Question

we often deal with weighted means, in which different data values carry different weights in the calculation of the mean. for example, if the final exam counts for 50% of your final grade and 2 midterms each count for 25%, then you must assign weights of 50% and 25% to the final and midterms, respectively, before computing the mean score for the term. apply the idea of weighted mean in the following exercise. a student has completed 16 credits in the table to the right during one semester. grades are weighted so that a = 4.0, a- = 3.7, b+ = 3.4, b = 3.0, b- = 2.7, c+ = 2.4 and c = 2.0. answer parts a and b below.

course | credits | grade
statistics | 4 | b
eastern religions | 4 | a-
french | 4 | c+
geology | 3 | c
geology lab | 1 | a

a. find the students gpa for the semester.
the students gpa is 2.90
(type an integer or decimal rounded to the nearest hundredth as needed.)

b. what grade would the student need to earn in french to raise her gpa over 3.20?
to earn a gpa over 3.20, the student would need to earn a minimum grade of

Explanation:

Identify given course grades and credits

Using the GPA Calculation and Weighted Mean Calculation knowledge points

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Total credits:

$$ \sum w_i = 4 + 4 + 4 + 3 + 1 = 16 $$

Set up inequality for target GPA

Using the GPA Calculation and Weighted Mean Calculation knowledge points
Let \(g\) be the grade value needed in French.

$$ \frac{(4 \times 3.0) + (4 \times 3.7) + (4 \times g) + (3 \times 2.0) + (1 \times 4.0)}{16} > 3.20 $$

Solve for the required grade value

Using the GPA Calculation and Weighted Mean Calculation knowledge points

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Determine the minimum letter grade

We compare the required value \(g > 3.6\) to the standard grade scale:

• \(\text{A} = 4.0\)
• \(\text{A-} = 3.7\)
• \(\text{B+} = 3.4\)

Since \(g\) must be strictly greater than \(3.6\), the minimum grade value that satisfies this is \(3.7\), which corresponds to an \(\text{A-}\).

Answer:

A-