grade points for each course based on the given scale: A = 4 points, B = 3 points, and C = 2 points.
2. List the credit hours and corresponding grade points for each course: Calculus (5 hours, 4 points), Chemistry (4 hours, 3 points), Speech (3 hours, 4 points), Psychology (3 hours, 2 points).
3. Calculate the weighted grade points for each course by multiplying the grade points by the credit hours: for example, weighted points for Calculus = 5 \times 4.
4. Sum all the weighted grade points from each course to get the total weighted points.
5. Sum all the credit hours to get the total number of hours, then divide the total weighted points by the total credit hours to find the weighted mean (GPA): \(\text{GPA} = \frac{\sum (\text{grade points} \times \text{credit hours})}{\sum \text{credit hours}}\).

Key Concepts

Weighted Mean

The weighted mean is an average where each value contributes proportionally based on its assigned weight. In this context, grades are weighted by the number of credit hours for each course, reflecting their relative importance in calculating the overall GPA.

Grade Point Conversion

Grades are converted into numerical values (e.g., A=4, B=3, C=2) to quantify academic performance. This conversion allows for mathematical operations like averaging to determine a student's GPA.

Grade Point Average (GPA) Calculation

GPA is calculated by multiplying each course's grade point by its credit hours, summing these products, and dividing by the total credit hours. This weighted average reflects the student's overall academic performance.