Let's first address each problem from the image you've uploaded.

Problem 3:

You are asked to determine a student's final grade based on:

• Quiz score: 85
• Midterm score: 75
• Final Exam score: 83

The formula for the final grade is given as:

• 20% of the average quiz score,
• 30% of the final exam score,
• 50% of the midterm score.

Step-by-step solution:

1. Average Quiz Score: Since only one quiz score (85) is provided, the average quiz score is just 85.

2. Weighting each component:

   • 20% of the average quiz score: $0.20 \times 85 = 17$
   • 30% of the final exam score: $0.30 \times 83 = 24.9$
   • 50% of the midterm score: $0.50 \times 75 = 37.5$

3. Final Grade: Now sum these up: $17 + 24.9 + 37.5 = 79.4$

Thus, the student's final grade is 79.4.

Problem 4:

Here, you're asked to compute the weighted mean for three questions and then interpret the result using the given table.

To compute the weighted mean for each question, we follow this formula: $\text{Weighted Mean} = \frac{\sum (\text{Frequency} \times \text{Rating})}{\text{Total number of responses}}$ where:

• The frequencies are given in the table (e.g., 15, 20, etc.),
• The ratings are 5, 4, 3, 2, and 1, corresponding to the level of agreement.

Example for Question 1:

1. Calculate total for Question 1: $(15 \times 5) + (20 \times 4) + (5 \times 3) + (0 \times 2) + (0 \times 1) = 75 + 80 + 15 + 0 + 0 = 170$

2. Total number of responses: $15 + 20 + 5 + 0 + 0 = 40$

3. Weighted Mean for Question 1: $\frac{170}{40} = 4.25$

This falls into the "Strongly Agree" (SA) category based on the interpretation table (4.20–5.00).

You can repeat this process for Questions 2 and 3.

Do you need further details on the weighted mean for the other questions? Feel free to ask!

Follow-up Questions:

1. What would happen if the weightings were different, say, 40% for the final exam?
2. How do you compute weighted means for categorical data?
3. Can you explain how the range of means (e.g., 1.00–1.79) corresponds to the different interpretations in Problem 4?
4. If the final grade formula changed, how would that affect the student’s score?
5. How would you calculate the standard deviation for the quiz scores?

Tip:

In weighted means, the weights should always sum to 1 (or 100%) to represent the whole distribution properly.