C.1 Check for Understanding
Activity C.1.1 Identify and compute the appropriate measures of central tendency using the step-by-step process of the following.
3.A movie website wants to compute the overall average rating of a movie, considering different reviewers who have rated the movie, with each reviewer having different numbers of followers (weight).
Reviewer A: Average rating = 4.5 (Followers = 200)
Reviewer B: Average rating = 4.0 (Followers = 150)
Reviewer C: Average rating = 3.5 (Followers = 100)

To compute the overall average rating of a movie based on different reviewers with varying numbers of followers, we need to use the concept of a **weighted average**. The number of followers for each reviewer represents the "weight" of their rating. Here's the step-by-step process to find the weighted average rating.

### Step 1: Identify the Data
- **Reviewer A**: Average rating = 4.5, Followers (weight) = 200
- **Reviewer B**: Average rating = 4.0, Followers (weight) = 150
- **Reviewer C**: Average rating = 3.5, Followers (weight) = 100

### Step 2: Set up the Formula for the Weighted Average
The formula for calculating the weighted average is:

\[
\text{Weighted Average} = \frac{\sum (\text{Rating} \times \text{Weight})}{\sum \text{Weight}}
\]

### Step 3: Multiply Each Rating by Its Weight
- For **Reviewer A**: \( 4.5 \times 200 = 900 \)
- For **Reviewer B**: \( 4.0 \times 150 = 600 \)
- For **Reviewer C**: \( 3.5 \times 100 = 350 \)

### Step 4: Add the Weighted Ratings
\[
900 + 600 + 350 = 1850
\]

### Step 5: Sum the Weights
\[
200 + 150 + 100 = 450
\]

### Step 6: Calculate the Weighted Average
\[
\text{Weighted Average} = \frac{1850}{450} \approx 4.11
\]

### Final Answer
The overall weighted average rating of the movie is approximately **4.11**.

---

Would you like more details on any step or have questions about the process?

### Related Questions:
1. How does the concept of weighted average differ from a simple average?
2. What happens to the weighted average if one reviewer has significantly more followers?
3. How do you calculate the overall average rating if all reviewers had the same number of followers?
4. Can the weighted average formula be used for other types of data, like prices or grades?
5. How does the weighted average change if a reviewer with fewer followers gives an extreme rating?

### Tip: 
When computing a weighted average, always make sure the weights (like followers in this case) correctly reflect the importance or relevance of each individual’s contribution.

A movie website wants to compute the overall average rating of a movie, considering different reviewers who have rated the movie, with each reviewer having different numbers of followers (weight). Reviewer A: Average rating = 4.5 (Followers = 200), Reviewer B: Average rating = 4.0 (Followers = 150), Reviewer C: Average rating = 3.5 (Followers = 100).

Learn how to compute the weighted average rating of a movie using ratings from multiple reviewers with different follower counts. This problem walks through a step-by-step process to find the weighted average using real data. Reviewer A (4.5 rating, 200 followers), Reviewer B (4.0 rating, 150 followers), and Reviewer C (3.5 rating, 100 followers). Suitable for students in Grades 8-10.

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