Question

at most colleges and universities, weighted means are used to compute students grade - point averages (gpas). at one college, the grades $a - f$ are assigned numerical values as follows.
$a = 4.0$ $c = 2.0$
$b+=3.5$ $d += 1.5$
$b = 3.0$ $d = 1.0$
$c+=2.5$ $f = 0.0$
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.

course	grade	number of credit - hours (weights)
theater	$c$	3
music appreciation	$d$	5
world history	$d +$	1

the gpa for these grades is 2.03.

Explanation:

Step1: Recall weighted - mean formula

The formula for the weighted mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}w_{i}}{\sum_{i = 1}^{n}w_{i}}$, where $x_{i}$ is the value of the variable and $w_{i}$ is the weight.

Step2: Calculate the product of grade - point and credit - hours for each course

For Intermediate Algebra ($B +$ with $x_1 = 3.5$ and $w_1=2$): $x_1w_1=3.5\times2 = 7$.
For Theater ($C$ with $x_2 = 2.0$ and $w_2 = 3$): $x_2w_2=2.0\times3=6$.
For Music Appreciation ($D$ with $x_3 = 1.0$ and $w_3 = 5$): $x_3w_3=1.0\times5 = 5$.
For World History ($D +$ with $x_4 = 1.5$ and $w_4 = 1$): $x_4w_4=1.5\times1=1.5$.

Step3: Calculate the sum of the products

$\sum_{i = 1}^{4}x_{i}w_{i}=7 + 6+5 + 1.5=19.5$.

Step4: Calculate the sum of the credit - hours

$\sum_{i = 1}^{4}w_{i}=2 + 3+5 + 1=11$.

Step5: Compute the GPA

$\text{GPA}=\frac{\sum_{i = 1}^{4}x_{i}w_{i}}{\sum_{i = 1}^{4}w_{i}}=\frac{19.5}{11}\approx1.77$.

Answer:

$1.77$