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To solve this problem, we need to calculate the **weighted mean** of the first statement in the survey. The table shows responses from 40 participants, and for each statement, respondents rated it on a scale from "Strongly Agree" to "Strongly Disagree". To calculate the weighted mean, we follow these steps:

### Step 1: Assign numerical values to each category.
- Strongly Agree = 5
- Agree = 4
- Undecided = 3
- Disagree = 2
- Strongly Disagree = 1

### Step 2: Extract the responses for the first statement:
Here are the values for the first statement:
- **Strongly Agree (5):** 15 respondents
- **Agree (4):** 10 respondents
- **Undecided (3):** 8 respondents
- **Disagree (2):** 4 respondents
- **Strongly Disagree (1):** 3 respondents

### Step 3: Multiply the number of responses by the assigned numerical value:
- Strongly Agree: \( 15 \times 5 = 75 \)
- Agree: \( 10 \times 4 = 40 \)
- Undecided: \( 8 \times 3 = 24 \)
- Disagree: \( 4 \times 2 = 8 \)
- Strongly Disagree: \( 3 \times 1 = 3 \)

### Step 4: Add these values together.
\[ 75 + 40 + 24 + 8 + 3 = 150 \]

### Step 5: Divide by the total number of respondents (40).
\[
\text{Weighted Mean} = \frac{150}{40} = 3.75
\]

Thus, the weighted mean of the first statement in the survey is **3.75**, which is not one of the provided answer choices (4.15, 4.20, or 4.25), so it seems the answer choices might be associated with a different question or there is a mistake in the answer choices provided.

Do you have any questions or want further details?

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Here are 5 related questions to expand your understanding:
1. What is the difference between an arithmetic mean and a weighted mean?
2. How does the scale of agreement (1 to 5) affect the calculation of weighted mean?
3. Why is it important to calculate the weighted mean in surveys?
4. How would the weighted mean change if more people strongly agreed?
5. How can rounding affect survey data analysis?

**Tip:** Always ensure the weights (like response values) accurately reflect the importance or ranking before calculating the weighted mean.

Calculate the weighted mean of the first statement in the survey.

Learn how to calculate the weighted mean for the first statement in a survey conducted by National University marketing students. This problem involves key concepts of weighted averages, applicable for Grades 9-12.

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