Question

1. finding a weighted mean

you are taking a class in which your grade is determined from five sources: 50% from your test mean, 15% from your midterm, 20% from your final exam, 10% from your computer lab work, and 5% from your homework. hint: change the score of 82 from the final exam to 95. what grade did the student get?

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$$\begin{array}{lccc} \\text{source} & \\text{score, } x & \\text{weight, } w & x \\cdot w \\\\ \\text{test mean} & 86 & 0.50 & 43.0 \\\\ \\text{midterm} & 96 & 0.15 & 14.4 \\\\ \\text{final exam} & 82 & 0.20 & 16.4 \\\\ \\text{computer lab} & 98 & 0.10 & 9.8 \\\\ \\text{homework} & 100 & 0.05 & 5.0 \\end{array}$$

Explanation:

Identify the modified values

We need to calculate the weighted mean grade.
The problem states: "HINT: CHANGE THE SCORE OF 82 FROM THE FINAL EXAM TO 95."
Thus, the final exam score \(x\) changes from 82 to 95.
All other scores and weights remain as given in the table.

List the scores and weights

Let's list the values of score \(x\) and weight \(w\) for each source:

• Test Mean: \(x_1 = 86\), \(w_1 = 0.50\)
• Midterm: \(x_2 = 96\), \(w_2 = 0.15\)
• Final Exam: \(x_3 = 95\), \(w_3 = 0.20\) (modified)
• Computer Lab: \(x_4 = 98\), \(w_4 = 0.10\)
• Homework: \(x_5 = 100\), \(w_5 = 0.05\)

Calculate the weighted products

We compute the product \(x \cdot w\) for each source:

• Test Mean: \(86 \cdot 0.50 = 43.0\)
• Midterm: \(96 \cdot 0.15 = 14.4\)
• Final Exam: \(95 \cdot 0.20 = 19.0\)
• Computer Lab: \(98 \cdot 0.10 = 9.8\)
• Homework: \(100 \cdot 0.05 = 5.0\)

Sum the weights and products

We sum the weights:

$$ \sum w = 0.50 + 0.15 + 0.20 + 0.10 + 0.05 = 1.00 $$

We sum the weighted products:

$$ \sum (x \cdot w) = 43.0 + 14.4 + 19.0 + 9.8 + 5.0 = 91.2 $$

Calculate the weighted mean

The formula for the weighted mean is:

$$ \bar{x} = \frac{\sum (x \cdot w)}{\sum w} $$

Substituting the values:

$$ \bar{x} = \frac{91.2}{1.00} = 91.2 $$

Answer:

\(91.2\)