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 the movie considering the different numbers of followers (weights) for each reviewer, we will calculate a **weighted mean**. The weighted mean takes into account both the ratings given and the number of followers each reviewer has, which affects the influence of their rating.

### Steps to Calculate the Weighted Mean:
1. **Identify the ratings and weights (followers):**
   - Reviewer A: Rating = 4.5, Followers = 200
   - Reviewer B: Rating = 4.0, Followers = 150
   - Reviewer C: Rating = 3.5, Followers = 100

2. **Multiply each reviewer's rating by their respective number of followers (weights):**
   - Reviewer A: \( 4.5 \times 200 = 900 \)
   - Reviewer B: \( 4.0 \times 150 = 600 \)
   - Reviewer C: \( 3.5 \times 100 = 350 \)

3. **Sum the products of the ratings and followers:**
   \[
   900 + 600 + 350 = 1850
   \]

4. **Sum the total number of followers:**
   \[
   200 + 150 + 100 = 450
   \]

5. **Divide the total weighted rating by the total number of followers:**
   \[
   \frac{1850}{450} \approx 4.11
   \]

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

Would you like more details or have any questions?

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Here are five related questions to deepen understanding:
1. What is the difference between a weighted mean and a simple mean?
2. How would the overall rating change if Reviewer C had more followers?
3. What happens to the weighted mean if all reviewers have the same number of followers?
4. Can a weighted mean be used for non-numerical data, such as ordinal ranks?
5. How would you calculate the median or mode in a weighted scenario?

**Tip:** Weighted averages are crucial when different groups contribute unequally to the overall result, like in polling or survey data.

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 calculate the overall average movie rating using a weighted mean, considering ratings from three reviewers with different follower counts. This problem introduces key concepts in statistics, such as weighted mean and measures of central tendency, suitable for Grades 9-12.

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