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.

Question

Accepted Answer

# Explanation:
## Step1: Find the numerical value of each grade
From the given table:
- For Intermediate Algebra ($D +$): $x_1 = 1.5$
- For Theater ($D$): $x_2=1.0$
- For Music Appreciation ($B +$): $x_3 = 3.5$
- For World History ($B$): $x_4=3.0$

## Step2: Find the weights
The weights ($w$) are:
- $w_1 = 1$
- $w_2 = 3$
- $w_3 = 4$
- $w_4 = 2$

## Step3: Calculate the numerator of the weighted - mean formula ($\sum_{i = 1}^{n}w_ix_i$)
$$
\begin{align*}
\sum_{i = 1}^{4}w_ix_i&=(1\times1.5)+(3\times1.0)+(4\times3.5)+(2\times3.0)\
&=1.5 + 3+14+6\
&=24.5
\end{align*}
$$

## Step4: Calculate the denominator of the weighted - mean formula ($\sum_{i = 1}^{n}w_i$)
$$
\begin{align*}
\sum_{i = 1}^{4}w_i&=1 + 3+4+2\
&=10
\end{align*}
$$

## Step5: Calculate the GPA (weighted mean)
The formula for the weighted mean $\bar{x}=\frac{\sum_{i = 1}^{n}w_ix_i}{\sum_{i = 1}^{n}w_i}$
$$
\bar{x}=\frac{24.5}{10}=2.45
$$

# Answer:
$2.45$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the numerical value of each grade

Step2: Find the weights

Step3: Calculate the numerator of the weighted - mean formula (\(\sum_{i = 1}^{n}w_ix_i\))

Step4: Calculate the denominator of the weighted - mean formula (\(\sum_{i = 1}^{n}w_i\))

Step5: Calculate the GPA (weighted mean)

Answer: