Question

Weighted Mean A student of the author earned grades of A, C, B, A, and D. Those courses had these corresponding numbers of credit hours: 3, 3, 3, 4, and 1. The grading system assigns quality points to letter grades as follows: A = 4; B = 3; C = 2; D = 1; F = 0. Compute the grade-point average (GPA) and round the result with two decimal places. If the dean’s list requires a GPA of 3.00 or greater, did this student make the dean’s list?

Short answer

The grade-point average (GPA) of a student is 3.14.

Yes, the student has made it to the dean’s list as the student's GPA is 3.14.

Step-by-step solution

Given information

The grades earned by a student are A,C,B,A, and D.

The credit hours corresponding to the grades are 3,3,3,4, and 1.

The quality points as per the grades are A = 4; B = 3; C = 2; D = 1; F = 0.

Describe the weights and data points

The weights are equivalent to the number of credit hours with each grade, which are $w=3,3,3,4,1$.

The value equivalent of the grades are A = 4; B = 3; C = 2; D = 1; F = 0.

The grades earned by the student are A,C,B,A, and D. Thus, the associated values of x are 4, 2, 3, 4, and 1.

Compute the GPA (grade-point average)

The grade-point average is described using the weighted mean formula as follows:

$\overline{x}=\frac{\sum \left(w\times x\right)}{\sum w}$

Substitute the values in the formula to compute the GPA (weighted mean) as:

$$\begin{gathered} \overline{x}=\frac{3\times 4+3\times 2+3\times 3+4\times 4+1\times 1}{3+3+3+4+1} \\ =\frac{44}{14} \\ =3.1429 \end{gathered}$$

Thus, the grade mean average is 3.14.

Compare the GPA with the dean’s list

The GPA required is 3 or greater.

As the GPA obtained is 3.14, which is higher than 3, the student made it to the dean’s list.

Thus, with a GPA of 3.14, the student would make it to the dean’s list.